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%%% -*-BibTeX-*-
%%% ====================================================================
%%%  BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "1.156",
%%%     date            = "14 August 2024",
%%%     time            = "12:16:28 MDT",
%%%     filename        = "benfords-law.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "01055 42644 187274 1888797",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; BibTeX; Benford's Law;
%%%                        Bradford's Law; First Digit Phenomenon;
%%%                        Gibrat's Law; Gibrat's Rule of Proportionate
%%%                        Growth; Hall--Petch effect; Heaps' Law;
%%%                        Herdan's Law; Law of Anomalous Numbers;
%%%                        Lotka's Law; Pareto Distribution; Pareto Law;
%%%                        Pareto Principle; power law; Significant
%%%                        Digit Law; Simon--Yule model of text
%%%                        generation; Stigler's Law; Yule process;
%%%                        Zipf's Law",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a bibliography about a numerical
%%%                        curiousity variously known as Benford's Law
%%%                        (see particularly entries Newcomb:1881:NFU,
%%%                        Benford:1938:LAN, Pinkham:1961:DFS,
%%%                        Logan:1978:FDP, Hill:1998:FDP, and
%%%                        Block:2010:GEB, Nigrini:2012:BLA), the Law of
%%%                        Anomalous Numbers, and the Significant Digit
%%%                        Law: in a table of physical constants (and in
%%%                        many other collections of measured numbers),
%%%                        the leading digits do not have equal
%%%                        probability of occurrence: the digit 1 is
%%%                        more common than 2, which is more common than
%%%                        3, and so on.
%%%
%%%                        Publications recorded here appear in about
%%%                        480 different journals from accounting,
%%%                        aerobiology, animal behavior, auditing,
%%%                        astronomy, bible studies, biology,
%%%                        biometrics, botany, business, chaos theory,
%%%                        chemistry, colloid science, complexity,
%%%                        computer science, conflict resolution,
%%%                        cognitive science, criminology, critical
%%%                        phenomena, demographics, drug design,
%%%                        dynamics, earthquake detection, economics,
%%%                        electoral studies, engineering, entropy,
%%%                        expert systems, extinction, finance,
%%%                        forensics, gambling, geography, geophysics,
%%%                        human resources, hydrology, imaging science,
%%%                        informetrics, language science, library
%%%                        science, linguistics, marine systems,
%%%                        marketing, mathematics, medicine, networking,
%%%                        neuroscience, nuclear engineering, nuclear
%%%                        medicine, nuclear science, operations
%%%                        research, pathology, physics, plasticity,
%%%                        political analysis, probability, psychology,
%%%                        risk analysis, signal processing, simulation,
%%%                        social sciences, sociology, statistical
%%%                        mechanics, statistics, stock-market trading,
%%%                        tax accounting, urban development, and urban
%%%                        growth, reflecting the broad interest in the
%%%                        unexpected phenomenon discovered and reported
%%%                        first by the Canadian/American astronomer and
%%%                        mathematician, Simon Newcomb, in a two-page
%%%                        note in 1881, and then independently, and
%%%                        with numerical evidence from much more
%%%                        measured data, by American physicist Frank
%%%                        Benford in 1938.
%%%
%%%                        In Benford's Law, the frequency of leading
%%%                        decimal digit p is roughly log10(1 + (1 /
%%%                        p)): that is, approximately 0.301, 0.176,
%%%                        0.125, 0.097, 0.079, 0.067, 0.058, 0.051, and
%%%                        0.046 for digits 1 through 9, instead of the
%%%                        expected 1/9 ~= 0.111 for values taken from a
%%%                        uniform distribution of random numbers.
%%%
%%%                        Another common statement of Benford's Law is
%%%                        that the probability that a decimal number
%%%                        representing a measured value begins with a
%%%                        nonzero digit not greater than p is log10(1 +
%%%                        p), that is, approximately 0.301, 0.477,
%%%                        0.602, 0.699, 0.778, 0.845, 0.903, 0.954, and
%%%                        1.000 for digits 1 through 9.
%%%
%%%                        A simple Benford-based rule of thumb is that
%%%                        about half the values start with digit 1 or
%%%                        2, about 10 percent with 8 or 9, and 5
%%%                        percent with 9.
%%%
%%%                        For the second digits, the probabilities are
%%%                        determined by the formula (see
%%%                        Todter:2009:BLI)
%%%
%%%                            sum(q = 1:9) log10(1 + 1 / (10*q + p)),
%%%
%%%                        that is, approximately 0.120, 0.114, 0.109,
%%%                        0.104, 0.100, 0.097, 0.093, 0.090, 0.088, and
%%%                        0.085, for second decimal digits p = 0
%%%                        through 9.
%%%
%%%                        Probabilities for later digits are even
%%%                        closer: see entries Newcomb:1881:NFU,
%%%                        Feldstein:1976:CED, and Todter:2009:BLI.
%%%
%%%                        Benford's Law is not restricted to decimal
%%%                        numbers: for base b (as long as b is not
%%%                        huge, according to entry Schatte:1998:BLV),
%%%                        just change the 10 values to b in the
%%%                        previous formulas.  Here are some results for
%%%                        selected bases commonly used in computers,
%%%                        showing the probability of the first (D1) or
%%%                        second (D2) digit (first index) for base b
%%%                        (second index):
%%%
%%%                        P[D1,  2]:        1.000
%%%                        P[D2,  2]: 0.585, 0.415
%%%
%%%                        P[D1,  4]:        0.500, 0.292, 0.208
%%%                        P[D2,  4]: 0.304, 0.261, 0.230, 0.206
%%%
%%%                        P[D1,  8]:        0.333, 0.195, 0.138, 0.107,
%%%                                   0.088, 0.074, 0.064
%%%                        P[D2,  8]: 0.151, 0.141, 0.133, 0.126, 0.120,
%%%                                   0.115, 0.110, 0.105
%%%
%%%                        P[D1, 10]:        0.301, 0.176, 0.125, 0.097,
%%%                                   0.079, 0.067, 0.058, 0.051, 0.046
%%%                        P[D2, 10]: 0.120, 0.114, 0.109, 0.104, 0.100,
%%%                                   0.097, 0.093, 0.090, 0.088, 0.085
%%%
%%%                        P[D1, 16]:        0.250, 0.146, 0.104, 0.080,
%%%                                   0.066, 0.056, 0.048, 0.042, 0.038,
%%%                                   0.034, 0.031, 0.029, 0.027, 0.025,
%%%                                   0.023
%%%                        P[D2, 16]: 0.074, 0.072, 0.070, 0.068, 0.066,
%%%                                   0.065, 0.064, 0.062, 0.061, 0.060,
%%%                                   0.059, 0.058, 0.057, 0.056, 0.055,
%%%                                   0.054
%%%
%%%                        A small filter applied to the 1990 US Census
%%%                        data in the Project Gutenberg file
%%%                        uscen902.txt reports these frequencies of
%%%                        first and second digits for the 5148 integer
%%%                        values with at least 3 digits:
%%%
%%%                        F[D1]:        0.298, 0.215, 0.113, 0.082,
%%%                               0.098, 0.056, 0.055, 0.034, 0.049
%%%                        F[D2]: 0.166, 0.090, 0.096, 0.081, 0.100,
%%%                               0.122, 0.076, 0.073, 0.066, 0.130
%%%
%%%                        For the 110 numbers in the atomic weights
%%%                        section of the GNU units utility data file,
%%%                        units.dat, we have
%%%
%%%                        F[D1]:        0.391, 0.309, 0.045, 0.036,
%%%                               0.055, 0.036, 0.036, 0.036, 0.055
%%%                        F[D2]: 0.173, 0.045, 0.109, 0.100, 0.145,
%%%                               0.145, 0.055, 0.055, 0.091, 0.082
%%%
%%%                        From a snapshot of the country-area section
%%%                        of the US CIA World Factbook
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2147rank.html
%%%
%%%                        taken at 18 November 2011, we find 1505
%%%                        numbers with these frequencies:
%%%
%%%                        F[D1]:        0.312, 0.275, 0.100, 0.067,
%%%                               0.058, 0.062, 0.046, 0.029, 0.050
%%%                        F[D2]: 0.167, 0.221, 0.092, 0.092, 0.062,
%%%                               0.067, 0.075, 0.067, 0.083, 0.075
%%%
%%%                        From the country-population section
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2119rank.html
%%%
%%%                        of that book, including only the 163 values
%%%                        of 1,000,000 or larger, we find
%%%
%%%                        F[D1]:        0.301, 0.202, 0.092, 0.135,
%%%                               0.055, 0.067, 0.055, 0.037, 0.055
%%%                        F[D2]: 0.147, 0.153, 0.110, 0.098, 0.098,
%%%                               0.123, 0.086, 0.043, 0.049, 0.092
%%%
%%%                        From the section with the infant mortality
%%%                        rates per 1000 births,
%%%
%%%                            https://www.cia.gov/library/publications/the-world-factbook/rankorder/2091rank.html
%%%
%%%                        there are 208 values with at least 4 digits,
%%%                        with these frequencies:
%%%
%%%                        F[D1]:        0.361, 0.293, 0.043, 0.072,
%%%                               0.062, 0.087, 0.038, 0.014, 0.029
%%%                        F[D2]: 0.303, 0.139, 0.077, 0.058, 0.077,
%%%                               0.077, 0.106, 0.067, 0.043, 0.053
%%%
%%%                        In the 2010 annual financial report for IBM
%%%                        Corporation (its hundredth year of business)
%%%
%%%                            ftp://public.dhe.ibm.com/annualreport/2010/2010_ibm_annual.pdf
%%%
%%%                        there are 6126 numbers of two or more digits
%%%                        that do not look like year dates (19xx and
%%%                        20xx), and they have these digit frequencies:
%%%
%%%                        F[D1]:        0.333, 0.160, 0.163, 0.086,
%%%                               0.068, 0.053, 0.047, 0.045, 0.046
%%%                        F[D2]: 0.172, 0.169, 0.096, 0.084, 0.085,
%%%                               0.095, 0.079, 0.074, 0.079, 0.068
%%%
%%%                        For the first 100,000 primes, we have
%%%
%%%                        F[D1]:        0.311, 0.091, 0.090, 0.087,
%%%                               0.086, 0.085, 0.084, 0.083, 0.082
%%%                        F[D2]: 0.152, 0.151, 0.150, 0.078, 0.078,
%%%                               0.078, 0.078, 0.079, 0.078, 0.078
%%%
%%%                        For the Fibonacci numbers, f(n), which
%%%                        satisfy the recurrence f(n) = f(n-1) + f(n-2)
%%%                        with f(1) = f(2) = 1, using the first 10000
%%%                        such numbers (the last of which has 2091
%%%                        digits), we find for the 9994 f(n) values
%%%                        with at least two digits these frequencies:
%%%
%%%                        F[D1]:        0.301, 0.176, 0.125, 0.097,
%%%                               0.079, 0.067, 0.058, 0.051, 0.046
%%%                        F[D2]: 0.120, 0.114, 0.109, 0.105, 0.100,
%%%                               0.097, 0.094, 0.090, 0.088, 0.085
%%%
%%%                        If we take the same set of Fibonacci numbers,
%%%                        we find these frequencies for values output
%%%                        in base 4:
%%%
%%%                        F[D1]:        0.500, 0.292, 0.208
%%%                        F[D2]: 0.303, 0.262, 0.230, 0.205
%%%
%%%                        The Fibonacci numbers, and the members of
%%%                        many other such sequences, can be proved
%%%                        mathematically to obey Benford's Law exactly
%%%                        (see entries Raimi:1976:FDP, Berger:2011:BLS,
%%%                        and Berger:2011:BTB).
%%%
%%%                        Simon Newcomb made another significant
%%%                        appearance in the history of science when he
%%%                        proposed that the then-not-understood
%%%                        perihelion advance of the planet Mercury
%%%                        could be explained by modifying Newton's law
%%%                        of gravitation from a $r^{-2}$ dependence to
%%%                        $r^{-2.000\,000\,157\,4}$.  His proposal was
%%%                        later shown to contradict more accurate
%%%                        measurements of the orbit of Earth's Moon.
%%%                        That story is told on pages 93--95 of
%%%                        Clifford M. Will's 1993 book, ``Was Einstein
%%%                        Right?'' (ISBN 0-465-09086-9).
%%%
%%%                        Although many papers purport to explain
%%%                        Benford's Law, a recent paper (entry
%%%                        Berger:2011:BLS) argues that several of the
%%%                        prior published explanations are flawed.  An
%%%                        earlier paper (entry Raimi:1976:FDP) examines
%%%                        the literature on Benford's Law up to 1976,
%%%                        and points out flaws in several previous
%%%                        explanations of the law.  That paper also
%%%                        gives a bibliography of previous important
%%%                        works on the problem.  A recent survey (entry
%%%                        Berger:2011:BTB) may provide stronger
%%%                        mathematical grounds for Benford's Law.
%%%
%%%                        Benford's Law has been applied to the problem
%%%                        of detection of fraud in data, elections, and
%%%                        finance (see, among other entries,
%%%                        Hill:1998:FDP, Nigrini:1992:DIE,
%%%                        Swanson:2003:DPF, Durtschi:2004:EUB,
%%%                        Geyer:2004:DFD, Bhattacharya:2005:CPA,
%%%                        Cleary:2005:ADA, Lu:2005:DFH, Lu:2006:AFD,
%%%                        Schneider:2006:RAS, Cho:2007:BBL,
%%%                        Diekmann:2007:FDU, Hand:2007:DDD,
%%%                        Todter:2009:BLI, Corazza:2010:CFM, and
%%%                        Roukema:2014:FDA, and the cautionary view in
%%%                        Diekmann:2010:BLF).
%%%
%%%                        Benford's Law also applies to floating-point
%%%                        numbers in computer arithmetic (see entries
%%%                        Konheim:1965:MDT, Hamming:1970:DN,
%%%                        Tsao:1974:DSD, Feldstein:1976:CED,
%%%                        Feldstein:1986:OUS, Schatte:1988:ASC), where
%%%                        it has implications for the frequency of
%%%                        significance loss in subtraction of
%%%                        like-signed numbers.
%%%
%%%                        This bibliography also includes publications
%%%                        about two related empirical laws: Heaps' Law
%%%                        and Zipf's Law, because they often occur in
%%%                        discussions of Benford's Law.
%%%
%%%                        Heaps' Law (see entry Heaps:1978:IRC) is an
%%%                        empirical observation from linguistics that
%%%                        the proportion of words from a vocabulary
%%%                        grows exponentially (but with a small
%%%                        exponent, often between 0.4 and 0.6) with the
%%%                        number of words in the text of documents.
%%%
%%%                        Zipf's Law says that if S is some stochastic
%%%                        (random) variable, the probability that S
%%%                        exceeds s is proportional to 1 / s.  The
%%%                        variable S might be, for example, the
%%%                        population of a city (small cities are more
%%%                        numerous than large ones).  Zipf's Law is
%%%                        a special case of the Pareto distribution
%%%                        (see remark in entry Pareto:1896:CEP).
%%%
%%%                        Zipf's law finds application in the design of
%%%                        information retrieval systems (e.g., hash
%%%                        tables, databases, filesystems, and Web
%%%                        searches), as well as in astronomy, biology,
%%%                        computer science, demography, earth science,
%%%                        economics, and physics.  See entry
%%%                        Newman:2005:PLP for an outstanding survey
%%%                        that deserves to be widely read by
%%%                        scientists, and entry Baldi:2003:MIW for a
%%%                        book-length treatment.
%%%
%%%                        There is an actively-maintained bibliography
%%%                        of Benford's Law at
%%%
%%%                            http://www.benfordonline.net/
%%%
%%%                        (see entry Berger:2009:BOB).  It includes
%%%                        material from entries Hurlimann:2006:BLB and
%%%                        Nigrini:1992:DIE.  Although BibTeX output is
%%%                        mentioned, it may not yet be implemented.
%%%
%%%                        There is an online bibliography of Zipf's Law
%%%                        at
%%%
%%%                            http://www.nslij-genetics.org/wli/zipf/
%%%
%%%                        (see entry Li:2011:ZLB).
%%%
%%%                        There is a collection of several papers on
%%%                        election-fraud detection, some of them using
%%%                        Benford's Law analyses, at
%%%
%%%                            http://www-personal.umich.edu/~wmebane/
%%%
%%%                        At version 1.156, the year coverage looked like
%%%                        this:
%%%
%%%                             1881 (   1)    1929 (   1)    1977 (   9)
%%%                             1882 (   0)    1930 (   0)    1978 (  11)
%%%                             1883 (   0)    1931 (   1)    1979 (   6)
%%%                             1884 (   0)    1932 (   2)    1980 (   8)
%%%                             1885 (   0)    1933 (   0)    1981 (  12)
%%%                             1886 (   0)    1934 (   1)    1982 (  10)
%%%                             1887 (   0)    1935 (   1)    1983 (   6)
%%%                             1888 (   0)    1936 (   2)    1984 (  16)
%%%                             1889 (   0)    1937 (   1)    1985 (  10)
%%%                             1890 (   0)    1938 (   2)    1986 (  16)
%%%                             1891 (   0)    1939 (   0)    1987 (  18)
%%%                             1892 (   0)    1940 (   0)    1988 (  12)
%%%                             1893 (   0)    1941 (   0)    1989 (  14)
%%%                             1894 (   0)    1942 (   0)    1990 (   9)
%%%                             1895 (   0)    1943 (   1)    1991 (  11)
%%%                             1896 (   1)    1944 (   1)    1992 (  15)
%%%                             1897 (   0)    1945 (   2)    1993 (  11)
%%%                             1898 (   0)    1946 (   1)    1994 (  12)
%%%                             1899 (   0)    1947 (   0)    1995 (  19)
%%%                             1900 (   0)    1948 (   2)    1996 (  23)
%%%                             1901 (   0)    1949 (   2)    1997 (  17)
%%%                             1902 (   0)    1950 (   3)    1998 (  21)
%%%                             1903 (   0)    1951 (   0)    1999 (  28)
%%%                             1904 (   0)    1952 (   1)    2000 (  22)
%%%                             1905 (   0)    1953 (   1)    2001 (  26)
%%%                             1906 (   0)    1954 (   1)    2002 (  34)
%%%                             1907 (   0)    1955 (   1)    2003 (  42)
%%%                             1908 (   0)    1956 (   0)    2004 (  46)
%%%                             1909 (   0)    1957 (   5)    2005 (  68)
%%%                             1910 (   1)    1958 (   1)    2006 (  60)
%%%                             1911 (   0)    1959 (   1)    2007 (  49)
%%%                             1912 (   1)    1960 (   1)    2008 (  54)
%%%                             1913 (   1)    1961 (   2)    2009 (  78)
%%%                             1914 (   1)    1962 (   2)    2010 (  97)
%%%                             1915 (   1)    1963 (   1)    2011 (  88)
%%%                             1916 (   1)    1964 (   1)    2012 (  59)
%%%                             1917 (   1)    1965 (   4)    2013 (  46)
%%%                             1918 (   0)    1966 (   4)    2014 (  52)
%%%                             1919 (   0)    1967 (   3)    2015 (  79)
%%%                             1920 (   1)    1968 (   4)    2016 (  25)
%%%                             1921 (   0)    1969 (  12)    2017 (  12)
%%%                             1922 (   1)    1970 (   8)    2018 (  13)
%%%                             1923 (   0)    1971 (   2)    2019 (   8)
%%%                             1924 (   0)    1972 (   7)    2020 (  16)
%%%                             1925 (   1)    1973 (  10)    2021 (  13)
%%%                             1926 (   1)    1974 (  12)    2022 (  10)
%%%                             1927 (   1)    1975 (  13)    2023 (   9)
%%%                             1928 (   2)    1976 (  13)    2024 (   3)
%%%                             20xx (   1)
%%%
%%%                             Article:       1167
%%%                             Book:            93
%%%                             InCollection:    53
%%%                             InProceedings:   64
%%%                             Manual:           1
%%%                             MastersThesis:    6
%%%                             Misc:            20
%%%                             PhdThesis:        8
%%%                             Proceedings:      8
%%%                             TechReport:      50
%%%                             Unpublished:      3
%%%
%%%                             Total entries: 1473
%%%
%%%                        Data for this bibliography have been
%%%                        collected from
%%%
%%%                            * the University of Utah Mathematics
%%%                              Department bibliography archives
%%%
%%%                            * the TeX User Group bibliography
%%%                              archives
%%%
%%%                            * the Karlsruhe Computer Science
%%%                              bibliography archives
%%%
%%%                            * the Karlsruhe virtual catalog at
%%%                              http://www.ubka.uni-karlsruhe.de/kvk_en.html
%%%
%%%                            * the US Library of Congress catalog at
%%%                              http://catalog.loc.gov/
%%%
%%%                            * the author's cattobib utility, which
%%%                              provides Z39.50 interfaces to many
%%%                              large libraries around the world, at
%%%                              https://www.math.utah.edu/pub/cattobib/
%%%
%%%                            * the American Institute of Physics
%%%                              Scitation database at
%%%                              http://scitation.aip.org/search_scitation
%%%
%%%                            * the American Physical Society PROLA
%%%                              database at
%%%                              http://publish.aps.org/search
%%%
%%%                            * the American Mathematical Society
%%%                              MathSciNet database at
%%%                              http://ams.rice.edu/mathscinet/search.html
%%%
%%%                            * the Bulletin of the Atomic Scientists
%%%                              (archives available, albeit inconveniently,
%%%                              via http://books.google.com/ and
%%%                              http://bos.sagepub.com/search)
%%%
%%%                            * the Canadian Journal of Physics
%%%                              database at
%%%                              http://www.nrcresearchpress.com/search/advanced
%%%
%%%                            * the European Mathematical Society
%%%                              Zentralblatt fuer Mathematik database
%%%                              at http://zb.msri.org/ZMATH/zmath/en/
%%%
%%%                            * the Europhysics journal archive at
%%%                              http://www.europhysicsnews.org/
%%%
%%%                            * the JSTOR database at
%%%                              http://www.jstor.org/
%%%
%%%                            * the Nature journal archive at
%%%                              http://www.nature.com/search/
%%%
%%%                            * the journal archives of the National
%%%                              Academy of Science at
%%%                              http://www.pnas.org/
%%%
%%%                            * the Project Euclid archives at
%%%                              http://projecteuclid.org/
%%%
%%%                            * the SAO/NASA Astrophysics Data System at
%%%                              http://adsabs.harvard.edu/
%%%
%%%                            * the Science journal archive at
%%%                              http://www.sciencemag.org/search
%%%
%%%                            * the SPIRES high-energy physics
%%%                              literature database at the Stanford
%%%                              Linear Accelerator at Stanford
%%%                              University at
%%%                              http://www.slac.stanford.edu/spires/hep/search/
%%%
%%%                            * the Springer journal database at
%%%                              http://www.springer.com/?SGWID=0-102-13-0-0
%%%
%%%                            * the Wiley journal database at
%%%                              http://onlinelibrary.wiley.com/
%%%
%%%                            * many online library catalogs, including
%%%                              those of the British Library, the
%%%                              Karlsruhe Virtual Library catalog, the
%%%                              Oxford University Library, the University of
%%%                              California library system, and the US
%%%                              Library of Congress.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility.",
%%%  }
%%% ====================================================================
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   "\ifx \undefined \polhk      \def \polhk #1{\setbox0=\hbox{#1}{\ooalign{\hidewidth \lower1.5ex\hbox{`}\hidewidth\crcr\unhbox0}}} \fi" #
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   "\ifx \undefined \url        \input{path.sty} \fi"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-mjn =   "Mark J. Nigrini"}

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

%%% ====================================================================
%%% Journal abbreviations:
@String{j-ACCOUNT-HIST-J        = "Accounting Historians Journal"}

@String{j-ACCOUNT-RES           = "Accountability in Research"}

@String{j-ACCOUNT-REV           = "The Accounting Review"}

@String{j-ACCOUNTANCY           = "Accountancy: The journal of the {Institute
                                  of Chartered Accountants in England and
                                  Wales}"}

@String{j-ACTA-ARITHMETICA      = "Acta Arithmetica"}

@String{j-ACTA-ASTRONAUT        = "Acta Astronautica"}

@String{j-ACTA-PHYS-POL-B       = "Acta Physica Polonica B"}

@String{j-ADV-APPL-STAT         = "Advances and Applications in Statistics"}

@String{j-ADV-COMPLEX-SYST      = "Advances in Complex Systems"}

@String{j-ADV-MATH              = "Advances in Mathematics"}

@String{j-ADV-QUANTUM-CHEM      = "Advances in Quantum Chemistry"}

@String{j-AEQUATIONES-MATHEMATICAE = "Aequationes Mathematicae"}

@String{j-AEROBIOLOGIA          = "Aerobiologia"}

@String{j-AM-DOC                = "American Documentation"}

@String{j-AM-J-APPL-SCI         = "American Journal of Applied Sciences"}

@String{j-AM-J-ECON-SOCIOL      = "The American Journal of Economics and
                                  Sociology"}

@String{j-AM-J-MATH             = "American Journal of Mathematics"}

@String{j-AM-J-MATH-MANAGE-SCI  = "American Journal of Mathematical and
                                  Management Sciences"}

@String{j-AM-SCI                = "American Scientist"}

@String{j-AMER-J-PHYSICS        = "American Journal of Physics"}

@String{j-AMER-J-PSYCHOLOGY     = "The American Journal of Psychology"}

@String{j-AMER-MATH-MONTHLY     = "American Mathematical Monthly"}

@String{j-AMER-STAT             = "The American Statistician"}

@String{j-ANALYST               = "The Analyst"}

@String{j-ANIM-BEHAV            = "Animal Behaviour"}

@String{j-ANN-APPL-PROBAB       = "Annals of Applied Probability"}

@String{j-ANN-INST-STAT-MATH-TOKYO = "Annals of the Institute of Statistical
                                  Mathematics (Tokyo)"}

@String{j-ANN-MATH-STAT         = "Annals of Mathematical Statistics"}

@String{j-ANN-PHYS              = "Annals of Physics"}

@String{j-ANN-PROBAB            = "Annals of Probability"}

@String{j-ANN-STAT              = "Annals of Statistics"}

@String{j-APPL-ECON-LETT        = "Applied Economics Letters"}

@String{j-APPL-FINANC-ECON      = "Applied Financial Economics"}

@String{j-APPL-MATH-COMP        = "Applied Mathematics and Computation"}

@String{j-APPL-STAT             = "Applied Statistics"}

@String{j-AQUAT-BOT             = "Aquatic Botany"}

@String{j-ARCH-HIST-EXACT-SCI   = "Archive for History of Exact Sciences"}

@String{j-ARKHIMEDES            = "Arkhimedes"}

@String{j-ASIA-PAC-MATH-NEWSL   = "Asia Pacific Mathematics Newsletter"}

@String{j-ASLIB-PROC            = "ASLIB Proceedings"}

@String{j-ASTROPART-PHYS        = "Astroparticle Physics"}

@String{j-ATMOS-ENV             = "Atmospheric Environment"}

@String{j-AUDITING              = "Auditing: A Journal of Practice \& Theory"}

@String{j-AUSTRALIAN-COMP-J     = "Australian Computer Journal"}

@String{j-AUSTRALIAN-MATH-SOC-GAZ = "Australian Mathematical Society Gazette"}

@String{j-BELL-SYST-TECH-J      = "The Bell System Technical Journal"}

@String{j-BIOINFORMATICS        = "Bioinformatics"}

@String{j-BIOMETRIKA            = "Biometrika"}

@String{j-BIOSYSTEMS            = "Biosystems (A6E)"}

@String{j-BIT-NUM-MATH          = "BIT Numerical Mathematics"}

@String{j-BMC-BIOINFORMATICS    = "BMC Bioinformatics"}

@String{j-BOLL-UNIONE-MAT-ITAL  = "Bollettino della Unione matematica italiana"}

@String{j-BRAIN-COGN            = "Brain and Cognition"}

@String{j-BULL-INST-MATH-STAT   = "Bulletin --- Institute of Mathematical
                                  Statistics"}

@String{j-C-R-ACAD-SCI-I        = "Comptes rendus de l'Acad{\'e}mie des
                                  sciences. S{\'e}rie I, Math{\'e}matique"}

@String{j-C-R-ACAD-SCI-PARIS-SER-AB = "Comptes Rendus Hebdomadaires des
                                  S{\'e}ances de l'Acad{\'e}mie des Sciences.
                                  S{\'e}ries A et B"}

@String{j-C-R-BIOL              = "Comptes Rendus Biologies"}

@String{j-CACM                  = "Communications of the ACM"}

@String{j-CAN-J-MATH            = "Canadian Journal of Mathematics = Journal
                                  canadien de math{\'e}matiques"}

@String{j-CHANCE                = "Chance: a magazine for people interested in
                                  the analysis of data"}

@String{j-CHAOS                 = "Chaos (Woodbury, NY)"}

@String{j-CHAOS-SOLITONS-FRACTALS = "Chaos, Solitons \& Fractals"}

@String{j-CHEM-PHYS-LETT        = "Chemical Physics Letters"}

@String{j-CHIN-PHYS-LETT        = "Chinese Physics Letters"}

@String{j-COGN-SCI              = "Cognitive Science"}

@String{j-COGNITION             = "Cognition"}

@String{j-COLLEGE-MATH-J        = "College Mathematics Journal"}

@String{j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE = "Collnet Journal of
                                  Scientometrics and Information Management"}

@String{j-COLLOQ-MATH           = "Colloquium Mathematicum"}

@String{j-COMM-NONLIN-SCI-NUM-SIM = "Communications in Nonlinear Science and
                                  Numerical Simulation"}

@String{j-COMM-PURE-APPL-MATH   = "Communications on Pure and Applied
                                  Mathematics (New York)"}

@String{j-COMM-THEOR-PHYS       = "Communications in Theoretical Physics"}

@String{j-COMMUN-DESIGN-Q-REVIEW = "Communication Design Quarterly Review"}

@String{j-COMMUN-MATH-STAT      = "Communications in Mathematics and Statistics"}

@String{j-COMMUN-STAT-SIMUL-COMPUT = "Communications in Statistics: Simulation
                                  and Computation"}

@String{j-COMMUN-STAT-THEORY-METH = "Communications in Statistics: Theory and
                                  Methods"}

@String{j-COMP-ARCH-NEWS        = "ACM SIGARCH Computer Architecture News"}

@String{j-COMP-COMM             = "Computer Communications"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-MUSIC-J          = "Computer Music Journal"}

@String{j-COMP-NET              = "Computer Networks"}

@String{j-COMP-NET-AMSTERDAM    = "Computer Networks (Amsterdam, Netherlands:
                                  1999)"}

@String{j-COMP-SURV             = "ACM Computing Surveys"}

@String{j-COMPLEXITY            = "Complexity"}

@String{j-COMPOS-MATH           = "Compositio Mathematica"}

@String{j-COMPUT-AIDED-DES      = "Computer-Aided Design"}

@String{j-COMPUT-MATH-APPL      = "Computers and Mathematics with Applications"}

@String{j-COMPUT-STAT-DATA-ANAL = "Computational Statistics \& Data Analysis"}

@String{j-COMPUTING             = "Computing: Archiv f{\"u}r Informatik und
                                  Numerik"}

@String{j-CONTEMP-PHYS          = "Contemporary Physics"}

@String{j-CRYPTOLOGIA           = "Cryptologia"}

@String{j-DEC-SUPP-SYS          = "Decision Support Systems"}

@String{j-DEMOGRAPHY            = "Demography"}

@String{j-DEUTSCH-MATH-V        = "Jber. Deutsch. Math.--Verein"}

@String{j-DISCRETE-CONTIN-DYN-SYST = "Discrete and Continuous Dynamical
                                  Systems. Series A"}

@String{j-DISCRETE-DYN-NAT-SOC  = "Discrete Dynamics in Nature and Society"}

@String{j-DISCRETE-MATH         = "Discrete Mathematics"}

@String{j-DOKL-AKAD-NAUK        = "Doklady Akademii Nauk SSSR"}

@String{j-DOKL-MATH             = "Doklady Mathematics"}

@String{j-DRUG-DISCOVERY-TODAY  = "Drug Discovery Today"}

@String{j-ECONOM-LETT           = "Economics Letters"}

@String{j-ECONOMIST             = "The Economist"}

@String{j-EDPACS                = "EDPACS"}

@String{j-ELECT-J-COMB          = "Electronic Journal of Combinatorics"}

@String{j-ELECT-NOTES-THEOR-COMP-SCI = "Electronic Notes in Theoretical
                                  Computer Science"}

@String{j-ELECT-STUDIES         = "Electoral Studies"}

@String{j-ELECTRON-COMMUN-PROBAB = "Electronic Communications in Probability"}

@String{j-ELECTRON-J-PROBAB     = "Electronic Journal of Probability"}

@String{j-ELEK-INFO-KYBER       = "Elektronische Informationsverarbeitung und
                                  Kybernetik (EIK)"}

@String{j-ELEM-MATH             = "Elemente der Mathematik"}

@String{j-EMPIRICA              = "Empirica"}

@String{j-ENTROPY               = "Entropy"}

@String{j-ESAIM-PROBAB-STATIST  = "ESAIM: Probability and Statistics"}

@String{j-EUR-J-OPER-RES        = "European Journal of Operational Research"}

@String{j-EUR-J-PHYS            = "European Journal of Physics"}

@String{j-EUR-PHYS-J-A          = "European Physical Journal A: Hadrons and
                                  Nuclei"}

@String{j-EUR-PHYS-J-B          = "European Physical Journal B: Condensed
                                  Matter and Complex Systems"}

@String{j-EURASIP-J-ADV-SIGNAL-PROCESS = "EURASIP Journal on Advances in Signal
                                  Processing"}

@String{j-EUROPHYS-LETT         = "Europhysics Letters"}

@String{j-EXP-MATH              = "Experimental Mathematics"}

@String{j-EXPERT-SYST-APPL      = "Expert Systems with Applications"}

@String{j-EXPO-MATH             = "Expositiones Mathematicae"}

@String{j-FIB-QUART             = "Fibonacci Quarterly"}

@String{j-FORUM-MATH            = "Forum Mathematicum"}

@String{j-FRACTALS              = "Fractals"}

@String{j-FUNDAM-MATH           = "Fundamenta mathematicae"}

@String{j-FUT-GEN-COMP-SYS      = "Future Generation Computer Systems"}

@String{j-GER-ECON-REV          = "German Economic Review"}

@String{j-GLOB-FINANCE-J        = "Global Finance Journal"}

@String{j-ICARUS-IJSSS          = "Icarus: International Journal of Solar
                                  System Studies"}

@String{j-IEEE-ANN-HIST-COMPUT  = "IEEE Annals of the History of Computing"}

@String{j-IEEE-POT              = "IEEE Potentials"}

@String{j-IEEE-SIGNAL-PROCESS-MAG = "IEEE Signal Processing Magazine"}

@String{j-IEEE-SPECTRUM         = "IEEE Spectrum"}

@String{j-IEEE-TRANS-ELEC-COMPUT = "IEEE Transactions on Electronic Computers"}

@String{j-IEEE-TRANS-ELECTROMAGN-COMPAT = "IEEE Transactions on
                                  Electromagnetic Compatibility"}

@String{j-IEEE-TRANS-FUZZY-SYSTEMS = "IEEE Transactions on Fuzzy Systems"}

@String{j-IEEE-TRANS-INF-THEORY = "IEEE Transactions on Information Theory"}

@String{j-IEEE-TRANS-NETWORKING = "IEEE\slash ACM Transactions on Networking"}

@String{j-IEEE-TRANS-NUCL-SCI   = "IEEE Transactions on Nuclear Science"}

@String{j-IEEE-TRANS-PAR-DIST-SYS = "IEEE Transactions on Parallel and
                                  Distributed Systems"}

@String{j-IEEE-TRANS-RELIAB     = "IEEE Transactions on Reliability"}

@String{j-IEEE-TRANS-VIS-COMPUT-GRAPH = "IEEE Transactions on Visualization
                                   and Computer Graphics"}

@String{j-IMA-J-APPL-MATH       = "IMA Journal of Applied Mathematics"}

@String{j-IMA-J-NUMER-ANAL      = "IMA Journal of Numerical Analysis"}

@String{j-IMAGE-VIS-COMPUT      = "Image and Vision Computing"}

@String{j-INF-CONTROL           = "Information and Control"}

@String{j-INFO-PROC-LETT        = "Information Processing Letters"}

@String{j-INFO-PROC-MAN         = "Information Processing and Management"}

@String{j-INFO-SCI              = "Information Sciences"}

@String{j-INFO-SYS              = "Information systems"}

@String{j-INT-ECON-REV          = "International Economic Review"}

@String{j-INT-J-ACCOUNT-INFO-SYS = "International Journal of Accounting
                                  Information Systems"}

@String{j-INT-J-FOUND-COMP-SCI  = "International Journal of Foundations of
                                  Computer Science (IJFCS)"}

@String{j-INT-J-PLAST           = "International Journal of Plasticity"}

@String{j-INT-J-MATH-EDU-SCI-TECH = "International Journal of Mathematical
                                  Education in Science and Technology"}

@String{j-INT-J-MATH-MATH-SCI   = "International Journal of Mathematics and
                                  Mathematical Sciences"}

@String{j-INT-J-MOD-PHYS-C      = "International Journal of Modern Physics C
                                  [Physics and Computers]"}

@String{j-INT-J-NUMBER-THEORY   = "International Journal of Number Theory"}

@String{j-INT-J-PROD-ECON       = "International Journal of Production
                                  Economics"}

@String{j-INT-J-PURE-APPL-MATH  = "International Journal of Pure and Applied
                                  Mathematics"}

@String{j-INT-J-RES-MARK        = "International Journal of Research in
                                  Marketing"}

@String{j-INT-J-SCI-ENG-RESEARCH = "International Journal of Scientific and
                                  Engineering Research"}

@String{j-INT-J-STAT-PROBAB     = "International Journal of Statistics
                                  and Probability"}

@String{j-INT-J-SYST-SCI        = "International Journal of Systems Science"}

@String{j-INT-J-THEOR-PHYS      = "International Journal of Theoretical
                                  Physics"}

@String{j-INTERNET-MATH         = "Internet Mathematics"}

@String{j-IZV-AKAD-NAUK-SSSR-MAT = "Izvestiia Akademii Nauk. USSR Seriia
                                  Matematicheskaia (Moscow)"}

@String{j-J-ACCOUNT-EDUC        = "Journal of Accounting Education"}

@String{j-J-ACCOUNTANCY         = "Journal of Accountancy"}

@String{j-J-ACM                 = "Journal of the ACM"}

@String{j-J-AM-SOC-INF-SCI      = "Journal of the American Society for
                                  Information Science"}

@String{j-J-AM-SOC-INF-SCI-TECHNOL = "Journal of the American Society for
                                  Information Science and Technology"}

@String{j-J-AM-STAT-ASSOC       = "Journal of the American Statistical
                                  Association"}

@String{j-J-APPL-ECONOMETRICS   = "Journal of Applied Econometrics"}

@String{j-J-APPL-PROBAB         = "Journal of Applied Probability"}

@String{j-J-APPL-STAT           = "Journal of Applied Statistics"}

@String{j-J-ASSET-MANAGE        = "Journal of Asset Management"}

@String{j-J-ASSOC-INF-SCI-TECHNOL = "Journal of the Association for Information
                                  Science and Technology"}

@String{j-J-ASTROPHYS-ASTRON    = "Journal of Astrophysics and Astronomy"}

@String{j-J-BUS-ECON-STAT       = "Journal of Business \& Economic Statistics"}

@String{j-J-CLIN-PATHOL         = "Journal of Clinical Pathology"}

@String{j-J-CLIN-PSYCHOL        = "Journal of Clinical Psychology"}

@String{j-J-COLLOID-INTERFACE-SCI = "Journal of Colloid and Interface Science"}

@String{j-J-COMB-THEORY-A       = "Journal of Combinatorial Theory (Series A)"}

@String{j-J-CONFL-RESOLUT       = "Journal of Conflict Resolution"}

@String{j-J-DIFFER-EQU          = "Journal of Differential Equations"}

@String{j-J-DIFFERENCE-EQU-APPL = "Journal of Difference Equations and
                                  Applications"}

@String{j-J-DOC                 = "Journal of Documentation"}

@String{j-J-DYN-DIFFER-EQU      = "Journal of Dynamics and Differential Equations"}

@String{j-J-ECON-DYN-CONTROL    = "Journal of Economic Dynamics and Control"}

@String{j-J-EMPIR-FINANCE       = "Journal of Empirical Finance"}

@String{j-J-EXP-PSYCH-GEN       = "Journal of Experimental Psychology:
                                  General"}

@String{j-J-FORENSIC-ACCOUNT    = "Journal of Forensic Accounting"}

@String{j-J-GAMBL-STUD          = "Journal of Gambling Studies"}

@String{j-J-GEN-PSYCH           = "The Journal of General Psychology"}

@String{j-J-HUM-RESOUR          = "Journal of Human Resources"}

@String{j-J-HYDROL              = "Journal of Hydrology"}

@String{j-J-INFO-ORG-SCI        = "Journal of Informational and Organizational
                                  Sciences"}

@String{j-J-INFO-PROC-CYBERNETICS-EIK = "Journal of Information Processing and
                                  Cybernetics: EIK"}

@String{j-J-INFO-SCI-PRINCIPLES-PRACTICE = "Journal of Information Science,
                                  Principles and Practice"}

@String{j-J-INFORMETRICS        = "Journal of Informetrics"}

@String{j-J-INT-ECON            = "Journal of International Economics"}

@String{j-J-INT-FINANC-MANAG-ACCOUNT = "Journal of International Financial
                                  Management and Accounting"}

@String{j-J-JPN-INT-ECON        = "Journal of the {Japanese} and International
                                  Economies"}

@String{j-J-MAR-SYST            = "Journal of Marine Systems"}

@String{j-J-MATH-ANAL-APPL      = "Journal of Mathematical Analysis and
                                  Applications"}

@String{j-J-MATH-ARTS           = "Journal of Mathematics and the Arts"}

@String{j-J-MATH-IMAG-VIS       = "Journal of Mathematical Imaging and Vision:
                                  JMIV"}

@String{j-J-MATH-PHYS           = "Journal of Mathematical Physics"}

@String{j-J-MATH-SOC-JPN        = "Journal of the {Mathematical Society of
                                  Japan}"}

@String{j-J-MOL-BIOL            = "Journal of Molecular Biology"}

@String{j-J-NETW-COMPUT-APPL    = "Journal of Network and Computer
                                  Applications"}

@String{j-J-NUMBER-THEORY       = "Journal of Number Theory"}

@String{j-J-PHYS-A              = "Journal of Physics A (Mathematical and
                                  General)"}

@String{j-J-PHYS-SOC-JAP        = "Journal of the Physical Society of Japan"}

@String{j-J-PROD-BRAND-MANAG    = "Journal of Product \& Brand Management"}

@String{j-J-QUANT-CRIMINOL      = "Journal of Quantitative Criminology"}

@String{j-J-QUANT-LINGUISTICS   = "Journal of Quantitative Linguistics"}

@String{j-J-R-STAT-SOC          = "Journal of the Royal Statistical Society"}

@String{j-J-R-STAT-SOC-SER-A-GENERAL = "Journal of the Royal Statistical
                                  Society. Series A (General)"}

@String{j-J-R-STAT-SOC-SER-A-STAT-SOC = "Journal of the Royal
                                  Statistical Society. Series A
                                  (Statistics in Society)"}

@String{j-J-R-STAT-SOC-SER-D-STATISTICIAN = "Journal of the Royal Statistical
                                  Society. Series D (The Statistician)"}

@String{j-J-REG-SCI             = "Journal of Regional Science"}

@String{j-J-RISK-UNCERT         = "Journal of Risk and Uncertainty"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                   Simulation"}

@String{j-J-STAT-MECH-THEORY-EXP = "Journal of Statistical Mechanics: Theory
                                  and Experiment"}

@String{j-J-STAT-PHYS           = "Journal of Statistical Physics"}

@String{j-J-SYST-SOFTW          = "The Journal of systems and software"}

@String{j-J-SUPERCOMPUTING      = "The Journal of Supercomputing"}

@String{j-J-THEOR-BIOL          = "Journal of Theoretical Biology"}

@String{j-J-THEOR-PROBAB        = "Journal of Theoretical Probability"}

@String{j-J-URBAN-ECON          = "Journal of Urban Economics"}

@String{j-J-WASH-ACAD-SCI       = "Journal of the Washington Academy of
                                  Sciences"}

@String{j-JOCCH                 = "Journal on Computing and Cultural
                                  Heritage (JOCCH)"}

@String{j-KNOWL-INFO-SYS        = "Knowledge and Information Systems"}

@String{j-LANG-SCI              = "Language Sciences"}

@String{j-LECT-NOTES-COMP-SCI   = "Lecture Notes in Computer Science"}

@String{j-LIBR-TRENDS           = "Library Trends"}

@String{j-MAT-ZAMETKI           = "Matematicheskie Zametki"}

@String{j-MATH-ANN              = "Mathematische Annalen"}

@String{j-MATH-COMP-MODELLING   = "Mathematical and Computer Modelling"}

@String{j-MATH-COMPUT           = "Mathematics of Computation"}

@String{j-MATH-GAZ              = "The Mathematical Gazette"}

@String{j-MATH-GEOL             = "Mathematical Geology"}

@String{j-MATH-GEOSCI           = "Mathematical Geosciences"}

@String{j-MATH-INTEL            = "The Mathematical Intelligencer"}

@String{j-MATH-MAG              = "Mathematics Magazine"}

@String{j-MATH-NACHR            = "Mathematische Nachrichten"}

@String{j-MATH-NOTES-ACAD-SCI-USSR = "Mathematical Notes of the {Academy of
                                  Sciences of the USSR = Matematicheskie
                                  Zametki}"}

@String{j-MATH-SOC-SCI          = "Mathematical Social Sciences"}

@String{j-MATH-USSR-IZV         = "Mathematics of the {USSR} --- Izvestiya"}

@String{j-METAB-CLIN-EXP        = "Metabolism, Clinical and Experimental"}

@String{j-METRIKA               = "Metrika"}

@String{j-MICROELECT-RELIABILITY = "Microelectronics and Reliability"}

@String{j-MOD-PHYS-LETT-A       = "Modern Physics Letters A (MPLA)"}

@String{j-MONAT-MATH            = "Monatshefte f{\"u}r Mathematik"}

@String{j-NAMS                  = "Notices of the American Mathematical Society"}

@String{j-NATURE                = "Nature"}

@String{j-NEW-J-PHYS            = "New Journal of Physics"}

@String{j-NEW-SCIENTIST         = "New Scientist"}

@String{j-NUCL-MED              = "Journal of Nuclear Medicine"}

@String{j-NUCLEAR-INSTR-METH-PHYS-RES-A = "Nuclear instruments and methods in
                                  physics research. Section A, Accelerators,
                                  spectrometers, detectors and associated
                                  equipment"}

@String{j-NY-TIMES              = "New York Times"}

@String{j-OPER-SYS-REV          = "Operating Systems Review"}

@String{j-PAP-REG-SCI           = "Papers in Regional Science"}

@String{j-PATTERN-RECOGN-LETT   = "Pattern Recognition Letters"}

@String{j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI = "Philosophical transactions
                                  of the Royal Society of London Series B,
                                  Biological sciences"}

@String{j-PHYS-LET-A            = "Physics Letters A"}

@String{j-PHYS-REV              = "Physical Review"}

@String{j-PHYS-REV-A            = "Physical Review A (Atomic, Molecular, and
                                  Optical Physics)"}

@String{j-PHYS-REV-C            = "Physical Review C (Nuclear Physics)"}

@String{j-PHYS-REV-E            = "Physical Review E (Statistical physics,
                                  plasmas, fluids, and related
                                  interdisciplinary topics)"}

@String{j-PHYS-REV-LET          = "Physical Review Letters"}

@String{j-PHYSICA-A             = "Physica A: Statistical Mechanics and its
                                  Applications"}

@String{j-PHYSICA-B-PLUS-C      = "Physica. B + C; B: Physics of condensed
                                  matter. C: Atomic, molecular and plasma
                                  physics; optics"}

@String{j-PHYSICA-D             = "Physica. D, Nonlinear phenomena"}

@String{j-PLOS-MED              = "PLoS Medicine"}

@String{j-PLOS-ONE              = "PLoS One"}

@String{j-POLIT-ANAL            = "Political Analysis"}

@String{j-PROB-ENG-INFO-SCI     = "Probability in the Engineering and
                                  Informational Sciences"}

@String{j-PROC-VLDB-ENDOWMENT   = "Proceedings of the VLDB Endowment"}

@String{j-PROBAB-SURV           = "Probability Surveys"}

@String{j-PROBAB-THEORY-RELAT-FIELDS = "Probability Theory and Related Fields"}

@String{j-PROC-AM-MATH-SOC      = "Proceedings of the American Mathematical
                                  Society"}

@String{j-PROC-AMER-PHIL-SOC    = "Proceedings of the American Philosophical
                                  Society"}

@String{j-PROC-INST-STATIST-MATH = "Proceedings of the Institute of
                                  Statistical Mathematics"}

@String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of
                                  Sciences of the United States of America"}

@String{j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI = "Proceedings of the Royal
                                  Society A: Mathematical, Physical, \&
                                  Engineering Sciences"}

@String{j-PROC-R-SOC-LOND-SER-B-BIO-SCI = "Proceedings of the Royal Society of
                                  London. Series B. Biological sciences"}

@String{j-PROG-THEOR-PHYS       = "Progress of Theoretical Physics"}

@String{j-PSYCHOL-REP           = "Psychological Reports"}

@String{j-Q-J-ECON              = "The Quarterly Journal of Economics"}

@String{j-QUAL-QUANT            = "Quality \& Quantity"}

@String{j-RAND-STRUCT           = "Random Structures and Algorithms"}

@String{j-REG-SCI-URBAN-ECON    = "Regional Science and Urban Economics"}

@String{j-RELIABLE-COMPUTING    = "Reliable Computing = Nadezhnye
                                  vychisleniia"}

@String{j-RESONANCE             = "Resonance"}

@String{j-REV-ECON-STAT         = "Review of Economics and Statistics"}

@String{j-REV-INT-ECON          = "Review of International Economics"}

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@String{ser-LNCS                = "Lecture Notes in Computer Science"}

@String{ser-LNM                 = "Lecture Notes in Mathematics"}

%%% ====================================================================
%%% Bibliography entries, sorted by year, and then by citation label:
@Article{Newcomb:1881:NFU,
  author =       "Simon Newcomb",
  title =        "Note on the frequency of use of the different digits
                 in natural numbers",
  journal =      j-AM-J-MATH,
  volume =       "4",
  number =       "1--4",
  pages =        "39--40",
  year =         "1881",
  CODEN =        "AJMAAN",
  ISSN =         "0002-9327 (print), 1080-6377 (electronic)",
  ISSN-L =       "0002-9327",
  bibdate =      "Thu Feb 15 16:35:24 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2369148",
  abstract =     "That the ten digits do not occur with equal frequency
                 must be evident to any one making much use of
                 logarithmic tables, and noticing how much faster the
                 first pages wear out than the last ones. The first
                 significant figure is oftener 1 than any other digit,
                 and the frequency diminishes up to 9.",
  acknowledgement = ack-nhfb,
  author-dates = "March 12, 1835--July 11, 1909",
  fjournal =     "American Journal of Mathematics",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 40: ``The law of probability of the occurrence
                 of numbers is such that all mantissas of their
                 logarithms are equally probable.''. The article
                 contains no references to earlier work.",
  remark-2 =     "The papers \cite{Boring:1920:LNL,Raimi:1976:FDP} are
                 the earliest citations of Newcomb's work that I have
                 yet found in connection with Benford's Law.",
  xxURL =        "http://en.wikipedia.org/wiki/Simon_Newcomb",
}

@Book{Pareto:1896:CEP,
  author =       "Vilfredo Pareto",
  title =        "Cours d'{\'e}conomie politique profess{\'e} a
                 l'universit{\'e} de {Lausanne}. (French) [{Course} on
                 political economy given at the {University of
                 Lausanne}]",
  publisher =    "F. Rouge",
  address =      "Lausanne, Switzerland",
  pages =        "????",
  year =         "1896--1897",
  LCCN =         "HB173 .P22",
  bibdate =      "Wed Nov 16 08:41:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
  remark =       "Two volumes issued in successive years. The Italian
                 economist and mathematician, Vilfredo Federico (born in
                 Paris, France, and initially named Wilfried Fritz)
                 Pareto (15 July 1848--19 August 1923), introduced the
                 80--20 rule in economics (80\% of the wealth is owned
                 by 20\% of the people, which was true at the time in
                 Italy, and found to be similar in other countries). He
                 developed the Pareto distribution, in which a random
                 variable $X$ has the property that the probability that
                 it is greater than some number $x$ is given by $ {\rm
                 Pr}(X > x) = (x_m / x)^\alpha $ for $ x > x_m $, and $
                 {\rm Pr}(X > x) = 1 $ otherwise. The positive value $
                 x_m $ is a cutoff, and as $ \alpha \to \infty $, the
                 Pareto distribution approaches a Dirac delta function,
                 $ \delta (x - x_m) $. When this models the distribution
                 of wealth, the exponent $ \alpha $ is called the {\em
                 Pareto index}.",
}

@Article{Doolittle:1910:SNF,
  author =       "C. L. Doolittle",
  title =        "{Simon Newcomb, F.R.S., LL.D., D.C.L.}",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "49",
  number =       "197",
  pages =        "iii--xviii",
  month =        oct # "\slash " # dec,
  year =         "1910",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Aug 24 19:37:51 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/procamerphilsoc1900.bib",
  URL =          "https://www.jstor.org/stable/984092",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Amer. Philos. Soc.",
  fjournal =     "Proceedings of the American Philosophical Society",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This obituary does not mention Newcomb's short paper
                 on the leading-digit phenomenon now known as Benford's
                 Law, but it does give an overview of Newcomb's humble
                 origins, education, life, and scientific influence.",
}

@Book{Poincare:1912:CPL,
  author =       "H. Poincar{\'e}",
  title =        "Calcul des Probabilit{\'e}s: Le{\c{c}}ons
                 profess{\'e}es pendant le deuxi{\`e} me semestre
                 1893--1894. ({French}) [{Calculation} of Probabilities:
                 Lectures from the second semester 1893--1894]",
  publisher =    "Gauthier-Villars",
  address =      "Paris, France",
  pages =        "ii + 274",
  year =         "1912",
  LCCN =         "QA273 .P75",
  bibdate =      "Mon Nov 14 10:08:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1854--1912",
  language =     "French",
  remark =       "See pp. 313--320.",
}

@Article{Auerbach:1913:GBG,
  author =       "Felix Auerbach",
  title =        "{Das Gesetz der Bev{\"o}lkerungskonzentration}.
                 ({German}) [{The} law of population concentration]",
  journal =      "{Petermann's Geographische Mitteilungen}",
  volume =       "59",
  number =       "1",
  pages =        "74--76",
  month =        "????",
  year =         "1913",
  CODEN =        "PGGMA3",
  ISSN =         "0031-6229",
  ISSN-L =       "0031-6229",
  bibdate =      "Thu Nov 24 10:49:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper is reported in \cite{Newman:2005:PLP} to be
                 the first discovery of {\em Zipf's Law\/} in connection
                 with city populations (see \cite{Zipf:1932:SSP}). See
                 also \cite{Estoup:1916:GSM}.",
  URL =          "http://hdl.handle.net/2027/mdp.39015035583528?urlappend=%3Bseq=122",
  acknowledgement = ack-nhfb,
  ajournal =     "Petermanns Geogr. Mitteilung",
  ajournal-2 =   "Petermanns Geogr. Mitt.",
  language =     "German",
}

@Article{Stamp:1914:NIP,
  author =       "J. C. Stamp",
  title =        "A New Illustration of {Pareto}'s Law",
  journal =      j-J-R-STAT-SOC,
  volume =       "77",
  number =       "2",
  pages =        "200--204",
  month =        jan,
  year =         "1914",
  DOI =          "https://doi.org/10.2307/2339802",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Sat Jan 24 11:18:04 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i315805;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1910.bib",
  URL =          "http://www.jstor.org/stable/2339802",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}

@Article{Weyl:1915:GZM,
  author =       "Hermann Weyl",
  title =        "{{\"U}ber die Gleichverteilung von Zahlen mod. Eins}.
                 ({German}) [{On} the uniform distribution of numbers
                 mod. one]",
  journal =      j-MATH-ANN,
  volume =       "77",
  number =       "3",
  pages =        "313--352",
  month =        "????",
  year =         "1915",
  CODEN =        "MAANA3",
  DOI =          "https://doi.org/10.1007/BF01475864",
  ISSN =         "0025-5831 (print), 1432-1807 (electronic)",
  ISSN-L =       "0025-5831",
  bibdate =      "Sun Nov 13 10:54:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Ann.",
  fjournal =     "Mathematische Annalen",
  journal-URL =  "http://link.springer.com/journal/208",
  language =     "German",
  xxyear =       "1916",
}

@Book{Estoup:1916:GSM,
  author =       "J. B. Estoup",
  title =        "Gammes St{\'e}nographiques: m{\'e}thode \& exercices
                 pour l'acquisition de la vitesse ({French})
                 [Stenographic ranges: method and exercises for
                 achieving speed]",
  publisher =    "Institut St{\'e}nographique de France",
  address =      "Paris, France",
  edition =      "Fourth",
  pages =        "151",
  year =         "1916",
  LCCN =         "????",
  bibdate =      "Thu Nov 24 14:24:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This on shorthand writing is the earliest known
                 publication of the power-law distribution of word
                 frequencies, generally credited to
                 \cite{Zipf:1932:SSP}.",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  language =     "French",
}

@Article{Franel:1917:PTL,
  author =       "J. Franel",
  title =        "{{\`A}} propos des tables de logarithmes. ({French})
                 [{On} tables of logarithms]",
  journal =      "Festschrift Naturforschenden der Gesellschaft in
                 Z{\"u}rich Vierteljahrsschrift",
  volume =       "62",
  number =       "??",
  pages =        "286--295",
  month =        "????",
  year =         "1917",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 10:09:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@Article{Boring:1920:LNL,
  author =       "Edwin G. Boring",
  title =        "The Logic of the Normal Law of Error in Mental
                 Measurement",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "31",
  number =       "1",
  pages =        "1--33",
  month =        jan,
  year =         "1920",
  CODEN =        "AJPCAA",
  ISSN =         "0002-9556 (print), 1939-8298 (electronic)",
  ISSN-L =       "0002-9556",
  bibdate =      "Thu Dec 01 21:35:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/1413989",
  acknowledgement = ack-nhfb,
  fjournal =     "The American journal of psychology",
  remark =       "A citation search in Google Scholar on 1-Dec-2011
                 found this article as the only one citing Newcomb's
                 work \cite{Newcomb:1881:NFU} before it was brought to
                 wider view by Raimi's frequently-cited paper
                 \cite{Raimi:1976:FDP}. Boring's article has only brief
                 mention of Newcomb's work, and then solely in
                 connection with the believed randomness of digits of
                 transcendental numbers.",
}

@InCollection{Macaulay:1922:PLG,
  author =       "F. R. Macaulay",
  editor =       "W. C. Mitchell",
  booktitle =    "Income in the {United States}: Its Amount and
                 Distribution: 1909--1919",
  title =        "{Pareto}'s law and the general problem of mathematical
                 describing the frequency of distribution of income",
  publisher =    "National Bureau of Economic Research",
  address =      "New York, NY, USA",
  pages =        "??--??",
  year =         "1922",
  LCCN =         "????",
  bibdate =      "Fri Nov 25 09:06:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Yule:1925:MTE,
  author =       "G. Udny Yule",
  title =        "A Mathematical Theory of Evolution, Based on the
                 Conclusions of {Dr. J. C. Willis, F.R.S.}",
  journal =      j-PHILOS-TRANS-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "213",
  number =       "??",
  pages =        "21--87",
  day =          "14",
  month =        may,
  year =         "1925",
  CODEN =        "PTRBAE",
  DOI =          "https://doi.org/10.1098/rstb.1925.0002",
  ISSN =         "0962-8436 (print), 1471-2970 (electronic)",
  ISSN-L =       "0962-8436",
  bibdate =      "Tue Nov 15 10:45:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rstb.royalsocietypublishing.org/content/213/402-410/21",
  acknowledgement = ack-nhfb,
  fjournal =     "Philosophical transactions of the Royal Society of
                 London Series B, Biological sciences",
}

@Article{Lotka:1926:FDS,
  author =       "Alfred J. Lotka",
  title =        "The Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-WASH-ACAD-SCI,
  volume =       "16",
  number =       "12",
  pages =        "317--323",
  day =          "19",
  month =        jun,
  year =         "1926",
  CODEN =        "JWASA3",
  ISSN =         "0043-0439",
  ISSN-L =       "0043-0439",
  bibdate =      "Thu Nov 24 14:36:11 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This is the earliest known publication on the
                 phenomenon known as Zipf's Law, here applied to
                 publication counts of chemists and physicists. Lotka's
                 Law (a term possibly first used in
                 \cite{Zipf:1949:HBP}) says that the number of authors
                 producing $n$ publications is about $ 1 / n^2 $ of the
                 number producing only one. This `law' seems to have
                 been misunderstood and misapplied in other fields; see
                 \cite{Potter:1981:LLR}.",
  URL =          "http://www.jstor.org/stable/24529203",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Washington Academy of Sciences",
  journal-URL =  "http://www.jstor.org/journal/jwashacadscie",
  keywords =     "Lotka's Law",
}

@Article{Yule:1927:RS,
  author =       "G. Udny Yule",
  title =        "On Reading a Scale",
  journal =      j-J-R-STAT-SOC,
  volume =       "90",
  number =       "3",
  pages =        "570--587",
  month =        "????",
  year =         "1927",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Wed Nov 23 12:29:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See related later work \cite{Preece:1981:DFD}.",
  URL =          "http://www.jstor.org/stable/2341205",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
  remark =       "This paper reports on human bias in the recording of
                 last digits in measurements, or from roundings, or from
                 later scale conversions.",
}

@Article{Condon:1928:SV,
  author =       "E. U. Condon",
  title =        "Statistics of vocabulary",
  journal =      j-SCIENCE,
  volume =       "67",
  number =       "1733",
  pages =        "300--??",
  day =          "16",
  month =        mar,
  year =         "1928",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.67.1733.300",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Fri Nov 25 09:04:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
}

@Article{Sun:1928:EFD,
  author =       "C. P. Sun",
  title =        "On the Examination of Final Digits by Experiments in
                 Artificial Sampling",
  journal =      j-BIOMETRIKA,
  volume =       "20A",
  number =       "1/2",
  pages =        "64--68",
  month =        jul,
  year =         "1928",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2331941",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 13:38:07 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315380;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1920.bib",
  URL =          "http://www.jstor.org/stable/2331941",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
}

@Article{Zipf:1929:RFD,
  author =       "George Kingsley Zipf",
  title =        "Relative frequency as a determinant of phonetic
                 change",
  journal =      "Harvard Studies in Classical Philology",
  volume =       "40",
  number =       "??",
  pages =        "1--95",
  month =        "????",
  year =         "1929",
  CODEN =        "????",
  ISSN =         "0073-0688",
  ISSN-L =       "0073-0688",
  bibdate =      "Fri Nov 25 09:02:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/journals/00730688.html;
                 http://www.jstor.org/stable/310585",
  acknowledgement = ack-nhfb,
}

@Book{Gibrat:1931:IE,
  author =       "Robert Gibrat",
  title =        "Les In{\'e}galit{\'e}s {\'e}conomiques",
  publisher =    "Librairie du Recueil Sirey",
  address =      "Paris, France",
  pages =        "286",
  year =         "1931",
  LCCN =         "HB251.GIB",
  bibdate =      "Mon Feb 18 14:43:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  note =         "Applications: aux in{\'e}galit{\'e}s des richesses,
                 {\`a} la concentration des entreprises, aux populations
                 des villes, aux statistiques des familles, etc. d'une
                 loi nouvelle. La loi de l'effet proportionnel.",
  URL =          "http://en.wikipedia.org/wiki/Gibrat%27s_law",
  acknowledgement = ack-nhfb,
  author-dates = "1904--1980",
  remark-1 =     "According to at least one library catalog (SWB), this
                 book may be the author's doctoral dissertation from
                 l'Universit{\'e} de Paris in 1931.",
  remark-2 =     "This book is cited as the origin of Gibrat's Law, or
                 Gibrat's rule of proportionate growth, that ``the size
                 of a firm and its growth rate are independent''.",
}

@Misc{Anonymous:1932:FL,
  author =       "Anonymous",
  title =        "Fishpole Lamp",
  howpublished = "Web site",
  day =          "30",
  month =        apr,
  year =         "1932",
  bibdate =      "Sat Feb 23 14:52:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This Web site reports that General Electric researcher
                 Frank Benford invented the electric light pointer, the
                 forerunner of the modern laser pointer.",
  URL =          "http://scienceservice.si.edu/pages/012020.htm",
  acknowledgement = ack-nhfb,
  remark =       "CD 2478048, E\&MP12.020, Electric Appliances \
                 Apparatus.",
}

@Book{Zipf:1932:SSP,
  author =       "George Kingsley Zipf",
  title =        "Selected studies of the principle of relative
                 frequency in language",
  publisher =    pub-HARVARD,
  address =      pub-HARVARD:adr,
  pages =        "51",
  year =         "1932",
  LCCN =         "P123 .Z5",
  bibdate =      "Wed Nov 16 09:03:46 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This book is the origin of {\em Zipf's Law}, but the
                 phenomenon was apparently first reported two decades
                 earlier in \cite{Auerbach:1913:GBG} for city
                 populations, in \cite{Estoup:1916:GSM} for word
                 frequencies, and in \cite{Lotka:1926:FDS} for
                 researcher publication counts.",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "Plautus, Titus Maccius; language and languages;
                 semantics; comparative linguistics; Chinese language;
                 phonology; Latin language; glossaries, vocabularies,
                 etc; dialects; China; Beijing",
}

@Article{Bradford:1934:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      "Engineering: An Illustrated Weekly Journal (London)",
  volume =       "137",
  number =       "??",
  pages =        "85--86",
  day =          "26",
  month =        jan,
  year =         "1934",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 25 11:47:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper (reprinted in \cite{Bradford:1985:SIS})
                 introduces an observation later known as Bradford's
                 Law: there are exponentially-diminishing returns of
                 extending a search for references in journals.",
  URL =          "http://en.wikipedia.org/wiki/Bradford%27s_law",
  acknowledgement = ack-nhfb,
}

@Book{Zipf:1935:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-HOUGHTON-MIFFLIN,
  address =      pub-HOUGHTON-MIFFLIN:adr,
  pages =        "ix + 336",
  year =         "1935",
  LCCN =         "P105 .Z5",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  subject =      "language and languages; semantics; comparative
                 linguistics",
}

@Article{Keyser:1936:VFD,
  author =       "C. J. Keyser",
  title =        "{Vilfredo Federico Damaso Pareto}. {Mathematician},
                 economist, sociologist",
  journal =      j-SCRIPTA-MATH,
  volume =       "4",
  number =       "??",
  pages =        "5--23",
  month =        "????",
  year =         "1936",
  ISSN =         "0036-9713",
  bibdate =      "Thu Oct 26 11:15:25 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scripta-math.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica: A Quarterly Journal Devoted to
                 the Philosophy, History, and Expository Treatment of
                 Mathematics",
  jfm =          "62.0027.01",
  ZBmath =       "2525107",
}

@Book{Moon:1936:SBI,
  author =       "Parry Moon",
  title =        "The Scientific Basis of Illuminating Engineering",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xi + 608",
  year =         "1936",
  LCCN =         "TH7703 .M65",
  bibdate =      "Mon Nov 14 10:11:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "See pages 420ff.",
}

@Article{Bresciani-Turroni:1937:PL,
  author =       "C. Bresciani-Turroni",
  title =        "On {Pareto}'s Law",
  journal =      j-J-R-STAT-SOC,
  volume =       "100",
  number =       "3",
  pages =        "421--432",
  month =        "????",
  year =         "1937",
  DOI =          "https://doi.org/10.2307/2980528",
  ISSN =         "0952-8385",
  ISSN-L =       "0952-8385",
  bibdate =      "Sat Jan 24 11:18:08 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349533;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1930.bib",
  URL =          "http://www.jstor.org/stable/2980528",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society",
  journal-URL =  "http://www.jstor.org/journals/09528385.html",
}

@Article{Benford:1938:LAN,
  author =       "Frank Benford",
  title =        "The Law of Anomalous Numbers",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "551--572",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Thu Feb 15 16:28:28 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See comments about Benford's biased rounding practices
                 \cite{Diaconis:1979:RP}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X%2819380331%2978%3A4%3C551%3ATLOAN%3E2.0.CO%3B2-G",
  ZMnumber =     "JFM 64.0555.03; Zbl 0018.26502",
  abstract =     "It has been observed that the first pages of a table
                 of common logarithms show more wear than do the last
                 pages, indicating that more used numbers begin with the
                 digit 1 than with the digit 9. A compilation of some
                 20,000 first digits taken from widely divergent sources
                 shows that there is a logarithmic distribution of first
                 digits when the numbers are composed of four or more
                 digits. An analysis of the numbers from different
                 sources shows that the numbers taken from unrelated
                 subjects, such as a group of newspaper items, show a
                 much better agreement with a logarithmic distribution
                 than do numbers from mathematical tabulations or other
                 formal data. There is here the peculiar fact that
                 numbers that individually are without relationship are,
                 when considered in large groups, in good agreement with
                 a distribution law---hence the name ``Anomalous
                 Numbers.''\par

                 A further analysis of the data shows a strong tendency
                 for bodies of numerical data to fall into geometric
                 series. If the series is made up of numbers containing
                 three or more digits the first digits form a
                 logarithmic series. If the numbers contain only single
                 digits the geometric relation still holds but the
                 simple logarithmic relation no longer applies.\par

                 An equation is given showing the frequencies of first
                 digits in the different orders of numbers 1 to 10, 10
                 to 100, etc.\par

                 The equation also gives the frequency of digits in the
                 second, third + place of a multi-digit number, and it
                 is shown that the same law applies to
                 reciprocals.\par

                 There are many instances showing that the geometric
                 series, or the logarithmic law, has long been
                 recognized as a common phenomenon in factual literature
                 and in the ordinary affairs of life. The wire gauge and
                 drill gauge of the mechanic, the magnitude scale of the
                 astronomer and the sensory response curves of the
                 psychologist are all particular examples of a
                 relationship that seems to extend to all human affairs.
                 The Law of Anomalous Numbers is thus a general
                 probability law of widespread application.",
  acknowledgement = ack-nhfb,
  author-dates = "1883--December 4, 1948",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From \cite{Logan:1978:FDP}: ``Benford's paper was
                 published in 1938 in a journal of rather limited
                 circulation and not usually read by mathematicians. It
                 so happened that it was immediately followed in the
                 same issue by a physics paper which became of some
                 importance for secret nuclear work during World War II
                 [H. A. Bethe, M. E. Rose, and L. P. Smith, `The
                 Multiple Scattering of Electrons', Proc. Amer. Phil.
                 Soc. 78(4), 573--585 (1938)]. That is why Benford's
                 paper caught the attention of physicists in the early
                 1940's and was much discussed. This led to the notes in
                 Nature by Goudsmit and Furry [3] and Furry and Hurwitz
                 [4] containing an effort to explain Benford's law. We
                 considered it at that time merely a welcome diversion
                 and did not expect that over thirty papers would be
                 devoted to this subject in subsequent years.'' The 2006
                 bibliography \cite{Hurlimann:2006:BLB} cites 325
                 publications about Benford's Law.",
  xxURL =        "http://en.wikipedia.org/wiki/Frank_Benford",
}

@Article{Bethe:1938:MSE,
  author =       "H. A. Bethe and M. E. Rose and L. P. Smith",
  title =        "The Multiple Scattering of Electrons",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "78",
  number =       "4",
  pages =        "573--585",
  month =        mar,
  year =         "1938",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Wed Nov 23 14:27:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "This paper, which immediately follows Benford's
                 \cite{Benford:1938:LAN} in this journal issue, is
                 reported in \cite[p. 197]{Logan:1978:FDP} to have been
                 of considerable interest to scientists involved in
                 secret nuclear physics work in World War II. That is
                 how Benford's paper ``in a journal of rather limited
                 circulation and not usually read by mathematicians''
                 came to be noticed by physicists.",
  URL =          "http://www.jstor.org/stable/984803",
  acknowledgement = ack-nhfb,
  author-dates = "Hans Albrecht Bethe (1906--2005)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "Biography supplement in \cite{Lee:2007:HAB} has this
                 as Proc. Am. Philos. Soc., 89, 373--383 (1938), but
                 that seems to be wrong: check??",
}

@Article{Benford:1943:PAG,
  author =       "Frank Benford",
  title =        "The Probable Accuracy of the General Physical
                 Constants",
  journal =      j-PHYS-REV,
  volume =       "63",
  number =       "5--6",
  pages =        "212--212",
  month =        mar,
  year =         "1943",
  CODEN =        "PHRVAO",
  DOI =          "https://doi.org/10.1103/PhysRev.63.212",
  ISSN =         "0031-899X (print), 1536-6065 (electronic)",
  ISSN-L =       "0031-899X",
  bibdate =      "Mon Nov 21 21:52:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRev.63.212",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review",
  journal-URL =  "http://prola.aps.org/browse/PR",
}

@Article{Goudsmit:1944:SFN,
  author =       "S. A. Goudsmit and W. H. Furry",
  title =        "Significant Figures of Numbers in Statistical Tables",
  journal =      j-NATURE,
  volume =       "154",
  number =       "3921",
  pages =        "800--801",
  day =          "23",
  month =        dec,
  year =         "1944",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/154800a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:57:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See later work \cite{Logan:1978:FDP}, and severe
                 criticism \cite{Raimi:1976:FDP,Raimi:1985:FDP}.",
  URL =          "http://www.nature.com/nature/journal/v154/n3921/pdf/154800a0.pdf",
  abstract =     "A rough qualitative explanation of this fact can
                 easily be given. If we consider tables in which the
                 entries become rarer the larger they are, we can draw
                 the obvious conclusion that in any interval, say,
                 between 10 and 99, or 10,000 and 99,999, there are more
                 entries on the small side than on the large side.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Furry:1945:DND,
  author =       "W. H. Furry and Henry Hurwitz",
  title =        "Distribution of Numbers and Distribution of
                 Significant Figures",
  journal =      j-NATURE,
  volume =       "155",
  number =       "3924",
  pages =        "52--53",
  day =          "13",
  month =        jan,
  year =         "1945",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/155052a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sun Sep 18 11:51:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.nature.com/nature/journal/v155/n3924/pdf/155052a0.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Unpublished{Stigler:1945:DLD,
  author =       "George J. Stigler",
  title =        "The distribution of leading digits in statistical
                 tables",
  year =         "1945",
  bibdate =      "Sat Nov 12 16:07:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished, but written about 1945--1946, and
                 presented in an 1975 address at Haskell Hall,
                 University of Chicago. Stigler's distribution is more
                 complex than that of Newcomb and Benford. Stigler has $
                 F_d = (d \ln (d) - (d + 1) \ln (d + 1) + (1 + (10 / 9)
                 \ln (10))) / 9 $, which gives leading-digit frequencies
                 of 0.2413, 0.1832, 0.1455, 0.1174, 0.0950, 0.0764,
                 0.0605, 0.0465, and 0.0342. See \cite{Lee:2010:SAR} for
                 a comparison of the Benford and Stigler distributions,
                 and their relations to Zipf and Pareto distributions.
                 For derivations of Stigler's distribution, see
                 \cite{Logan:1978:FDP,Raimi:1985:FDP}.",
  URL =          "http://www.nobelprize.org/nobel_prizes/economics/laureates/1982/",
  acknowledgement = ack-nhfb,
  remark =       "Stigler won the 1982 Sveriges Riksbank Prize in
                 Economic Sciences in Memory of Alfred Nobel (often
                 called the Nobel Prize in Economics, although that
                 field was not among the original ones funded by Nobel's
                 will).",
}

@Book{Furlan:1946:HSU,
  author =       "Luigi Vladimir Furlan",
  title =        "{Das Harmoniegesetz der Statistik: Eine Untersuchung
                 {\"u}ber die metrische Interdependenz der sozialen
                 Erscheinungen}. ({German}) [{The} {Law of Harmony} in
                 statistics: an investigation of the metrical
                 interdependence of social phenomena]",
  volume =       "2",
  publisher =    "Verlag f{\"u}r Recht und Gesellschaft A.-G.",
  address =      "Basel, Switzerland",
  pages =        "xii + 504",
  year =         "1946",
  LCCN =         "HA29 .F85",
  bibdate =      "Mon Nov 14 09:40:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "{Beihefte zum Assekuranzjahrbuch}",
  acknowledgement = ack-nhfb,
  author-dates = "1886--",
  keywords =     "Benford--Furlan Law",
  language =     "German",
}

@Article{Geiringer:1948:RVF,
  author =       "Hilda Geiringer",
  title =        "Review of {L. V. Furlan}'s book: {Das Harmoniegesetz
                 der Statistik: Eine Untersuchung {\"u}ber die metrische
                 Interdependenz der sozialen Erscheinungen}. ({German})
                 [{The} {Law of Harmony} in statistics: an investigation
                 of the metrical interdependence of social phenomena]",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "43",
  number =       "242",
  pages =        "325--328",
  month =        jun,
  year =         "1948",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon Nov 14 09:42:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See \cite{Furlan:1946:HSU}.",
  URL =          "http://www.jstor.org/stable/2280379",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Hsu:1948:ESM,
  author =       "E. H. Hs{\"u}",
  title =        "An Experimental Study on ``Mental Numbers'' and a New
                 Application",
  journal =      j-J-GEN-PSYCH,
  volume =       "38",
  number =       "1",
  pages =        "57--67",
  month =        "????",
  year =         "1948",
  CODEN =        "JGPSAY",
  DOI =          "https://doi.org/10.1080/00221309.1948.9711768",
  ISSN =         "0022-1309 (print), 1940-0888 (electronic)",
  ISSN-L =       "0022-1309",
  bibdate =      "Sat Jan 07 09:29:53 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00221309.1948.9711768",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of General Psychology",
  keywords =     "Benford's Law",
  onlinedate =   "06 Jul 2010",
}

@Book{Hardy:1949:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  pages =        "xvi + 396",
  year =         "1949",
  LCCN =         "QA295 .H29",
  bibdate =      "Wed Nov 16 08:14:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
}

@Book{Zipf:1949:HBP,
  author =       "George Kingsley Zipf",
  title =        "Human behaviour and the principle of least effort",
  publisher =    "Hafner Pub. Co.",
  address =      "New York, NY, USA",
  pages =        "xi + 573",
  year =         "1949",
  LCCN =         "H91 .Z5 1949a",
  bibdate =      "Tue Nov 15 09:35:14 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprinted 1965.",
  subject =      "Human ecology",
}

@Article{Anonymous:1950:BRZ,
  author =       "Anonymous",
  title =        "Book review: {Zipf, George K., \booktitle{Human
                 behavior and the principle of least effort}. Cambridge,
                 (Mass.): Addison-Wesley, 1949, pp. 573}",
  journal =      j-J-CLIN-PSYCHOL,
  volume =       "6",
  number =       "3",
  pages =        "306--306",
  year =         "1950",
  CODEN =        "JCPYAO",
  DOI =          "https://doi.org/10.1002/1097-4679(195007)6:3<306::AID-JCLP2270060331>3.0.CO%3B2-7",
  ISSN =         "0021-9762 (print), 1097-4679 (electronic)",
  ISSN-L =       "0021-9762",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Psychology",
}

@Book{Feller:1950:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "????",
  year =         "1950",
  LCCN =         "QA273 .F37",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Article{Macon:1950:DFD,
  author =       "N. Macon and L. Moser",
  title =        "On the distribution of first digits of powers",
  journal =      "Scripta Mathematica",
  volume =       "16",
  number =       "??",
  pages =        "290--291",
  month =        "????",
  year =         "1950",
  CODEN =        "????",
  ISSN =         "0036-9713",
  ISSN-L =       "0036-9713",
  bibdate =      "Sat Nov 12 16:28:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Scripta Math.",
  fjournal =     "Scripta Mathematica",
}

@Article{Tsuji:1952:UDN,
  author =       "M. Tsuji",
  title =        "On the uniform distribution of numbers $ \bmod 1 $",
  journal =      j-J-MATH-SOC-JPN,
  volume =       "4",
  number =       "3--4",
  pages =        "313--322",
  month =        "????",
  year =         "1952",
  CODEN =        "NISUBC",
  DOI =          "https://doi.org/10.2969/jmsj/00430313",
  ISSN =         "0025-5645",
  ISSN-L =       "0025-5645",
  bibdate =      "Sun Feb 17 06:33:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.jmsj/1261415780",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Mathematical Society of Japan}",
}

@InProceedings{Mandelbrot:1953:ITS,
  author =       "Beno{\^\i}t B. Mandelbrot",
  editor =       "Willis Jackson",
  booktitle =    "{Communication theory: papers read at a Symposium on
                 ``Applications of Communication Theory'' held at the
                 Institution of Electrical Engineers, London, September
                 22nd--26th 1952}",
  title =        "An Informational Theory of the Statistical Structure
                 of Languages",
  publisher =    pub-BUTTERWORTHS,
  address =      pub-BUTTERWORTHS:adr,
  bookpages =    "xii + 532",
  pages =        "486--502",
  year =         "1953",
  LCCN =         "Q350 .S92 1952",
  bibdate =      "Wed Nov 16 09:37:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://lccn.loc.gov/53004215;
                 http://www.nytimes.com/2010/10/17/us/17mandelbrot.html",
  acknowledgement = ack-nhfb,
  remark =       "The paper is incorrectly referenced as a book in
                 \cite{Baek:2011:ZLU}. Mandelbrot got his Master of
                 Science in Aeronautics at CalTech in 1948, and his
                 Docteur d'{\'E}tat {\`e}s Sciences Math{\'e}matiques in
                 1952 in Paris, so perhaps this is a translation of his
                 thesis work.",
}

@Book{Blackwell:1954:TGS,
  author =       "David Blackwell and Meyer A. Girshick",
  title =        "Theory of Games and Statistical Decisions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 355",
  year =         "1954",
  LCCN =         "QA269 .B5",
  bibdate =      "Mon Nov 14 10:04:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://catalog.hathitrust.org/Record/000577721",
  acknowledgement = ack-nhfb,
  author-dates = "David Blackwell (1919--2010)",
  keywords =     "Benford's Law",
  remark =       "Brief mention of Benford's Law on page 74, problem
                 2.7.2 (??).",
}

@Article{Simon:1955:CSD,
  author =       "Herbert A. Simon",
  title =        "On a Class of Skew Distribution Functions",
  journal =      j-BIOMETRIKA,
  volume =       "42",
  number =       "3/4",
  pages =        "425--440",
  month =        dec,
  year =         "1955",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2333389",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  MRclass =      "62.0X",
  MRnumber =     "0073085 (17,380e)",
  MRreviewer =   "H. A. David",
  bibdate =      "Sat Jun 21 14:32:48 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315425;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1950.bib",
  URL =          "http://www.jstor.org/stable/2333389",
  acknowledgement = ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://biomet.oxfordjournals.org/content/by/year;
                 http://www.jstor.org/journals/00063444.html",
  keywords =     "distribution of income; distribution of species among
                 genera; distributions of city populations;
                 distributions of document word frequencies;
                 distributions of scientific publication counts; Zipf's
                 Law",
  remark =       "This work is an extension of Yule's work
                 \cite{Yule:1925:MTE}. See discussion
                 \cite{Mandelbrot:1959:NCS} and comments
                 \cite{Mitzenmacher:2003:BHG}.",
}

@Article{Devooght:1957:LZM,
  author =       "J. Devooght",
  title =        "Sur la loi de {Zipf--Mandelbrot}. ({French}) [On the
                 {Zipf--Mandelbrot} law]",
  journal =      "Acad. Roy. Belg. Bull. Cl. Sci. (5)",
  volume =       "43",
  pages =        "244--251",
  year =         "1957",
  CODEN =        "????",
  ISSN =         "0001-4141",
  ISSN-L =       "0001-4141",
  MRclass =      "94.0X",
  MRnumber =     "0088412 (19,516a)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acad{\'e}mie Royale de Belgique. Bulletin de la Classe
                 des Sciences. Koninklijke Belgische Academie.
                 Mededelingen van de Klasse der Wetenschappen. 5e
                 S{\'e}rie",
  language =     "French",
}

@Book{Feller:1957:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "461 (vol. 1), 626 (vol. 2)",
  year =         "1957",
  LCCN =         "QA273 .F3712",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://catdir.loc.gov/catdir/toc/onix01/57010805.html",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
}

@Article{Gini:1957:SFD,
  author =       "Corrado Gini",
  title =        "Sulla frequenza delle cifre iniziali dei numeri
                 osservati. ({Italian}) [{On} the frequency of initial
                 digits of observed numbers]",
  journal =      "{Bulletin de l'Institut International de
                 Statistique}",
  volume =       "35",
  number =       "2",
  pages =        "57--76",
  year =         "1957",
  CODEN =        "BISQA3",
  ISSN =         "????",
  MRclass =      "62.00",
  MRnumber =     "0117807 (22 \#8581)",
  bibdate =      "Sun Sep 18 11:54:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "29th session, 2nd delivery, Rio de Janerio.",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Internat. Stat.",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
  xxvolume =     "34 (wrong!)",
}

@Article{Herzel:1957:SDD,
  author =       "Amato Herzel",
  title =        "Sulla distribuzione della cifre iniziali dei numeri
                 statistici. ({Italian}) [{On} the frequency of initial
                 digits of statistical numbers]",
  journal =      "{Atti dell XV e XVII Riunione, Societa Italiana di
                 Statistica}",
  volume =       "??",
  number =       "??",
  pages =        "205--228",
  year =         "1957",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Sep 18 12:00:07 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  language =     "Italian",
}

@Article{Miller:1957:SEI,
  author =       "George A. Miller",
  title =        "Some Effects of Intermittent Silence",
  journal =      j-AMER-J-PSYCHOLOGY,
  volume =       "70",
  number =       "2",
  pages =        "311--314",
  month =        jun,
  year =         "1957",
  CODEN =        "AJPCAA",
  ISSN =         "0002-9556 (print), 1939-8298 (electronic)",
  ISSN-L =       "0002-9556",
  bibdate =      "Tue Nov 15 09:40:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/1419346",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Psychology",
  keywords =     "Zipf's Law",
}

@Book{Zeller:1958:TLG,
  author =       "Karl Zeller",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "242",
  year =         "1958",
  LCCN =         "QA295 .Z4",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "{Ergebnisse der Mathematik und ihrer Grenzgebiete}",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@Article{Mandelbrot:1959:NCS,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "A note on a class of skew distribution functions:
                 analysis and critique of a paper by {H. A. Simon}",
  journal =      j-INF-CONTROL,
  volume =       "2",
  number =       "??",
  pages =        "90--99",
  month =        apr,
  year =         "1959",
  CODEN =        "IFCNA4",
  DOI =          "https://doi.org/10.1016/S0019-9958(59)90098-1",
  ISSN =         "0019-9958 (print), 1878-2981 (electronic)",
  ISSN-L =       "0019-9958",
  bibdate =      "Wed Nov 16 09:45:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Simon:1955:CSD}.",
  abstract =     "This note is a discussion of H. A. Simon's model
                 (1955) concerning the class of frequency distributions
                 generally associated with the name of G. K. Zipf. The
                 main purpose is to show that Simon's model is
                 analytically circular in the case of the linguistic
                 laws of Estoup--Zipf and Willis--Yule. Insofar as the
                 economic law of Pareto is concerned, Simon has himself
                 noted that his model is a particular case of that of
                 Champernowne; this is correct, with some reservation. A
                 simplified version of Simon's model is included.",
  acknowledgement = ack-nhfb,
  fjournal =     "Information and Control",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00199958",
}

@Article{Mandelbrot:1960:PLL,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "The {Pareto--Levy} law and the distribution of
                 income",
  journal =      j-INT-ECON-REV,
  volume =       "1",
  number =       "??",
  pages =        "79--106",
  month =        "????",
  year =         "1960",
  CODEN =        "INERAE",
  ISSN =         "0020-6598 (print), 1468-2354 (electronic)",
  ISSN-L =       "0020-6598",
  bibdate =      "Wed Nov 23 11:07:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ingenta.com/journals/browse/bpl/iere",
  acknowledgement = ack-nhfb,
  fjournal =     "International Economic Review",
  journal-URL =  "http://www.jstor.org/journal/inteeconrevi",
}

@Article{Cigler:1961:NET,
  author =       "J. Cigler and G. Helmberg",
  title =        "{Neuere Entwicklungen der Theorie der
                 Gleichverteilung}. ({German}) [{Recent} developments in
                 the theory of uniform distribution]",
  journal =      j-DEUTSCH-MATH-V,
  volume =       "64",
  number =       "??",
  pages =        "1--50",
  month =        "????",
  year =         "1961",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Nov 12 16:33:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Jber. Deutsch. Math.--Verein",
  language =     "German",
}

@Article{Pinkham:1961:DFS,
  author =       "Roger S. Pinkham",
  title =        "On the Distribution of First Significant Digits",
  journal =      j-ANN-MATH-STAT,
  volume =       "32",
  number =       "4",
  pages =        "1223--1230",
  month =        dec,
  year =         "1961",
  CODEN =        "AASTAD",
  ISSN =         "0003-4851",
  ISSN-L =       "0003-4851",
  bibdate =      "Sat Sep 17 10:19:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2237922",
  abstract =     "It has been noticed by astute observers that well used
                 tables of logarithms are invariably dirtier at the
                 front than at the back. Upon reflection one is led to
                 inquire whether there are more physical constants with
                 low order first significant digits than high. Actual
                 counts by Benford [2] show that not only is this the
                 case but that it seems to be an empirical truth that
                 whenever one has a large body of physical data,
                 Farmer's Almanac, Census Reports, Chemical Rubber
                 Handbook, etc., the proportion of these data with first
                 significant digit $n$ or less is approximately $
                 \log_{10}(n + 1) $. Any reader formerly unaware of this
                 ``peculiarity'' will find an actual sampling experiment
                 wondrously tantalizing. Thus, for example,
                 approximately $ 0.7 $ of the physical constants in the
                 Chemical Rubber Handbook begin with $4$ or less ($
                 \log_{10}(4 + 1) = 0.699 $ ). This is to be contrasted
                 with the widespread intuitive evaluation $ 4 / 9 $
                 ths.",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoms/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "From p. 1223: ``\ldots{} the proportion of these data
                 with first significant digit $n$ or less is
                 approximately $ \log_{10}(n + 1) $.''\par

                 \ldots{} ``The only distribution for first significant
                 digits which is invariant under scale change of the
                 underlying distribution is $ \log_{10}(n + 1) $.
                 Contrary to suspicion this is a non-trivial
                 mathematical result, for the variable $n$ is
                 discrete.''.\par

                 From p. 1230: ``The foregoing results bear on questions
                 of round-off in computing machines. Since $ d(u v) = u
                 d v + v d u $, the error resulting from multiplying two
                 rounded numbers will be governed primarily by the first
                 significant digits of the two numbers being multiplied.
                 Now the distribution of first significant digits,
                 favoring as it does low order digits, tends to produce
                 less error than would be the case if first significant
                 digits were uniform as has sometimes been
                 assumed.''\par

                 Cited in \cite{Sterbenz:1974:FPC}.",
}

@Book{Hamming:1962:NMS,
  author =       "R. W. (Richard Wesley) Hamming",
  title =        "Numerical methods for scientists and engineers",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "xvii + 411",
  year =         "1962",
  LCCN =         "QA297 .H28",
  MRclass =      "65.00",
  MRnumber =     "0137279",
  MRreviewer =   "G. E. Forsythe",
  bibdate =      "Mon Aug 6 07:24:38 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International Series in Pure and Applied Mathematics",
  acknowledgement = ack-nhfb,
  HDnumber =     "51",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
  subject =      "Numerical analysis; Electronic digital computers;
                 random numbers",
  tableofcontents = "1. The difference calculus \\
                 2. Roundoff noise \\
                 3. The summation calculus \\
                 4. Evaluation of infinite series \\
                 5. Finite difference equations \\
                 6. The finite Fourier series \\
                 7--9. Polynomial approximation introduction \\
                 10. A uniform method for finding formulas \\
                 11. On finding the error term of a formula \\
                 12. Formulas for definite integrals \\
                 13. Indefinite integrals \\
                 14. Introduction to differential equations \\
                 15. A general theory of predictor-corrector methods \\
                 16. Special methods of integrating ordinary
                 differential equations \\
                 17--18. Least squares theory and practice \\
                 19. Chebyshev polynomials \\
                 20. Rational functions \\
                 21--22. Periodic functions --- Fourier series \\
                 23. Nonperiodic functions --- the Fourier integral \\
                 24. Linear filters --- smoothing and differentiating
                 \\
                 25. Integrals and differential equations \\
                 26. Exponential approximation \\
                 27. Singularities \\
                 28. On finding zeros \\
                 29. Simultaneous linear algebraic equations \\
                 30. Inversion of matrices and eigenvalues \\
                 31. Some examples of the simulation of situations and
                 processes \\
                 32. Random numbers and Monte Carlo methods \\
                 $N+1$: The art of computing for scientists and
                 engineers",
}

@TechReport{Mandelbrot:1962:SNR,
  author =       "Beno{\^\i}t Mandelbrot",
  title =        "Statistics of natural resources and the law of
                 {Pareto}",
  type =         "Research Note",
  number =       "NC-146",
  institution =  "IBM",
  address =      "Yorktown Heights, NY, USA",
  day =          "29",
  month =        jun,
  year =         "1962",
  bibdate =      "Mon Sep 10 17:35:59 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Weaver:1963:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: The Theory of Probability",
  publisher =    "Doubleday Anchor Series",
  address =      "New York, NY, USA",
  pages =        "392",
  year =         "1963",
  LCCN =         "QA273 .W4",
  bibdate =      "Mon Nov 14 09:54:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Benford's Law is discussed on pp. 270--277.",
  acknowledgement = ack-nhfb,
  author-dates = "Warren, Weaver (1894--1978)",
  remark =       "Reprinted in \cite{Weaver:1982:LLT}.",
}

@Article{Cigler:1964:MSU,
  author =       "J. Cigler",
  title =        "Methods of summability and uniform distribution $
                 \bmod 1 $",
  journal =      j-COMPOS-MATH,
  volume =       "16",
  number =       "??",
  pages =        "44--51",
  year =         "1964",
  CODEN =        "CMPMAF",
  ISSN =         "0010-437X (print), 1570-5846 (electronic)",
  ISSN-L =       "0010-437X",
  bibdate =      "Mon Nov 14 10:15:31 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Compositio Mathematica",
}

@Article{Good:1965:LE,
  author =       "I. J. Good",
  title =        "Letter to the Editor",
  journal =      j-AMER-STAT,
  volume =       "19",
  number =       "3",
  pages =        "43--43",
  month =        jun,
  year =         "1965",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 09:56:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2681423",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law",
  remark =       "Refers to \cite{Pinkham:1961:DFS}, and cites a review
                 of that article published by Good in Mathematical
                 Reviews (1962), page 214, which I have not yet been
                 able to locate.",
}

@Article{Hamming:1965:NLB,
  author =       "R. W. Hamming and W. L. Mammel",
  title =        "A Note on the Location of the Binary Point in a
                 Computing Machine",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "260--261",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264258",
  ISSN =         "0367-7508",
  ISSN-L =       "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038414",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
  remark =       "The authors consider the low-level multiplication
                 circuit efficiency of placing the binary point before
                 or after the first bit. If the leading bit is equally
                 likely to be a 0 or a 1, then their analysis shows that
                 it is better to place the point before the leading bit.
                 However, they report that a more likely distribution is
                 logarithmic (as predicted by Benford's Law, although
                 the Newcomb / Benford work is neither mentioned nor
                 cited), in which case there is no advantage for either
                 choice of placement of the binary point. They conclude
                 that it would be humane to place it after the leading
                 digit, by analogy with how people learn decimal
                 arithmetic.",
}

@Article{Konheim:1965:MDT,
  author =       "Alan G. Konheim",
  title =        "Mantissa Distributions (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "143--144",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.2307/2004111",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}

@Book{Zipf:1965:PBL,
  author =       "George Kingsley Zipf",
  title =        "The psycho-biology of language: an introduction to
                 dynamic philology",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  pages =        "xv + 336",
  year =         "1965",
  LCCN =         "P105 .Z5 1965",
  bibdate =      "Wed Nov 16 09:07:09 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1902--1950",
  remark =       "Reprint of \cite{Zipf:1935:PBL}.",
  subject =      "language; philology; semantics; psycholinguistics;
                 comparative linguistics",
}

@Article{Ball:1966:BRB,
  author =       "R. J. Ball",
  title =        "Book Review: {{\booktitle{Random Processes and the
                 Growth of Firms: A Study of the Pareto Law}}, by Josef
                 Steindl}",
  journal =      j-J-R-STAT-SOC-SER-A-GENERAL,
  volume =       "129",
  number =       "4",
  pages =        "600--601",
  month =        "????",
  year =         "1966",
  CODEN =        "JSSAEF",
  DOI =          "https://doi.org/10.2307/2982275",
  ISSN =         "0035-9238",
  ISSN-L =       "0035-9238",
  bibdate =      "Sat Jan 24 11:18:12 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349635;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1960.bib",
  URL =          "http://www.jstor.org/stable/2982275",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series A
                 (General)",
  journal-URL =  "http://www.jstor.org/journals/00359238.html",
}

@Book{Feller:1966:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xviii + 626",
  year =         "1966",
  ISSN =         "0271-6232",
  LCCN =         "QA273 .F3727 1966",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley series in probability and mathematical
                 statistics. Probability and mathematical statistics",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Benford's Law is discussed on p. 62.",
}

@Article{Flehinger:1966:PRI,
  author =       "B. J. (Betty J.) Flehinger",
  title =        "On the probability that a random integer has initial
                 digit {$A$}",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "73",
  number =       "10",
  pages =        "1056--1061",
  month =        dec,
  year =         "1966",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2314636",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Nov 12 15:33:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2314636",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Book{Petersen:1966:RMT,
  author =       "Gordon Marshall Petersen",
  title =        "Regular Matrix Transformations",
  publisher =    pub-MCGRAW-HILL,
  address =      pub-MCGRAW-HILL:adr,
  pages =        "viii + 142",
  year =         "1966",
  LCCN =         "QA263 .P415 1966",
  bibdate =      "Mon Nov 14 10:18:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duncan:1967:AUD,
  author =       "R. L. Duncan",
  title =        "An Application of Uniform Distributions to the
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "5",
  number =       "2",
  pages =        "137--140",
  month =        apr,
  year =         "1967",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:04:52 MDT 2011",
  bibsource =    "http://www.fq.math.ca/5-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/5-2/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Groos:1967:BCB,
  author =       "Ole V. Groos",
  title =        "Brief Communications: {Bradford's Law} and the
                 {Keenan--Atherton} data",
  journal =      j-AM-DOC,
  volume =       "18",
  number =       "1",
  pages =        "46--46",
  month =        jan,
  year =         "1967",
  CODEN =        "AMDOA7",
  DOI =          "https://doi.org/10.1002/asi.5090180108",
  ISSN =         "0096-946X (print), 1936-6108 (electronic)",
  ISSN-L =       "0096-946X",
  bibdate =      "Fri Sep 11 06:21:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amdoc.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Documentation",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643/",
  onlinedate =   "23 Apr 2007",
}

@Article{Mosteller:1967:DSR,
  author =       "Frederick Mosteller and Cleo Youtz and Douglas Zahn",
  title =        "The Distribution of Sums of Rounded Percentages",
  journal =      j-DEMOGRAPHY,
  volume =       "4",
  number =       "2",
  pages =        "850--858",
  month =        jun,
  year =         "1967",
  CODEN =        "????",
  ISSN =         "0070-3370 (print), 1533-7790 (electronic)",
  ISSN-L =       "0070-3370",
  bibdate =      "Thu Nov 24 08:03:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "See \cite{Diaconis:1979:RP} for further work.",
  URL =          "http://muse.jhu.edu/journals/dem/;
                 http://www.biomedsearch.com/nih/Distribution-Sums-Rounded-Percentages/21318695.html;
                 http://www.jstor.org/stable/2060324",
  abstract =     "When percentages are computed for counts in several
                 categories or for several positive measurements0 each
                 taken as a fraction of their sum, the rounded
                 percentages often fail to add to 100 percent. We
                 investigate how frequently this failure occurs and what
                 the distributions of sums of rounded percentages are
                 for (1) an empirical set of data, (2) the multinomial
                 distribution in small samples, (3) spacings between
                 points dropped on an interval --- the broken-stick
                 model; and (4) for simulation for several categories.
                 The several methods produce similar distributions.We
                 find that the probability that the sum of rounded
                 percentages adds to exactly 100 percent is certain for
                 two categories, about three-fourths for three
                 categories, about two-thirds for four categories, and
                 about [Formula: see text] for larger numbers of
                 categories, c, on the average when categories are not
                 improbable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Demography",
  pubmedid =     "21318695",
}

@Article{Adhikari:1968:DMS,
  author =       "A. K. Adhikari and B. P. Sarkar",
  title =        "Distribution of most significant digit in certain
                 functions whose arguments are random variables",
  journal =      j-SANKHYA-B,
  volume =       "30",
  number =       "??",
  pages =        "47--58",
  month =        "????",
  year =         "1968",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:09:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Book{Feller:1968:IPT,
  author =       "William Feller",
  title =        "Introduction to Probability Theory and its
                 Applications",
  volume =       "2",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Third",
  pages =        "xviii + 509",
  year =         "1968",
  ISBN =         "0-471-25708-7",
  ISBN-13 =      "978-0-471-25708-0",
  LCCN =         "QA273 .F3713",
  bibdate =      "Mon Nov 14 09:57:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Berger:2010:FFFa,Berger:2010:FFFb} for a
                 discussion of flaws in the derivation of Benford's Law
                 in this book.",
  acknowledgement = ack-nhfb,
  author-dates = "William Feller (1906--1970)",
  remark =       "Pages 63--64 (of xxiv + 669) in 1971 printing have
                 only brief mention of two papers
                 \cite{Benford:1938:LAN,Pinkham:1961:DFS}.",
}

@Article{Shenton:1968:PDM,
  author =       "L. R. Shenton",
  title =        "Periodicity and Density of Modified {Fibonacci}
                 Sequences",
  journal =      j-FIB-QUART,
  volume =       "6",
  number =       "2",
  pages =        "109--116",
  month =        apr,
  year =         "1968",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:02 MDT 2011",
  bibsource =    "http://www.fq.math.ca/6-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/6-2/shenton.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
  keywords =     "Benford's Law",
}

@Article{Wilk:1968:PPM,
  author =       "M. B. Wilk and R. Gnanadesikan",
  title =        "Probability Plotting Methods for the Analysis of
                 Data",
  journal =      j-BIOMETRIKA,
  volume =       "55",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1968",
  CODEN =        "BIOKAX",
  DOI =          "https://doi.org/10.2307/2334448",
  ISSN =         "0006-3444 (print), 1464-3510 (electronic)",
  ISSN-L =       "0006-3444",
  bibdate =      "Sat Jun 21 14:33:29 MDT 2014",
  bibsource =    "http://www.jstor.org/journals/00063444.html;
                 http://www.jstor.org/stable/i315458;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/biometrika1960.bib",
  URL =          "http://www.jstor.org/stable/2334448",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Biometrika",
  journal-URL =  "http://www.jstor.org/journals/00063444.html",
  keywords =     "empirical cumulative distribution function (ECDF);
                 percent ($p$--$p$) plots; quantile ($q$--$q$) plots",
  remark =       "This article does not mention Benford's Law, but MJN
                 \cite{Nigrini:2012:BLA} lists this reference for
                 analysis of data.",
}

@Article{Adhikari:1969:SRD,
  author =       "A. K. Adhikari",
  title =        "Some results on the distribution of the most
                 significant digit",
  journal =      j-SANKHYA-B,
  volume =       "31",
  number =       "??",
  pages =        "413--420",
  month =        "????",
  year =         "1969",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:12:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Bumby:1969:FAM,
  author =       "R. Bumby and E. Ellentuck",
  title =        "Finitely additive measures and the first digit
                 problem",
  journal =      j-FUNDAM-MATH,
  volume =       "65",
  number =       "??",
  pages =        "33--42",
  month =        "????",
  year =         "1969",
  CODEN =        "????",
  ISSN =         "0016-2736 (print), 1730-6329 (electronic)",
  ISSN-L =       "0016-2736",
  bibdate =      "Sat Nov 12 16:19:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fundamenta mathematicae",
}

@Article{Duncan:1969:NID,
  author =       "R. L. Duncan",
  title =        "Note on the Initial Digit Problem",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "474--475",
  month =        dec,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/7-5/duncan.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Fairthorne:1969:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "25",
  number =       "4",
  pages =        "313--343",
  month =        dec,
  year =         "1969",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026481",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprinted in \cite{Fairthorne:2005:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Unpublished{Hafner:1969:CSR,
  author =       "Everett M. Hafner",
  title =        "Circular slide roulette",
  year =         "1969",
  bibdate =      "Mon Nov 14 10:00:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unpublished but dated 1969. Presented in 1975 in an
                 address at Hampshire College, Amherst, MA, USA",
  acknowledgement = ack-nhfb,
}

@Article{Haight:1969:TPD,
  author =       "F. A. Haight",
  title =        "Two probability distributions connected with {Zipf}'s
                 rank-size conjecture",
  journal =      j-ZASTOS-MAT,
  volume =       "10",
  pages =        "225--228",
  year =         "1969",
  CODEN =        "ZAMTAK",
  ISSN =         "0044-1899",
  ISSN-L =       "0044-1899",
  MRclass =      "62.31",
  MRnumber =     "0246425 (39 \#7729)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Polska Akademia Nauk. Instytut Matematyczny.
                 Zastosowania Matematyki",
}

@Article{Holewijn:1969:UDS,
  author =       "Dr. P. J. Holewijn",
  title =        "On the uniform distribution of sequences of random
                 variables",
  journal =      j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
  volume =       "14",
  number =       "2",
  pages =        "89--92",
  month =        "????",
  year =         "1969",
  CODEN =        "ZWVGAA",
  DOI =          "https://doi.org/10.1007/BF00537514",
  ISSN =         "0044-3719",
  ISSN-L =       "0044-3719",
  bibdate =      "Sat Apr 26 19:23:29 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00537514",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
                 verwandte Gebiete",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Book{Knuth:1969:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xi + 624",
  year =         "1969",
  ISBN =         "0-201-03802-1",
  ISBN-13 =      "978-0-201-03802-6",
  LCCN =         "QA76.5 .K57",
  MRclass =      "68.00 (65.00)",
  MRnumber =     "44 \#3531",
  MRreviewer =   "M. Muller",
  bibdate =      "Wed Dec 15 15:47:38 1993",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$19.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is discussed on pp. 219--229.",
  tableofcontents = "3: Random Numbers \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 9 \\
                 3.2.1. The Linear Congruential Method / 9 \\
                 3.2.1.1. Choice of modulus / 11 \\
                 3.2.1.2. Choice of multiplier / 15 \\
                 3.2.1.3. Potency / 21 \\
                 3.2.2. Other Methods / 25 \\
                 3.3. Statistical Tests / 34 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 35 \\
                 3.3.2. Empirical Tests / 54 \\
                 *3.3.3. Theoretical Tests / 69 \\
                 3.3.4. The Spectral Test / 82 \\
                 3.4. Other Types of Random Quantities / 100 \\
                 3.4.1. Numerical Distributions / 101 \\
                 3.4.2. Random Sampling and Shuffling / 121 \\
                 *3.5. What is a Random Sequence? / 127 \\
                 3.6. Summary / 155 \\
                 4: Arithmetic \\
                 4.1. Positional Number Systems / 162 \\
                 4.2. Floating-Point Arithmetic / 180 \\
                 4.2.1. Single-Precision Calculations / 180 \\
                 4.2.2. Accuracy of Floating-Point Arithmetic / 195 \\
                 *4.2.3. Double-Precision Calculations / 210 \\
                 4.2.4. Statistical Distribution / 218 \\
                 4.3. Multiple-Precision Arithmetic / 229 \\
                 4.3.1. The Classical Algorithms / 229 \\
                 *4.3.2. Modular Arithmetic / 248 \\
                 *4.3.3. How Fast Can We Multiply? / 258 \\
                 4.4. Radix Conversion / 280 \\
                 4.5. Rational Arithmetic / 290 \\
                 4.5.1. Fractions / 290 \\
                 4.5.2. The Greatest Common Divisor / 293 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 316 \\
                 4.5.4. Factoring into Primes / 339 \\
                 4.6. Polynomial Arithmetic / 360 \\
                 4.6.1. Division of Polynomials / 363 \\
                 *4.6.2. Factorization of Polynomials / 381 \\
                 4.6.3. Evaluation of Powers / 398 \\
                 4.6.4. Evaluation of Polynomials / 422 \\
                 *4.7. Manipulation of Power Series / 444 \\
                 Answers to Exercises / 452 \\
                 Appendix A: MIX / 565 \\
                 1. Description of MIX / 565 \\
                 2. The MIX Assembly Language / 584 \\
                 Appendix B: Tables of Numerical Quantities / 596 \\
                 1. Fundamental Constants (decimal) / 596 \\
                 2. Fundamental Constants (octal) / 597 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 598 \\
                 Appendix C: Index to Notations / 600 \\
                 Index and Glossary / 605",
  xxyear =       "{\noopsort{1968c}}1969",
}

@Article{Kuipers:1969:RPR,
  author =       "L. Kuipers",
  title =        "Remark on a Paper by {R. L. Duncan} Concerning the
                 Uniform Distribution Mod $1$ of the Sequence of the
                 Logarithms of the {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "7",
  number =       "5",
  pages =        "465--466",
  month =        dec,
  year =         "1969",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:21 MDT 2011",
  bibsource =    "http://www.fq.math.ca/7-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/7-5/kuipers-a.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Raimi:1969:DFS,
  author =       "R. A. Raimi",
  title =        "On the Distribution of First Significant Figures",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "76",
  number =       "4",
  pages =        "342--348",
  month =        apr,
  year =         "1969",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2316424",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:39:22 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Raimi:1969:PDF,
  author =       "R. Raimi",
  title =        "The peculiar distribution of first significant
                 digits",
  journal =      j-SCI-AMER,
  volume =       "221",
  number =       "6",
  pages =        "109--120",
  month =        dec,
  year =         "1969",
  CODEN =        "SCAMAC",
  DOI =          "https://doi.org/10.1038/scientificamerican1269-109",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Sat Nov 12 16:39:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@PhdThesis{Wong:1969:GDS,
  author =       "James Teng Wong",
  title =        "On the Generalization of the Distribution of the
                 Significant Digits Under Computation",
  type =         "{Ph.D.} thesis",
  school =       "Department of Mathematics, Oregon State University",
  address =      "Corvallis, OR, USA",
  pages =        "52",
  year =         "1969",
  bibdate =      "Fri Nov 25 15:41:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/302476508?accountid=14677",
  acknowledgement = ack-nhfb,
}

@Article{Aigner:1970:EPL,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "330",
  pages =        "712--723",
  month =        jun,
  year =         "1970",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:44 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314212;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2284582",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Blum:1970:SID,
  author =       "M. Blum",
  title =        "On the Sums of Independently Distributed {Pareto}
                 Variates",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "19",
  number =       "1",
  pages =        "191--198",
  month =        jul,
  year =         "1970",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
}

@Article{Brown:1970:MOU,
  author =       "J. L. {Brown, Jr.} and R. L. Duncan",
  title =        "Modulo One Uniform Distribution of the Sequence of
                 Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "8",
  number =       "5",
  pages =        "482--486",
  month =        dec,
  year =         "1970",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:31 MDT 2011",
  bibsource =    "http://www.fq.math.ca/8-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See remark \cite{Kuipers:1973:RPD}.",
  URL =          "http://www.fq.math.ca/Scanned/8-5/brown.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Hamming:1970:DN,
  author =       "R. W. Hamming",
  title =        "On the Distribution of Numbers",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "49",
  number =       "8",
  pages =        "1609--1625",
  month =        oct,
  year =         "1970",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  ISSN-L =       "0005-8580",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1970/BSTJ.1970.4908.html;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/bstj-vol49-issue08.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol49/bstj49-8-1609.pdf;
                 http://www.alcatel-lucent.com/bstj/vol49-1970/articles/bstj49-8-1609.pdf",
  abstract =     "This paper examines the distribution of the mantissas
                 of floating-point numbers and shows how the arithmetic
                 operations of a computer transform various
                 distributions toward the limiting distribution $$ r(x)
                 = 1 / (x \ln b) \qquad (1 / b \leq x \leq 1) $$ (where
                 $b$ is the base of the number system). The paper also
                 gives a number of applications to hardware, software,
                 and general computing which show that this distribution
                 is not merely an amusing curiosity. A brief examination
                 of the distribution of exponents is include.",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}

@Article{Hill:1970:ZLP,
  author =       "Bruce M. Hill",
  title =        "{Zipf}'s law and prior distributions for the
                 composition of a population",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "65",
  number =       "331",
  pages =        "1220--1232",
  month =        sep,
  year =         "1970",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62.35",
  MRnumber =     "0279936 (43 \#5657)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  URL =          "http://www.jstor.org/stable/2284288",
  ZMnumber =     "Zbl 0224.92011",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Orlov:1970:GZM,
  author =       "Ju. K. Orlov",
  title =        "A generalization of the {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "57",
  pages =        "37--40",
  year =         "1970",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "94.50",
  MRnumber =     "0274234 (42 \#9109)",
  MRreviewer =   "T. Nemetz",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Taguchi:1970:ZLC,
  author =       "Tokio Taguchi",
  title =        "On {Zipf}'s law. {A} characterization of distributions
                 in linguistics and demography",
  journal =      j-PROC-INST-STATIST-MATH,
  volume =       "17",
  pages =        "83--90",
  year =         "1970",
  CODEN =        "????",
  ISSN =         "0912-6112",
  ISSN-L =       "0912-6112",
  bibdate =      "Sat Nov 12 10:39:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0238.68026",
  acknowledgement = ack-nhfb,
  ajournal =     "Proc. Inst. Statist. Math.",
  classmath =    "68Q45 (Formal languages)",
  fjournal =     "Proceedings of the Institute of Statistical
                 Mathematics",
  language =     "Japanese",
}

@Book{Zeller:1970:TLG,
  author =       "Karl Zeller and Wolfgang Beekmann",
  title =        "{Theorie der Limitierungsverfahren}. (German)
                 [{Theory} of limiting processes]",
  volume =       "15",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xii + 314",
  year =         "1970",
  LCCN =         "QA295 .Z4 1970",
  bibdate =      "Wed Nov 16 06:43:43 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Ergebnisse der Mathematik und ihrer Grenzgebiete",
  acknowledgement = ack-nhfb,
  language =     "German",
  subject =      "series; convergence",
}

@Article{Thorp:1971:PCD,
  author =       "E. Thorp and R. Whitley",
  title =        "{Poincar{\'e}}'s conjecture and the distribution of
                 digits in logarithm tables",
  journal =      j-COMPOS-MATH,
  volume =       "21",
  number =       "??",
  pages =        "233--250",
  month =        "????",
  year =         "1971",
  CODEN =        "CMPMAF",
  ISSN =         "0010-437X (print), 1570-5846 (electronic)",
  ISSN-L =       "0010-437X",
  bibdate =      "Sat Nov 12 16:36:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comp. Math.",
  fjournal =     "Compositio Mathematica",
}

@Article{Wlodarski:1971:FLN,
  author =       "J. Wlodarski",
  title =        "{Fibonacci} and {Lucas} Numbers Tend to Obey
                 {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "9",
  number =       "1",
  pages =        "87--88",
  month =        feb,
  year =         "1971",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:05:33 MDT 2011",
  bibsource =    "http://www.fq.math.ca/9-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/9-1/wlodarski2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Aigner:1972:CEP,
  author =       "Dennis J. Aigner and Arthur S. Goldberger",
  title =        "Corrigenda: Estimation of {Pareto's Law} from Grouped
                 Observations",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "67",
  number =       "337",
  pages =        "252--252",
  month =        mar,
  year =         "1972",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:45 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314217;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2284755",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Krevitt:1972:BCC,
  author =       "Beth Krevitt and Belver C. Griffith",
  title =        "Brief Communications: A comparison of several
                 {Zipf}-type distributions in their goodness of fit to
                 language data",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "23",
  number =       "3",
  pages =        "220--221",
  month =        may,
  year =         "1972",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630230310",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:44 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Krevitt:1972:CSZ,
  author =       "Beth Krevitt and Belver C. Griffith",
  title =        "A comparison of several {Zipf}-type distributions in
                 their goodness of fit to language data",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "23",
  number =       "3",
  pages =        "220--221",
  year =         "1972",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630230310",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Varian:1972:LEB,
  author =       "Hal R. Varian",
  title =        "Letter to the {Editor}: {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "26",
  number =       "3",
  pages =        "65--66",
  month =        jun,
  year =         "1972",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Mar 30 11:34:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://links.jstor.org/sici?sici=0003-1305%28197206%2926%3A3%3C62%3ALTTE%3E2.0.CO%3B2-Q",
  abstract =     "Around 1938 the physicist Frank Benford observed a
                 rather strange fact: tables of logarithms in libraries
                 tend to be dirtier at the beginning than at the end.
                 This indicated to Benford that people had more occasion
                 to calculate with numbers beginning with 1 or 2 than
                 with 8 or 9.\par

                 Benford also found that the frequency of the digit $p$
                 being the first digit of a decimal number was very
                 closely approximated by $ \log (p + 1) - \log p $
                 [i.e., $ \log (1 + 1 / p) $ ]. This has become known as
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Vlachy:1972:VFS,
  author =       "Jan Vlach{\'y}",
  title =        "Variable Factors in Scientific Communities
                 (Observations on {Lotka's Law})",
  journal =      "Teorie a Metoda",
  volume =       "4",
  number =       "??",
  pages =        "91--120",
  month =        "????",
  year =         "1972",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Fri Nov 25 07:53:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  xxvolume =     "6",
}

@Article{Whitney:1972:MNI,
  author =       "R. E. Whitney",
  title =        "Mathematical Notes: Initial Digits for the Sequence of
                 Primes",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "79",
  number =       "2",
  pages =        "150--152",
  month =        feb,
  year =         "1972",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2316536",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 28 12:36:38 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Wilkinson:1972:ABL,
  author =       "Elizabeth A. Wilkinson",
  title =        "The Ambiguity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "28",
  number =       "2",
  pages =        "122--130",
  month =        "????",
  year =         "1972",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026534",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:20:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@TechReport{Diaconis:1973:LMI,
  author =       "Persi Diaconis",
  title =        "Limits of measures of the integers with applications
                 to random number generators and the distribution of
                 leading digits",
  type =         "Memorandum",
  number =       "NS-211",
  institution =  "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  day =          "22",
  month =        mar,
  year =         "1973",
  bibdate =      "Sat Nov 12 16:23:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Kreifelts:1973:OBG,
  author =       "Thomas Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine
                 Gleitkomma-Arithmetik}. ({German}) [{Optimal} Choice of
                 Basis for a Floating-Point Arithmetic]",
  journal =      j-COMPUTING,
  volume =       "11",
  number =       "4",
  pages =        "353--363",
  month =        dec,
  year =         "1973",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Jan 2 17:40:51 MST 2001",
  bibsource =    "Compendex database;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 INSPEC Axiom database (1968--date)",
  note =         "See correction \cite{Kreifelts:1975:OBF}.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  affiliation =  "Inst. Numerische Datenverarbeitung, Bonn, West
                 Germany",
  classification = "723; 921; C5230",
  description =  "digital arithmetic",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Comput (Vienna/NY)",
  keywords =     "base; computer programming; floating point arithmetic;
                 mathematical techniques; optimal choice; rounding
                 errors",
  language =     "German",
}

@Article{Kuipers:1973:RPD,
  author =       "L. Kuipers and Jau-shyong Shiue",
  title =        "Remark on a Paper by {Duncan} and {Brown} on the
                 Sequence of Logarithms of Certain Recursive Sequences",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "3",
  pages =        "292--293",
  month =        oct,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:42 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-3.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  note =         "See \cite{Brown:1970:MOU}.",
  URL =          "http://www.fq.math.ca/Scanned/11-3/kuipers.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Loynes:1973:SRP,
  author =       "R. M. Loynes",
  title =        "Some results in the probabilistic theory of asymptotic
                 uniform distribution modulo 1",
  journal =      j-Z-WAHRSCHEINLICHKEITSTHEOR-VERW-GEB,
  volume =       "26",
  number =       "1",
  pages =        "33--41",
  month =        "????",
  year =         "1973",
  CODEN =        "ZWVGAA",
  DOI =          "https://doi.org/10.1007/BF00533958",
  ISSN =         "0044-3719",
  ISSN-L =       "0044-3719",
  bibdate =      "Sat Apr 26 19:24:39 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/z-wahrscheinlichkeits-theor-verw-geb.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00533958",
  acknowledgement = ack-nhfb,
  fjournal =     "Zeitschrift f{\"u}r Wahrscheinlichkeitstheorie und
                 verwandte Gebiete",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Article{Murphy:1973:BCL,
  author =       "Larry J. Murphy",
  title =        "Brief Communications: ``{Lotka's Law} in the
                 humanities?''",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "24",
  number =       "6",
  pages =        "461--462",
  month =        nov,
  year =         "1973",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630240607",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:48 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Murphy:1973:LLH,
  author =       "Larry J. Murphy",
  title =        "{Lotka's Law} in the Humanities?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "24",
  number =       "6",
  pages =        "461--462",
  month =        nov # "\slash " # dec,
  year =         "1973",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630240607",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:09:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Petruszewycz:1973:LLE,
  author =       "M. Petruszewycz",
  title =        "{L'histoire} de la loi d'{Estoup--Zipf}: documents.
                 ({French}) [{The} history of the {Estoup--Zipf} law]",
  journal =      "Math. Sci. Humaines",
  volume =       "??",
  number =       "44",
  pages =        "41--56",
  year =         "1973",
  CODEN =        "????",
  ISSN =         "0025-5815",
  ISSN-L =       "0025-5815",
  MRclass =      "92A25",
  MRnumber =     "0354071 (50 \#6553)",
  MRreviewer =   "J. S. Joel",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Centre de Math{\'e}matique Sociale. \'Ecole Pratique
                 des Hautes \'Etudes. Math{\'e}matiques et Sciences
                 Humaines",
  language =     "French",
}

@Article{Sarkar:1973:OSD,
  author =       "B. P. Sarkar",
  title =        "An observation on the significant digits of the
                 binomial coefficients and factorials",
  journal =      j-SANKHYA-B,
  volume =       "35",
  number =       "??",
  pages =        "363--364",
  month =        "????",
  year =         "1973",
  CODEN =        "SANBBV",
  ISSN =         "0581-5738",
  ISSN-L =       "0581-5738",
  bibdate =      "Sat Nov 12 16:29:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sankhya Ser. B (Indian J. of Statist.)",
  fjournal =     "Sankhy{\=a} (Indian Journal of Statistics), Series B.
                 Methodological",
}

@Article{Schatte:1973:VMG,
  author =       "Peter Schatte",
  title =        "{Zur Verteilung der Mantisse in der
                 Gleitkommadarstellung einer Zufallsgr{\"o}{\ss}e}.
                 ({German}) [Distribution of the mantissa in the
                 floating-point representation of a random variable]",
  journal =      j-Z-ANGE-MATH-MECH,
  volume =       "53",
  number =       "??",
  pages =        "553--565",
  month =        "????",
  year =         "1973",
  CODEN =        "ZAMMAX",
  ISSN =         "0044-2267 (print), 1521-4001 (electronic)",
  ISSN-L =       "0044-2267",
  bibdate =      "Mon Nov 14 16:35:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Angewandte Mathematik und
                 Mechanik}",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1521-4001",
  language =     "German",
}

@Article{Sentance:1973:FAB,
  author =       "W. A. Sentance",
  title =        "A Further Analysis of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "11",
  number =       "5",
  pages =        "490--494",
  month =        dec,
  year =         "1973",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:58:46 MDT 2011",
  bibsource =    "http://www.fq.math.ca/11-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/11-5/sentance.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Banks:1974:AMN,
  author =       "William P. Banks and David K. Hill",
  title =        "The apparent magnitude of number scaled by random
                 production",
  journal =      j-J-EXP-PSYCH-GEN,
  volume =       "102",
  number =       "2",
  pages =        "353--376",
  month =        feb,
  year =         "1974",
  CODEN =        "JPGEDD",
  DOI =          "https://doi.org/10.1037/h0035850",
  ISSN =         "0096-3445 (print), 1939-2222 (electronic)",
  ISSN-L =       "0096-3445",
  bibdate =      "Fri Feb 15 06:32:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://psycnet.apa.org/journals/xge/102/2/353/;
                 http://psycnet.apa.org/psycinfo/1974-24305-001",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Experimental Psychology: General",
}

@PhdThesis{Diaconis:1974:WSA,
  author =       "Persi Diaconis",
  title =        "Weak and Strong Averages in probability and the theory
                 numbers",
  type =         "{Ph.D.} thesis",
  school =       "Department of Statistics, Harvard University",
  address =      "Cambridge, MA, USA",
  pages =        "xvii + 117",
  year =         "1974",
  bibdate =      "Mon Nov 14 10:26:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Duran:1974:ACS,
  author =       "J. Peter Duran",
  title =        "Almost convergence, summability and ergodicity",
  journal =      j-CAN-J-MATH,
  volume =       "26",
  number =       "??",
  pages =        "372--387",
  month =        "????",
  year =         "1974",
  CODEN =        "CJMAAB",
  DOI =          "https://doi.org/10.4153/CJM-1974-039-6",
  ISSN =         "0008-414X (print), 1496-4279 (electronic)",
  ISSN-L =       "0008-414X",
  bibdate =      "Sat Sep 10 15:38:45 MDT 2011",
  bibsource =    "http://cms.math.ca/cjm/v26/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/canjmath1970.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Canadian Journal of Mathematics = Journal canadien de
                 math{\'e}matiques",
  journal-URL =  "http://cms.math.ca/cjm/",
  remark =       "In relation to Benford's Law, see theorem 6.2.",
}

@Article{Hill:1974:RFF,
  author =       "Bruce M. Hill",
  title =        "The rank-frequency form of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "69",
  number =       "348",
  pages =        "1017--1026",
  month =        dec,
  year =         "1974",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15",
  MRnumber =     "0426242 (54 \#14188)",
  MRreviewer =   "S. M. Samuels",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0301.60011",
  acknowledgement = ack-nhfb,
  classification = "B0240 (Probability and statistics); C1140
                 (Probability and statistics)",
  corpsource =   "Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI,
                 USA",
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Bose--Einstein allocation; distribution; random
                 processes; rank frequency form; statistics; Zipf's
                 law",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Kuipers:1974:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 390",
  year =         "1974",
  ISBN =         "0-471-51045-9",
  ISBN-13 =      "978-0-471-51045-1",
  LCCN =         "QA292 .K84",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Pure and applied mathematics",
  acknowledgement = ack-nhfb,
  remark =       "``A Wiley-Interscience publication.''.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Article{Schorr:1974:LLL,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Library Science",
  journal =      "RQ",
  volume =       "14",
  number =       "1",
  pages =        "32--33",
  month =        "Fall",
  year =         "1974",
  CODEN =        "????",
  ISSN =         "0033-7072",
  ISSN-L =       "0033-7072",
  bibdate =      "Fri Nov 25 08:12:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "RQ",
  fjournal =     "Reference Quarterly",
}

@Unpublished{Singmaster:1974:RSB,
  author =       "D. Singmaster",
  title =        "Recurrent sequences and {Benford}'s law",
  year =         "1974",
  bibdate =      "Sat Nov 12 16:25:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint submitted to Fibonacci Quarterly in 1974, but
                 never published there.",
  acknowledgement = ack-nhfb,
}

@Book{Sterbenz:1974:FPC,
  author =       "Pat H. Sterbenz",
  title =        "Floating Point Computation",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xiv + 316",
  year =         "1974",
  ISBN =         "0-13-322495-3",
  ISBN-13 =      "978-0-13-322495-5",
  LCCN =         "QA76.8.I12 S771 1974",
  MRclass =      "68A05 (65G05)",
  MRnumber =     "50 1556",
  bibdate =      "Sat May 29 08:01:36 1999",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  series =       "Prentice-Hall Series in Automatic Computation.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  keywords =     "Compiling (Electronic computers); Computation by
                 computer systems --- Floating point representation;
                 Floating-point arithmetic; IBM 360 (Computer) ---
                 Programming",
  remark =       "From p. 116: ``There is general agreement that the
                 mantissas of floating-point numbers are not uniformly
                 distributed. [See Hamming (1962)
                 [\cite{Hamming:1962:NMS}], Pinkham (1961)
                 [Pinkham:1961:DFS], or Knuth (1969) [Knuth:1969:SNM].]
                 Instead, it is customary to assume that they are
                 distributed logarithmically, that is, that the
                 probability density function is

                  $$ (3.12.9) f(m) = \frac {1}{m \ln r}, \qquad r^{-1}
                 \leq m \leq 1. $$

                 This assumption is based on the following observations:
                 First, this distribution reproduces itself under
                 multiplication, but a uniform distribution does not.
                 [See Hamming (1962) [\cite{Hamming:1962:NMS}] and
                 Exercise 20.] A second justification is based on the
                 fact that many of the numbers that arise in computation
                 represent measurable quantities such as lengths,
                 forces, etc., and it is reasonable to believe that the
                 distribution of the mantissas of such quantities is
                 independent of the units in which they are measured.
                 Pinkham (1961) shows that this leads to the conclusion
                 that the distribution of mantissas must be
                 logarithmic.''",
  reviewer =     "F. J. Murray",
  tableofcontents = "Preface / ix \\
                 1. Floating-Point Number Systems / 1 \\
                 1.1 Fixed-Point Calculation / 1 \\
                 1.2 Floating-Decimal Representation of Numbers / 4 \\
                 1.3 Floating-Decimal Arithmetic / 6 \\
                 1.4 Floating-Point Number Systems / 9 \\
                 1.5 FP(r, p, c) and FP(r, p, R) / 12 \\
                 1.6 Laws of Algebra / 14 \\
                 1.7 Inequalities in FP(r,p, c) / 21 \\
                 1.8 FP(r, p, clq) / 22 \\
                 1.9 The Solution of a * x = b in FP(r,p, c) / 29 \\
                 1.10 Division / 33 \\
                 Exercises / 35 \\
                 2. Floating-Point Overflow and Underflow / 39 \\
                 2.1 Bounds for Exponents / 39 \\
                 2.2 $\Omega$-Zero Fixup / 41 \\
                 2.3 Interrupt / 44 \\
                 2.4 Messages and Tests / 46 \\
                 2.5 ON OVERFLOW and ON UNDERFLOW in PL/I / 49 \\
                 2.6 Example / 50 \\
                 2.7 Counting Mode / 57 \\
                 2.8 Gradual Underflow / 59 \\
                 2.9 Imprecise Interrupt / 61 \\
                 2.10 Changing the Treatment of Spill / 62 \\
                 2.11 Virtual Overflow and Underflow / 64 \\
                 2.12 Division by Zero and Indeterminant Forms / 66 \\
                 Exercises / 67 \\
                 3. Error Analysis / 71 \\
                 3.1 Significant Digits / 71 \\
                 3.2 Relative Error / 73 \\
                 3.3 Relative Error in FP(r,p, clq) / 75 \\
                 3.4 Approximate Laws of Algebra / 80 \\
                 3.5 Propagation of Rounding Error / 87 \\
                 3.6 X**N / 92 \\
                 3.7 Condition / 98 \\
                 3.8 Error Analysis of a Program / 103 \\
                 3.9 Backward Error Analysis / 105 \\
                 3.10 Examples / 107 \\
                 3.11 Changing the Problem / 109 \\
                 3.12 Statistical Error Analysis / 113 \\
                 Exercises / 117 \\
                 4. Example / 123 \\
                 4.1 Quadrature / 123 \\
                 4.2 Power Series / 130 \\
                 4.3 Exact Sums and Differences in FP(r, p, clq) / 137
                 \\
                 4.4 Dismantling Floating-Point Numbers / 143 \\
                 Exercises / 146 \\
                 5. Double-Precision Calculation / 154 \\
                 5.1 Programs Using Double-Precision Arithmetic / 155
                 \\
                 5.2 Implicit Typing of Names / 162 \\
                 5.3 Routines to Perform Double-Precision Arithmetic /
                 163 \\
                 5.4 Double-Precision Multiplication / 165 \\
                 5.5 Double-Precision Addition and Subtraction / 168 \\
                 5.6 Double-Precision Division / 171 \\
                 5.7 Writing Double-Precision Programs Without Language
                 Support / 178 \\
                 5.8 Uses of Double-Precision / 180 \\
                 5.9 Higher-Precision Arithmetic / 185 \\
                 Exercises / 186 \\
                 6. Rounding / 189 \\
                 6.1 General Considerations / 189 \\
                 6.2 Uses of Rounding / 191 \\
                 6.3 Implementation of Rounding / 192 \\
                 6.4 Bias Removal / 194 \\
                 6.5 Other ``Rounding'' Procedures / 197 \\
                 Exercises / 198 \\
                 7. Automatic Analysis of Error / 201 \\
                 7.1 Introduction / 201 \\
                 7.2 Significance Arithmetic / 202 \\
                 7.3 Noisy Mode / 205 \\
                 7.4 Interval Arithmetic / 207 \\
                 7.5 Rerunning the Program in Higher-Precision / 213 \\
                 Exercises / 222 \\
                 8. Radix Conversion / 224 \\
                 8.1 Equivalent Number of Digits / 224 \\
                 8.2 Properties of Conversion Transformations / 228 \\
                 8.3 Conversion Techniques / 232 \\
                 Exercises / 238 \\
                 9/ Carefully Written Programs / 240 \\
                 9.1 Introduction / 240 \\
                 9.2 Average Problem / 240 \\
                 9.3 Quadratic Equation / 246 \\
                 Exercises / 252 \\
                 10. Checking and Testing / 255 \\
                 10.1 Range Checking / 255 \\
                 10.2 Mathematical Checks / 256 \\
                 10.3 Testing / 259 \\
                 Exercises / 261 \\
                 11. Language Features for Floating-Point Computation /
                 263 \\
                 11.1 Introduction / 263 \\
                 11.2 Predictability, Controllability, Observability /
                 264 \\
                 11.3 Ease of Programming / 265 \\
                 11.4 Machine Independence / 267 \\
                 Exercises / 269 \\
                 12. Floating-Point Hardware / 271 \\
                 12.1 Choice of Radix / 271 \\
                 12.2 The Representation of Floating-Point Numbers / 273
                 \\
                 12.3 FP(r, p, c) and FP(r, p, R) / 277 \\
                 12.4 Unnormalized Numbers and Unnormalized Arithmetic /
                 278 \\
                 Exercises / 282 \\
                 13. Complex Numbers / 285 \\
                 13.1 Programs Using Complex Numbers / 285 \\
                 13.2 Relative Error / 286 \\
                 13.3 Complex Arithmetic / 287 \\
                 Exercises / 297 \\
                 Bibliography / 301 \\
                 Glossary of Symbols / 309 \\
                 Index / 311",
}

@Article{Tsao:1974:DSD,
  author =       "Nai Kuan Tsao",
  title =        "On the Distributions of Significant Digits and
                 Roundoff Errors",
  journal =      j-CACM,
  volume =       "17",
  number =       "5",
  pages =        "269--271",
  month =        may,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65G05",
  MRnumber =     "49 6595",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Mon Jan 22 07:26:38 MST 2001",
  bibsource =    "Compendex database;
                 ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm17.html#Tsao74;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Generalized logarithmic law is derived for the
                 distribution of the first $t$ significant digits of a
                 random digital integer. This result is then used to
                 determine the distribution of the roundoff errors in
                 floating-point operations, which is a mixture of
                 uniform and reciprocal distributions.",
  acknowledgement = ack-nhfb,
  classcodes =   "C5230 (Digital arithmetic methods)",
  classification = "921",
  corpsource =   "Aerospace Res. Labs., Wright-Patterson AFB, OH, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  journalabr =   "Commun ACM",
  keywords =     "Benford's Law; digital arithmetic; digital integer;
                 distributions; error analysis; floating point
                 operations; Law of Anomalous Numbers; logarithmic law;
                 mathematical techniques; mean value; random;
                 reciprocal; roundoff errors; significant digits;
                 uniform distribution; variance; Zipf's Law",
  oldlabel =     "Tsao74",
  treatment =    "T Theoretical or Mathematical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Tsao74",
}

@Article{Voos:1974:BCL,
  author =       "Henry Voos",
  title =        "Brief Communications: {Lotka} and information
                 science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "25",
  number =       "4",
  pages =        "270--272",
  month =        jul,
  year =         "1974",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630250410",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:50 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Voos:1974:LIS,
  author =       "Henry Voos",
  title =        "{Lotka} and Information Science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "25",
  number =       "4",
  pages =        "270--272",
  month =        jul # "\slash " # aug,
  year =         "1974",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:14:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Lotka's Law",
}

@Article{Yavuz:1974:ZLE,
  author =       "Davras Yavuz",
  title =        "{Zipf}'s law and entropy",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "20",
  number =       "5",
  pages =        "650--650",
  year =         "1974",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/TIT.1974.1055269",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Nov 12 10:43:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0295.94048",
  acknowledgement = ack-nhfb,
  classmath =    "94A15 (General topics of information theory)",
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@InProceedings{Bennett:1975:SDI,
  author =       "John M. Bennett",
  booktitle =    "Int. Comput. Symp. 1975, Proc., Antibes, (1975)",
  title =        "Storage design for information retrieval: {Scarrott}'s
                 conjecture and {Zipf}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "233--237",
  year =         "1975",
  bibdate =      "Sat Nov 12 10:49:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0322.68068",
  acknowledgement = ack-nhfb,
  classmath =    "68P20 (Information storage and retrieval) 68N01
                 (General)",
}

@Book{Hardy:1975:ITN,
  author =       "Godfrey H. Hardy and Edward M. Wright",
  title =        "An Introduction to the Theory of Numbers",
  publisher =    pub-CLARENDON,
  address =      pub-CLARENDON:adr,
  edition =      "Fourth",
  pages =        "421",
  year =         "1975",
  ISBN =         "0-19-853310-1",
  ISBN-13 =      "978-0-19-853310-8",
  LCCN =         "????",
  bibdate =      "Fri Jun 24 12:32:14 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hill:1975:SFZ,
  author =       "Bruce M. Hill and Michael Woodroofe",
  title =        "Stronger forms of {Zipf}'s law",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "70",
  number =       "349",
  pages =        "212--219",
  month =        mar,
  year =         "1975",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62E15 (62D05)",
  MRnumber =     "0440763 (55 \#13633)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  ZMnumber =     "Zbl 0326.92014",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Kemperman:1975:BDM,
  author =       "J. H. B. Kemperman",
  title =        "Bounds on the discrepancy modulo $1$ of a real random
                 variable",
  journal =      j-BULL-INST-MATH-STAT,
  volume =       "4",
  number =       "1",
  pages =        "138--138",
  month =        "????",
  year =         "1975",
  CODEN =        "SMBCVA",
  ISSN =         "0146-3942",
  ISSN-L =       "0146-3942",
  bibdate =      "Sat Nov 12 16:26:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Abstract no. 75t-47.",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
  keywords =     "Benford's Law",
}

@Article{Kreifelts:1975:OBF,
  author =       "T. Kreifelts",
  title =        "{Optimale Basiswahl f{\"u}r eine Gleitkomma-Arithmetik
                 (Berichtigung)} ({German}) {Optimal Basis Choice for a
                 Floating-Point Arithmetic (Correction)}",
  journal =      j-COMPUTING,
  volume =       "14",
  number =       "3",
  pages =        "313--314",
  month =        sep,
  year =         "1975",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:39 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Kreifelts:1973:OBG}.",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  language =     "German",
}

@Article{Partridge:1975:DDW,
  author =       "D. Partridge",
  title =        "A dynamic database which automatically removes
                 unwanted generalisation for the efficient analysis of
                 language features that exhibit a disparate frequency
                 distribution",
  journal =      j-COMP-J,
  volume =       "18",
  number =       "1",
  pages =        "43--48",
  month =        feb,
  year =         "1975",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/43.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/44.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/45.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/46.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/47.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_18/Issue_01/tiff/48.tif",
  abstract =     "A self-organising database was developed as part of a
                 general language analysis system. The periodic,
                 automatic reorganisation of the database was aimed at
                 increasing the efficiency of analysis of a language in
                 which the constituent features exhibit a Zipfian type
                 rank-frequency relationship. Such a distribution means
                 that only a small number of features account for a
                 large proportion of the information, while a large
                 number of possible features are seldom encountered and
                 thus seldom accessed within the database. The mechanism
                 described aims at reconciling two conflicting
                 procedures: condensation by generalisation of language
                 features to minimise the total size of the database,
                 and the particularisation of the few commonly occurring
                 features to minimise the average analysis time. Results
                 are presented for the application of this mechanism to
                 the analysis of batches of FORTRAN programs that
                 constituted part of the `normal' workload for computers
                 within five different environments.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C7820 (Humanities
                 computing)",
  classification = "723",
  corpsource =   "Univ. Nairobi, Kenya",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "analysis; data bases; data processing; disparate
                 frequency distribution; dynamic database; file
                 organisation; language; language translation and
                 linguistics; self organising; unwanted generalisation",
  treatment =    "P Practical",
}

@Article{Pope:1975:BLP,
  author =       "Andrew Pope",
  title =        "{Bradford's Law} and the periodical literature of
                 information science",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "4",
  pages =        "207--213",
  month =        jul,
  year =         "1975",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630260403",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:54 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Schorr:1975:BCL,
  author =       "Alan Edward Schorr",
  title =        "Brief Communications: {Lotka's Law} and {Map
                 Librarianship}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "3",
  pages =        "189--190",
  month =        may,
  year =         "1975",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630260308",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Schorr:1975:LLH,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and the History of Legal Medicine",
  journal =      "Research in Librarianship",
  volume =       "30",
  number =       "??",
  pages =        "205--209",
  month =        sep,
  year =         "1975",
  CODEN =        "????",
  ISSN =         "0034-5245",
  ISSN-L =       "0034-5245",
  bibdate =      "Fri Nov 25 08:17:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Res. Librarianship",
}

@Article{Schorr:1975:LLM,
  author =       "Alan E. Schorr",
  title =        "{Lotka's Law} and Map Librarianship",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "26",
  number =       "3",
  pages =        "189--190",
  month =        may # "\slash " # jun,
  year =         "1975",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:11:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Webb:1975:DFD,
  author =       "William Webb",
  title =        "Distribution of the First Digits of {Fibonacci}
                 Numbers",
  journal =      j-FIB-QUART,
  volume =       "13",
  number =       "4",
  pages =        "334--336",
  month =        dec,
  year =         "1975",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:03 MDT 2011",
  bibsource =    "http://www.fq.math.ca/13-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/13-4/webb.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
  keywords =     "Benford's Law",
}

@Article{Woodroofe:1975:ZL,
  author =       "Michael Woodroofe and Bruce Hill",
  title =        "On {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "12",
  number =       "3",
  pages =        "425--434",
  month =        sep,
  year =         "1975",
  CODEN =        "JPRBAM",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "62E20 (62P10)",
  MRnumber =     "0440764 (55 \#13634)",
  MRreviewer =   "I. J. Good",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3212857",
  ZMnumber =     "Zbl 0343.60012",
  abstract =     "A Zipf's law is a probability distribution on the
                 positive integers which decays algebraically. Such laws
                 describe (approximately) a large class of phenomena. We
                 formulate a model for such phenomena and, in terms of
                 our model, give necessary and sufficient conditions for
                 a Zipf's law to hold.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "classical occupancy problem; laws of large numbers:
                 weak convergence; regularly varying functions",
}

@Article{Worthen:1975:ABL,
  author =       "Dennis B. Worthen",
  title =        "The Application of {Bradford's Law} to Monographs",
  journal =      j-J-DOC,
  volume =       "31",
  number =       "1",
  pages =        "19--25",
  month =        "????",
  year =         "1975",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026590",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:18:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Allison:1976:LLP,
  author =       "Paul D. Allison and Derek de Solla Price and Belver C.
                 Griffith and Michael J. Moravcsik and John A. Stewart",
  title =        "{Lotka's Law}: a Problem in Its Interpretation and
                 Application",
  journal =      j-SOC-STUD-SCI,
  volume =       "6",
  number =       "2",
  pages =        "269--276",
  day =          "1",
  month =        may,
  year =         "1976",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631277600600205",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:29 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631277600600205",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
  keywords =     "Lotka's Law of scientific authorship for the relative
                 contributions of the most prolific authors",
}

@Article{Billera:1976:PSC,
  author =       "Louis J. Billera and Robert E. Bixby",
  title =        "{Pareto} Surfaces of Complexity $1$",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "30",
  number =       "1",
  pages =        "81--89",
  month =        jan,
  year =         "1976",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  classification = "B0250 (Combinatorial mathematics); C1160
                 (Combinatorial mathematics)",
  corpsource =   "Dept. of Math., Cornell Univ., Ithaca, NY, USA",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  keywords =     "1-commodity representation; attainable sets;
                 complexity 1; game theory; graph theory; Pareto
                 surfaces; set theory",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brambilla:1976:DDA,
  author =       "Francisco Brambilla",
  title =        "La distribuzione delle aziende secondo le dimensioni.
                 {Verifica} empirica della legge logonormale e di quella
                 di {Zipf} e nuovi modelli interpretativi. ({Italian})
                 [{The} distribution of firms by size. {Empirical} test
                 of the log-normal law and {Zipf}'s law and new models
                 of interpretation]",
  journal =      "Giornale degli Economisti e Annali de Economia (Nuova
                 Serie)",
  volume =       "35",
  number =       "3--4",
  pages =        "131--153, 235",
  month =        mar # "\slash " # apr,
  year =         "1976",
  CODEN =        "????",
  ISSN =         "0017-0097",
  ISSN-L =       "0017-0097",
  MRclass =      "90A15",
  MRnumber =     "0452510 (56 \#10789)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/23242834",
  acknowledgement = ack-nhfb,
  ajournal =     "Giorn. Econom. Ann. Econom. (N.S.)",
  fjournal =     "Giornale degli Economisti e Annali de Economia",
  language =     "Italian",
}

@Article{Cohen:1976:EFD,
  author =       "Daniel I. A. Cohen",
  title =        "An explanation of the first digit phenomenon",
  journal =      j-J-COMB-THEORY-A,
  volume =       "20",
  number =       "3",
  pages =        "367--370",
  month =        may,
  year =         "1976",
  CODEN =        "JCBTA7",
  ISSN =         "0097-3165 (print), 1096-0899 (electronic)",
  ISSN-L =       "0097-3165",
  bibdate =      "Thu Feb 15 16:29:51 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Combinatorial Theory (Series A)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00973165",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Davis:1976:SRI,
  author =       "Basil Davis",
  title =        "Some Remarks on Initial Digits",
  journal =      j-FIB-QUART,
  volume =       "14",
  number =       "1",
  pages =        "13--14",
  month =        feb,
  year =         "1976",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:05 MDT 2011",
  bibsource =    "http://www.fq.math.ca/14-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/14-1/davis.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Feldstein:1976:CED,
  author =       "Alan Feldstein and Richard Goodman",
  title =        "Convergence Estimates for the Distribution of Trailing
                 Digits",
  journal =      j-J-ACM,
  volume =       "23",
  number =       "2",
  pages =        "287--297",
  month =        apr,
  year =         "1976",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321941.321948",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Wed Jan 15 18:12:53 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An analysis is made of the distribution of trailing
                 digits (tail end digits) of positive real
                 floating-point numbers represented in arbitrary base $
                 \beta $ and randomly chosen from a logarithmic
                 distribution. The analysis shows that the $n$ th digit
                 for $ n \geq 2 $ is actually approximately uniformly
                 distributed. The approximation depends upon both $n$
                 and the base beta. It becomes better as $n$ increases,
                 and it is exact in the limit as $ n \rightarrow \infty
                 $. A table of this distribution is presented for
                 various $ \beta $ and $n$, along with a table of the
                 maximum digit by digit deviation $ \Delta $ of the
                 logarithmic distribution from the uniform distribution.
                 Various asymptotic results for $ \Delta $ are
                 included.",
  acknowledgement = ack-nhfb,
  classification = "723",
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
  journalabr =   "J Assoc Comput Mach",
  keywords =     "Benford's Law; computer arithmetic; computer
                 programming; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Haspers:1976:YFB,
  author =       "Jan H. Haspers",
  title =        "The yield formula and {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "27",
  number =       "5",
  pages =        "281--287",
  month =        sep,
  year =         "1976",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630270503",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:57 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Hubert:1976:NIB,
  author =       "John J. Hubert",
  title =        "On the {Naranan} interpretation of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "27",
  number =       "5",
  pages =        "339--341",
  month =        sep,
  year =         "1976",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630270510",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:57 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Orlov:1976:CBP,
  author =       "Ju. K. Orlov",
  title =        "The connection between the {Pareto} distribution and
                 the generalized {Zipf--Mandelbrot} law",
  journal =      "Sakharthvelos SSR Mecnierebatha Akademiis Moambe",
  volume =       "83",
  number =       "1",
  pages =        "57--60",
  year =         "1976",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "90A15",
  MRnumber =     "0434355 (55 \#7321)",
  MRreviewer =   "S. Krcevinac",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Sakharth. SSR Mech. Akad. Moambe",
}

@Article{Raimi:1976:FDP,
  author =       "Ralph A. Raimi",
  title =        "The first digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "83",
  number =       "7",
  pages =        "521--538",
  month =        aug # "\slash " # sep,
  year =         "1976",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2319349",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Sat Nov 12 15:49:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2319349",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "This article surveys the literature up to 1976,
                 reports defects in several earlier mathematical
                 `explanations' of Benford's Law, and gives a 52-entry
                 bibliography of prior work. All of those entries are
                 incorporated in this bibliography. It criticizes parts
                 of \cite{Goudsmit:1944:SFN} as `dead wrong' (and the
                 author reiterates that view in \cite{Raimi:1985:FDP}).
                 See also later work \cite{Logan:1978:FDP}. On page 529,
                 Raimi writes ``If the first digits of all the tables in
                 the universe obey some fixed distribution law,
                 Stigler's or Benford's or some other, that law must
                 surely be independent of the system of units chosen,
                 since God is not known to favor either the metric
                 system or the English system. In other words, a
                 universal first digit law, if it exists, must be
                 scale-invariant.''",
  remark-2 =     "This is so far the second earliest reference that I
                 have found to \cite{Newcomb:1881:NFU}; the earliest is
                 \cite{Boring:1920:LNL}, which has only brief mention of
                 the question of digit frequencies. Raimi comments on p.
                 522: ``This assertion, whatever it may mean, will be
                 called Benford's Law because it has been thought by
                 many writers to have originated with the General
                 Electric Company physicist Frank Benford [2]. Certainly
                 Benford popularized the problem, and he may well have
                 been unaware that the polymathic Simon Newcomb,
                 primarily an astronomer but also sometime editor of The
                 American Journal of Mathematics, had also formulated
                 the same law 57 years earlier [1]. There is ample
                 precedent for naming laws and theorems for persons
                 other than their discoverers, else half of analysis
                 would be named after Euler. Besides, even Newcomb
                 implied that the observation giving rise to the Benford
                 law was an old one in his day. One would hate to change
                 the name of the law now only to find later that another
                 change was called for.''",
}

@Article{Rouault:1976:PAE,
  author =       "Alain Rouault",
  title =        "Propri{\'e}t{\'e}s asymptotiques d'un
                 {$n$}-{\'e}chantillon d'une variable al{\'e}atoire
                 d{\'e}nombrable connues sous le nom de lois de {Zipf}.
                 ({French}) [Asymptotic properties of an $n$-sample of a
                 denumerable random variable known under the name of
                 {Zipf}'s law]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "6",
  pages =        "Aiv, A379--A380",
  year =         "1976",
  CODEN =        "CHASAP",
  ISSN =         "0151-0509",
  ISSN-L =       "0151-0509",
  MRclass =      "62E20",
  MRnumber =     "0423644 (54 \#11619)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Rouault:1976:SML,
  author =       "Alain Rouault",
  title =        "Sources markoviennes et lois de {Zipf}. ({French})
                 [{Markovian} source and {Zipf} laws]",
  journal =      j-C-R-ACAD-SCI-PARIS-SER-AB,
  volume =       "283",
  number =       "10",
  pages =        "Aiii, A789--A790",
  year =         "1976",
  CODEN =        "CHASAP",
  ISSN =         "0151-0509",
  ISSN-L =       "0151-0509",
  MRclass =      "62E20",
  MRnumber =     "0423645 (54 \#11620)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Hebdomadaires des S{\'e}ances de
                 l'Acad{\'e}mie des Sciences. S{\'e}ries A et B",
  language =     "French",
}

@Article{Vlachy:1976:TFL,
  author =       "Jan Vlach{\'y}",
  title =        "Time Factor in {Lotka's Law}",
  journal =      "Probleme de Informare si Documentare",
  volume =       "10",
  number =       "2",
  pages =        "44--87",
  month =        "????",
  year =         "1976",
  CODEN =        "PIDCA6",
  ISSN =         "0032-924X",
  ISSN-L =       "0032-924X",
  bibdate =      "Fri Nov 25 07:56:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Prob. inf. \& doc.",
}

@Article{Brookes:1977:TBL,
  author =       "Bertram C. Brookes",
  title =        "Theory of the {Bradford Law}",
  journal =      j-J-DOC,
  volume =       "33",
  number =       "3",
  pages =        "180--209",
  month =        "????",
  year =         "1977",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026641",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:16:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Clark:1977:ESL,
  author =       "Douglas W. Clark and C. Cordell Green",
  title =        "An Empirical Study of List Structure in {Lisp}",
  journal =      j-CACM,
  volume =       "20",
  number =       "2",
  pages =        "78--87",
  month =        feb,
  year =         "1977",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon Jan 22 06:31:28 MST 2001",
  bibsource =    "Compendex database;
                 ftp://ftp.ira.uka.de/pub/bibliography/Compiler/garbage.collection.bib;
                 http://dblp.uni-trier.de/db/journals/cacm/cacm20.html#ClarkG77;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Static measurements of the list structure of five
                 large Lisp programs are reported and analyzed. These
                 measurements reveal substantial regularity, or
                 predictability, among pointers to atoms and especially
                 among pointers to lists. Pointers to atoms are found to
                 obey, roughly, Zipf's law, which governs word
                 frequencies in natural languages; pointers to lists
                 usually point to a location physically nearby in
                 memory. The use of such regularities in the
                 space-efficient representation of list structure is
                 discussed.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6130 (Data handling techniques); C6140D (High level
                 languages)",
  classification = "723",
  comment =      "Great paper; evidence pro CDR-coding, con fancy CONS",
  corpsource =   "Carnegie-Mellon Univ., Pittsburgh, PA, USA",
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  journalabr =   "Commun ACM",
  keywords =     "computer programming languages; data processing ---
                 Data Structures; empirical study; LISP; list structure;
                 measurements; regularity",
  oldlabel =     "ClarkG77",
  treatment =    "P Practical",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/ClarkG77",
}

@Article{Coile:1977:LFD,
  author =       "Russell C. Coile",
  title =        "{Lotka}'s Frequency Distribution of Scientific
                 Productivity",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "6",
  pages =        "366--370",
  month =        nov,
  year =         "1977",
  CODEN =        "AISJB6",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 08:08:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Lotka's Law",
}

@Article{Diaconis:1977:DLD,
  author =       "Persi Diaconis",
  title =        "The distribution of leading digits and uniform
                 distribution $ \bmod 1 $",
  journal =      j-ANN-PROBAB,
  volume =       "5",
  number =       "1",
  pages =        "72--81",
  month =        feb,
  year =         "1977",
  CODEN =        "APBYAE",
  DOI =          "https://doi.org/10.1214/aop/1176995891",
  ISSN =         "0091-1798 (print), 2168-894X (electronic)",
  ISSN-L =       "0091-1798",
  bibdate =      "Sun Apr 20 10:44:17 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annprobab1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.aop/1176995891",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aop",
  keywords =     "Benford's Law",
}

@Article{Goudsmit:1977:PEP,
  author =       "Samuel Goudsmit",
  title =        "Pitfalls in Elementary Probability",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "121",
  number =       "2",
  pages =        "188--189",
  day =          "29",
  month =        apr,
  year =         "1977",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 22 08:50:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Based on a lecture presented November 11, 1976.",
  URL =          "http://www.jstor.org/stable/986527",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  keywords =     "Benford's Law; biased coin flips; biased dice throws;
                 roulette wheels",
}

@Article{Hubert:1977:LEL,
  author =       "John J. Hubert",
  title =        "Letters to the {Editor}: {Lotka's Law} in the
                 humanities",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "1",
  pages =        "66--66",
  month =        jan,
  year =         "1977",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630280115",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Krisciunas:1977:LEL,
  author =       "Kevin Krisciunas",
  title =        "Letters to the {Editor}: {Lotka's Law} --- year by
                 year",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "28",
  number =       "1",
  pages =        "65--66",
  month =        jan,
  year =         "1977",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630280114",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Kubovy:1977:RAA,
  author =       "M. Kubovy",
  title =        "Response Availability and the Apparent Spontaneity of
                 Numerical Choices",
  journal =      "Journal of Experimental Psychology: Human Performance
                 and Performance",
  volume =       "3",
  number =       "2",
  pages =        "359--364",
  month =        may,
  year =         "1977",
  DOI =          "https://doi.org/10.1037/0096-1523.3.2.359",
  ISSN =         "0096-1523 (print), 1939-1277 (electronic)",
  ISSN-L =       "0096-1523",
  bibdate =      "Sat Sep 10 12:51:40 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://psycnet.apa.org/index.cfm?fa=search.displayrecord&uid=1977-30946-001",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Ylvisaker:1977:TR,
  author =       "Donald Ylvisaker",
  title =        "Test Resistance",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "72",
  number =       "359",
  pages =        "551--556",
  month =        sep,
  year =         "1977",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Jan 25 08:05:48 MST 2012",
  bibsource =    "http://www.jstor.org/journals/01621459.html;
                 http://www.jstor.org/stable/i314242;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc1970.bib",
  URL =          "http://www.jstor.org/stable/2286216",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Brady:1978:MBL,
  author =       "W. G. Brady",
  title =        "More on {Benford}'s Law",
  journal =      j-FIB-QUART,
  volume =       "16",
  number =       "1",
  pages =        "51--52",
  month =        feb,
  year =         "1978",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 17:59:24 MDT 2011",
  bibsource =    "http://www.fq.math.ca/16-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/16-1/brady.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Brookes:1978:FRD,
  author =       "Bertram C. Brookes and Jos{\'e} M. Griffiths",
  title =        "Frequency-rank distributions",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "1",
  pages =        "5--13",
  month =        jan,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290104",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 10:40:13 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.4630290104/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@PhdThesis{Chen:1978:ZL,
  author =       "Wen-Chen Chen",
  title =        "On {Zipf}'s law",
  type =         "Thesis ({Ph.D.})",
  school =       "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  pages =        "114",
  year =         "1978",
  MRclass =      "Thesis",
  MRnumber =     "2627928",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:7822871",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.
                 Author given name appears as Wen-Cheng in MathSciNet
                 database.",
}

@Article{Drott:1978:EEB,
  author =       "M. Carl Drott and Belver C. Griffith",
  title =        "An empirical examination of {Bradford's Law} and the
                 scattering of scientific literature",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "5",
  pages =        "238--246",
  month =        sep,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290506",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Elshoff:1978:SSC,
  author =       "James L. Elshoff",
  title =        "A study of the structural composition of {PL/I}
                 programs",
  journal =      j-SIGPLAN,
  volume =       "13",
  number =       "6",
  pages =        "29--37",
  month =        jun,
  year =         "1978",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/987515.987518",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Wed Jun 18 16:08:52 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Some research on a theory of the structural
                 composition of an algorithm has recently been reported.
                 The theory embodies models of operator and operand
                 distributions that have been proposed by Bayer, Zipf,
                 and Zweben. This paper reports a study in which the
                 three models of operator distributions are compared
                 with the measured distributions found in 34 PL/I
                 programs. Two of three models, one by Zipf and one by
                 Zweben, are shown to correlate highly with the measured
                 distributions. Two variations of the Zipf model are
                 then formulated and tested with good results. Also, the
                 relationship between the method of counting operators
                 and the models is investigated.",
  acknowledgement = ack-nhfb,
  classification = "C4240 (Programming and algorithm theory); C6140D
                 (High level languages)",
  corpsource =   "Computer Sci. Dept., General Motors Res. Labs.,
                 Warren, MI, USA",
  fjournal =     "ACM SIG{\-}PLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  keywords =     "counting operators; operator distributions; PL/1; PL/1
                 programs; programming theory; structural composition",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Heaps:1978:IRC,
  author =       "Harold Stanley Heaps",
  title =        "Information retrieval, computational and theoretical
                 aspects",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xii + 344",
  year =         "1978",
  ISBN =         "0-12-335750-0",
  ISBN-13 =      "978-0-12-335750-2",
  LCCN =         "Z699 .H38",
  bibdate =      "Sat Nov 12 11:36:39 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Library and information science",
  acknowledgement = ack-nhfb,
  remark =       "Heaps's Law is given on pp. 206--208.",
  subject =      "Information storage and retrieval systems",
}

@Article{Hubert:1978:BCR,
  author =       "John J. Hubert",
  title =        "Brief Communications: A relationship between two forms
                 of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "3",
  pages =        "159--161",
  month =        may,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290311",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "23 Mar 2007",
}

@Article{Logan:1978:FDP,
  author =       "Jonothan L. Logan and Samuel A. Goudsmit",
  title =        "The First Digit Phenomenon",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "122",
  number =       "4",
  pages =        "193--197",
  day =          "18",
  month =        aug,
  year =         "1978",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Fri Mar 30 11:20:35 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains derivations of both Stigler's Law
                 and Benford's Law, and receives strong criticism in
                 \cite{Raimi:1985:FDP}. This paper contains an important
                 historical note that is recorded in entry
                 \cite{Benford:1938:LAN}.",
  URL =          "http://links.jstor.org/sici?sici=0003-049X(19780818)122%3A4%3C193%3ATFDP%3E2.0.CO%3B2-C;
                 http://www.jstor.org/stable/986530",
  abstract =     "Forty years ago an article appeared in these
                 Proceedings, which has since then attracted much
                 attention of mathematicians and some physicists. It was
                 written by Frank Benford, a physicist from the General
                 Electric Company at Schenectady. He had examined a
                 large number of numerical tables, the kind that are
                 printed in almanacs, and in scientific and technical
                 handbooks. He noticed a most unusual and unexpected
                 property of many of these tables. Consider, for
                 example, the numbers representing the populations of
                 states or all the countries in the world, or their
                 areas, their budgets, their numbers of hospital beds,
                 etc. One would expect that on the average just as many
                 of these entries would begin with the digit $1$ as with
                 $2$ or $3$ or $4$, and so on. But Benford noticed that
                 small values of the first digits occur far more
                 often.",
  acknowledgement = ack-nhfb,
  author-dates = "Samuel A. Goudsmit (July 11, 1902--December 4, 1978)",
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "In 1925, Samuel Goudsmit and George Uhlenbeck proposed
                 the concept of electron spin, a critical step forward
                 in the quantum mechanics of many-electron systems.
                 Surprisingly, that work did not get them the Nobel
                 Prize, but it did spur Wolfgang Pauli to present his
                 Exclusion Principle in 1925, for which he received the
                 1945 Nobel Prize in Physics. After World War II,
                 Goudsmit was the scientific head of the Alsos mission
                 to capture German nuclear scientists. In the 1950s, he
                 founded the journal Physical Review Letters. During the
                 1960s and 1970s, he was Editor-in-Chief of the main
                 American physics journal, the Physical Review.",
}

@Article{Praunlich:1978:BDN,
  author =       "Peter Praunlich and Michael Kroll",
  title =        "{Bradford}'s distribution: a new formulation",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "29",
  number =       "2",
  pages =        "51--55",
  month =        mar,
  year =         "1978",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630290203",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Rouault:1978:LZS,
  author =       "Alain Rouault",
  title =        "Lois de {Zipf} et sources markoviennes. ({French})
                 [{Zipf}'s law and {Markovian} sources]",
  journal =      "Ann. Inst. H. Poincar{\'e} Sect. B (N.S.)",
  volume =       "14",
  number =       "2",
  pages =        "169--188",
  year =         "1978",
  CODEN =        "AHPBAR",
  ISSN =         "0020-2347",
  ISSN-L =       "0020-2347",
  MRclass =      "62E99 (60J20 62P99)",
  MRnumber =     "507732 (80c:62026a)",
  MRreviewer =   "Bruce M. Hill",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de l'Institut Henri Poincar{\'e}. Section B.
                 Calcul des Probabilit{\'e}s et Statistique. Nouvelle
                 S{\'e}rie",
  language =     "French",
}

@Article{Samson:1978:STU,
  author =       "W. B. Samson and R. H. Davis",
  title =        "Search Times Using Hash Tables for Records with
                 Non-Unique Keys",
  journal =      j-COMP-J,
  volume =       "21",
  number =       "3",
  pages =        "210--214",
  month =        aug,
  year =         "1978",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/210.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/211.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/212.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/213.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_21/Issue_03/tiff/214.tif",
  abstract =     "Recent research in hash coding has concentrated on
                 unique keys, or uniform distributions of keys. This
                 paper is intended to clarify the effect of non-unique
                 keys with various distributions on search times in the
                 hash table thus enabling recommendations to be made to
                 those who must deal with hash tables of this type. It
                 is found that extreme rank-order frequency distribution
                 of keys, such as the Zipf distribution, result in much
                 higher access times than more uniform distributions,
                 but it is possible to reduce these to some extent by
                 loading records with common keys on to the hash table
                 first.",
  acknowledgement = ack-nhfb,
  classcodes =   "C6120 (File organisation); C6130 (Data handling
                 techniques)",
  classification = "723",
  corpsource =   "Dept. of Math. and Computer Studies, Dundee Coll. of
                 Technol., Dundee, UK",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  journalabr =   "Comput J",
  keywords =     "common keys; compiler symbol; computer programming;
                 data handling; data processing --- Data Structures;
                 direct access files; distribution; extreme; file
                 organisation; hash tables; higher access times; non
                 unique keys; overflow method; rank order frequency
                 distribution of keys; records; search times;
                 simulation; tables; uniform distributions; Zipf",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Brookes:1979:LEB,
  author =       "B. C. Brookes",
  title =        "Letters to the {Editor}: The {Bradford Law}: a new
                 calculus for the social sciences?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "4",
  pages =        "233--234",
  month =        jul,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300412",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:05 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Diaconis:1979:RP,
  author =       "Persi Diaconis and David Freedman",
  title =        "On Rounding Percentages",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "74",
  number =       "366",
  pages =        "359--364",
  month =        jun,
  year =         "1979",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Nov 23 11:24:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bethe-hans.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  note =         "The authors extend prior work on correctness of sums
                 of rounded percentages \cite{Mosteller:1967:DSR}, and
                 criticize biased rounding practices in
                 \cite{Benford:1938:LAN}.",
  URL =          "http://www.jstor.org/stable/2284288",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  keywords =     "Benford's Law",
  remark =       "When percentage-column entries are rounded, their sum
                 may differ from 100\%. The authors use a prior proof
                 \cite{Mosteller:1967:DSR} that for $ n \gg 2 $ rounded
                 values, the probability of a correct sum is $ \sqrt {6
                 / (\pi n)} \approx 1.382 / \sqrt {n} $. They show that
                 rounding may produce large changes in computed
                 chi-squared values, and they conclude their article
                 with this recommendation: ``it is important to
                 calculate with many-digit accuracy when computing $
                 \chi^2 $ for large sample sizes.''",
}

@Article{Marulli:1979:BCB,
  author =       "Luciana Marulli and Michael E. D. Koenig",
  title =        "Brief Communications: {Bradford} distribution of data
                 elements",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "2",
  pages =        "107--108",
  month =        mar,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300209",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Mohanty:1979:MMQ,
  author =       "Siba N. Mohanty",
  title =        "Models and Measurements for Quality Assessment of
                 Software",
  journal =      j-COMP-SURV,
  volume =       "11",
  number =       "3",
  pages =        "251--275",
  month =        sep,
  year =         "1979",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356778.356783",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:25:12 MDT 2008",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD/1979.bib;
                 http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See also \cite{Dunn:1980:SFW,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  annote =       "Several software quality assessment methods which span
                 the software life cycle are discussed. The quality of a
                 system design can be estimated by measuring the system
                 entropy function or the system work function. The
                 quality improvement due to reconfiguration can be
                 determined by calculating system entropy loading
                 measures. Software science and Zipf's law are shown to
                 be useful for estimating program length and
                 implementation time.",
  country =      "USA",
  date =         "11/10/79",
  descriptors =  "Software; design; software engineering; reliability;
                 measurement; model; fundamentals in statistics;
                 performance evaluation",
  enum =         "2189",
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
  references =   "65",
}

@Article{Radhakrishnan:1979:LLC,
  author =       "T. Radhakrishnan and R. Kernizan",
  title =        "{Lotka's Law} and Computer Science Literature",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "30",
  number =       "1",
  pages =        "51--54",
  month =        jan,
  year =         "1979",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630300109",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Nov 25 07:45:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "6 September 2007",
  remark =       "This paper analyzes publication statistics from
                 Communications of the Association for Computing
                 Machinery (CACM) and in the Journal of the ACM
                 (JACM).",
}

@Article{Vlachy:1979:FDS,
  author =       "Jan Vlach{\'y}",
  title =        "Frequency Distribution of Scientific Performance: a
                 Bibliography of {Lotka's Law} and Related Phenomena",
  journal =      j-SCIENTOMETRICS,
  volume =       "1",
  number =       "1",
  pages =        "107--130",
  month =        sep,
  year =         "1979",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016844",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Fri Nov 25 07:59:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016844;
                 http://www.springerlink.com/content/0138-9130/",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
  xxjournal =    "Scientometrics, Bibliography Section",
}

@Article{Brookes:1980:FISa,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part I}.
                 {Philosophical} aspects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "3--4",
  pages =        "125--133",
  month =        jun,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "https://doi.org/10.1177/016555158000200302",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/3-4/125.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1980:FISb,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part II}.
                 {Quantitative} aspects: classes of things and the
                 challenge of human individuality",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "5",
  pages =        "209--221",
  month =        oct,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "https://doi.org/10.1177/016555158000200502",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 11:01:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/5/209.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Brookes:1980:FISc,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part III}.
                 {Quantitative} aspects: Objective maps and subjective
                 landscapes",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "2",
  number =       "6",
  pages =        "269--275",
  month =        dec,
  year =         "1980",
  CODEN =        "JISCDI",
  DOI =          "https://doi.org/10.1177/016555158000200602",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/2/6/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Chen:1980:WFZ,
  author =       "Wen Chen Chen",
  title =        "On the weak form of {Zipf}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "17",
  number =       "3",
  pages =        "611--622",
  year =         "1980",
  CODEN =        "JPRBAM",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "62E10 (62F10)",
  MRnumber =     "580021 (81m:62021)",
  MRreviewer =   "Patrick L. Brockett",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3212955",
  ZMnumber =     "Zbl 0435.60017",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
}

@Article{Dunn:1980:SFW,
  author =       "Stanley Dunn",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "255--255",
  month =        jun,
  year =         "1980",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356810.356817",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Mohanty:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Leimkuhler:1980:EFB,
  author =       "Ferdinand F. Leimkuhler",
  title =        "An Exact Formulation of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "36",
  number =       "4",
  pages =        "285--292",
  month =        "????",
  year =         "1980",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026699",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:14:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "An exact, discrete formulation of Bradford's law
                 describing the distribution of articles in journals is
                 derived by showing that Bradford's law is a special
                 case of the Zipf--Mandelbrot `rank frequency' law. A
                 relatively simple method is presented for fitting the
                 model to empirical data and estimating the number of
                 journals and articles in a subject collection. This
                 method is demonstrated with an example application.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{McKee:1980:POR,
  author =       "Arnold F. McKee",
  title =        "The {Pareto} Optimum: Reconcilable with Social
                 Thought?",
  journal =      "International Journal of Social Economics",
  volume =       "7",
  number =       "7",
  pages =        "366--375",
  month =        "????",
  year =         "1980",
  CODEN =        "ISLEBC",
  DOI =          "https://doi.org/10.1108/eb013878",
  ISSN =         "0306-8293 (print), 1758-6712 (electronic)",
  ISSN-L =       "0306-8293",
  bibdate =      "Fri Nov 25 07:01:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mohanty:1980:SFW,
  author =       "Siba Mohanty",
  title =        "Surveyor's Forum: {Working} on Interpretations",
  journal =      j-COMP-SURV,
  volume =       "12",
  number =       "2",
  pages =        "256--256",
  month =        jun,
  year =         "1980",
  CODEN =        "CMSVAN",
  DOI =          "https://doi.org/10.1145/356810.356818",
  ISSN =         "0010-4892",
  ISSN-L =       "0360-0300",
  bibdate =      "Thu Jun 19 09:27:10 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/surveys/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mohanty:1979:MMQ,Dunn:1980:SFW}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Computing Surveys",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J204",
}

@Article{Asai:1981:GFB,
  author =       "Isao Asai",
  title =        "A general formulation of {Bradford}'s distribution:
                 the graph-oriented approach",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "32",
  number =       "2",
  pages =        "113--119",
  month =        mar,
  year =         "1981",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630320206",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:10 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Brookes:1981:FIS,
  author =       "Bertram C. Brookes",
  title =        "The foundations of information science. {Part IV}.
                 {Information} science: the changing paradigm",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "3",
  number =       "1",
  pages =        "3--12",
  month =        feb,
  year =         "1981",
  CODEN =        "JISCDI",
  DOI =          "https://doi.org/10.1177/016555158100300102",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Mon Feb 25 10:36:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jis.sagepub.com/content/3/1/3",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  journal-URL =  "http://jis.sagepub.com/",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Book{Fleiss:1981:SMR,
  author =       "Joseph L. Fleiss",
  title =        "Statistical Methods for Rates and Proportions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xviii + 321",
  year =         "1981",
  ISBN =         "0-471-06428-9",
  ISBN-13 =      "978-0-471-06428-2",
  LCCN =         "QA279 .F58 1981",
  bibdate =      "Fri Mar 22 08:46:57 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and mathematical
                 statistics",
  URL =          "http://www.loc.gov/catdir/description/wiley032/80026382.html;
                 http://www.loc.gov/catdir/enhancements/fy0607/80026382-b.html;
                 http://www.loc.gov/catdir/toc/onix02/80026382.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Analysis of variance; Sampling (Statistics);
                 Biometry",
}

@Article{Kennard:1981:MDF,
  author =       "Robert W. Kennard and John E. Reith",
  title =        "{M32}. {On} the distribution of first digits",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "10",
  number =       "1",
  pages =        "97--98",
  year =         "1981",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610918108812195",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:15 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/03610918108812195",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law",
  onlinedate =   "27 Jun 2007",
}

@Article{Morse:1981:IEB,
  author =       "Philip M. Morse",
  title =        "Implications of the exact {Bradford} distribution",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "32",
  number =       "1",
  pages =        "43--50",
  month =        jan,
  year =         "1981",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630320106",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:10 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "22 Mar 2007",
}

@Article{Pavlov:1981:DFF,
  author =       "A. I. Pavlov",
  title =        "On the distribution of fractions and {F. Benford}'s
                 law",
  journal =      j-IZV-AKAD-NAUK-SSSR-MAT,
  volume =       "45",
  number =       "4",
  pages =        "760--774, 927",
  year =         "1981",
  CODEN =        "IZAMAT",
  ISSN =         "0373-2436",
  ISSN-L =       "0373-2436",
  MRclass =      "10K10",
  MRnumber =     "631437 (83m:10093)",
  MRreviewer =   "Michael Keane",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Izvestiia Akademii Nauk. USSR Seriia Matematicheskaia
                 (Moscow)",
  xxtitle =      "On the distribution mod one and {Benford}'s law",
}

@Article{Peters:1981:EFB,
  author =       "James V. Peters",
  title =        "An Equivalent Form of {Benford's Law}",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "1",
  pages =        "74--76",
  month =        feb,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "60C05 (10K10 60-01)",
  MRnumber =     "606117 (82k:60024)",
  MRreviewer =   "L. E. Clarke",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-1/peters.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Peters:1981:SCC,
  author =       "James V. Peters",
  title =        "Short Communications: a combinatoric proof of
                 {Benford}'s law",
  journal =      j-AEQUATIONES-MATHEMATICAE,
  volume =       "23",
  number =       "1",
  pages =        "122--123",
  year =         "1981",
  CODEN =        "AEMABN",
  DOI =          "https://doi.org/10.1007/BF02188018",
  ISSN =         "0001-9054 (print), 1420-8903 (electronic)",
  ISSN-L =       "0001-9054",
  MRclass =      "Contributed Item",
  MRnumber =     "1553878",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/BF02188018",
  acknowledgement = ack-nhfb,
  fjournal =     "Aequationes Mathematicae",
  journal-URL =  "http://link.springer.com/journal/10",
}

@Article{Potter:1981:LLR,
  author =       "William Gray Potter",
  title =        "{Lotka's Law} revisited",
  journal =      j-LIBR-TRENDS,
  volume =       "31",
  number =       "2",
  pages =        "21--39",
  month =        "Summer",
  year =         "1981",
  CODEN =        "LIBTA3",
  ISSN =         "0024-2594 (print), 1559-0682 (electronic)",
  ISSN-L =       "0024-2594",
  bibdate =      "Thu Nov 24 14:41:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.172.9842",
  acknowledgement = ack-nhfb,
  fjournal =     "Library Trends",
}

@Article{Preece:1981:DFD,
  author =       "D. A. Preece",
  title =        "Distributions of Final Digits in Data",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "30",
  number =       "1",
  pages =        "31--60",
  month =        mar,
  year =         "1981",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Wed Nov 23 12:19:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2987702",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
  remark =       "This paper extends previous work \cite{Yule:1927:RS}
                 on human bias in the recording of last digits in
                 measurements, or from roundings, or from later scale
                 conversions, and how such bias can be detected.",
}

@Article{Schatte:1981:RVL,
  author =       "Peter Schatte",
  title =        "On random variables with logarithmic mantissa
                 distribution relative to several bases",
  journal =      j-ELEK-INFO-KYBER,
  volume =       "17",
  number =       "??",
  pages =        "293--295",
  month =        "????",
  year =         "1981",
  CODEN =        "EIVKAX",
  ISSN =         "0013-5712",
  ISSN-L =       "0013-5712",
  bibdate =      "Sat Nov 12 15:53:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elektronische Informationsverarbeitung und Kybernetik
                 (EIK)",
}

@Article{Washington:1981:BLF,
  author =       "Lawrence C. Washington",
  title =        "{Benford's Law} for {Fibonacci} and {Lucas} Numbers",
  journal =      j-FIB-QUART,
  volume =       "19",
  number =       "2",
  pages =        "175--177",
  month =        apr,
  year =         "1981",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "10A30 (10A35)",
  MRnumber =     "614056 (82f:10009)",
  MRreviewer =   "S. P. Mohanty",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/19-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/19-2/washington.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Fedorowicz:1982:TFZ,
  author =       "Jane Fedorowicz",
  title =        "The Theoretical Foundation of {Zipf's Law} and Its
                 Application to the Bibliographic Database Environment",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "33",
  number =       "5",
  pages =        "285--293",
  year =         "1982",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630330507",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Fedorowicz:1982:ZMA,
  author =       "Jane Fedorowicz",
  title =        "A {Zipfian} Model of an Automatic Bibliographic
                 System: An Application to {MEDLINE}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "33",
  number =       "4",
  pages =        "223--232",
  month =        jul,
  year =         "1982",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630330406",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:14 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "6 Sep 2007",
}

@Article{Lefort:1982:LOA,
  author =       "B. Lefort",
  title =        "{L}'Emploi des Outils au Cours de Taches d'Entretien
                 et la Loi de {Zipf--Mandelbrot}. ({French}) [The Use of
                 Tools in Maintenance Tasks and the {Zipf--Mandelbrot
                 Law}]",
  journal =      j-TRAV-HUM,
  volume =       "45",
  number =       "2",
  pages =        "307--316",
  month =        "????",
  year =         "1982",
  CODEN =        "TRHUAH",
  ISSN =         "0041-1868 (print), 2104-3663 (electronic)",
  ISSN-L =       "0041-1868",
  bibdate =      "Mon Sep 10 07:17:32 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/40657805",
  acknowledgement = ack-nhfb,
  fjournal =     "Le Travail Humain",
  language =     "French",
}

@Article{MacRoberts:1982:REL,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "A Re-evaluation of {Lotka}'s {Law of Scientific
                 Productivity}",
  journal =      j-SOC-STUD-SCI,
  volume =       "12",
  number =       "3",
  pages =        "443--450",
  day =          "1",
  month =        aug,
  year =         "1982",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631282012003005",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:38 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631282012003005",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
  keywords =     "Lotka's Law of scientific authorship for the relative
                 contributions of the most prolific authors",
}

@Article{Pavlov:1982:DFP,
  author =       "A. I. Pavlov",
  title =        "On the Distribution of Fractional Parts and {Benford's
                 Law}",
  journal =      j-MATH-USSR-IZV,
  volume =       "19",
  number =       "1",
  pages =        "65--77",
  month =        "????",
  year =         "1982",
  CODEN =        "MUSIAE",
  DOI =          "https://doi.org/10.1070/IM1982v019n01ABEH001411",
  ISSN =         "0025-5726 (print), 2169-5075 (electronic)",
  ISSN-L =       "0025-5726",
  bibdate =      "Sun Nov 13 10:46:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://stacks.iop.org/0025-5726/19/i=1/a=A05",
  abstract =     "This article investigates the distribution of the
                 first digits (from the left) in the $q$-nary expansions
                 of numerical sequences and functions ($q$ an integer $
                 \geq 2 $ )",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of the {USSR} --- Izvestiya",
  journal-URL =  "http://iopscience.iop.org/0025-5726",
}

@PhdThesis{Perline:1982:EVM,
  author =       "Richard K. Perline",
  title =        "An extreme value model of weakly harmonic
                 ({Pareto--Zipf} type) laws",
  type =         "Thesis ({Ph.D.})",
  school =       "Department of Behavioral Sciences, The University of
                 Chicago",
  address =      "Chicago, IL, USA",
  pages =        "129",
  month =        dec,
  year =         "1982",
  MRnumber =     "2611828",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/251796701",
  acknowledgement = ack-nhfb,
  remark =       "Available from ProQuest LLC, Ann Arbor, MI, USA.",
}

@Article{Regazzini:1982:BFL,
  author =       "Eugenio Regazzini",
  title =        "The {Benford--Furlan} law as a statistical law",
  journal =      j-STATISTICA-BOLOGNA,
  volume =       "42",
  number =       "3",
  pages =        "351--370",
  year =         "1982",
  CODEN =        "STATDJ",
  ISSN =         "0390-590X (print), 1973-2201 (electronic)",
  ISSN-L =       "0390-590X",
  MRclass =      "62E99 (10K05 62A15)",
  MRnumber =     "695467 (84h:62032)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistica (Bologna)",
}

@Article{Turner:1982:DLS,
  author =       "Peter R. Turner",
  title =        "The distribution of leading significant digits",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "2",
  number =       "4",
  pages =        "407--412",
  month =        oct,
  year =         "1982",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/2.4.407",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G99 (60E05)",
  MRnumber =     "84f:65038",
  MRreviewer =   "Seppo Linnainmaa",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Book{Weaver:1982:LLT,
  author =       "Warren Weaver",
  title =        "{Lady Luck}: the theory of probability",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "392",
  year =         "1982",
  ISBN =         "0-486-24342-7",
  ISBN-13 =      "978-0-486-24342-9",
  LCCN =         "QA273 .W4 1982",
  bibdate =      "Mon Nov 14 11:35:17 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/description/dover031/82007396.html",
  acknowledgement = ack-nhfb,
  author-dates = "1894--1978",
  remark =       "Reprint of \cite{Weaver:1963:LLT}.",
  subject =      "Probabilities",
}

@Article{White:1982:FSS,
  author =       "Warren H. White",
  title =        "On the form of steady-state solutions to the
                 coagulation equations",
  journal =      j-J-COLLOID-INTERFACE-SCI,
  volume =       "87",
  number =       "1",
  pages =        "204--208",
  month =        may,
  year =         "1982",
  CODEN =        "JCISA5",
  DOI =          "https://doi.org/10.1016/0021-9797(82)90382-4",
  ISSN =         "0021-9797 (print), 1095-7103 (electronic)",
  ISSN-L =       "0021-9797",
  bibdate =      "Thu Feb 28 10:46:13 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0021979782903824",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Colloid and Interface Science",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Iyengar:1983:SPL,
  author =       "S. Sitharama Iyengar and A. K. Rajagopal and V. R. R.
                 Uppuluri",
  title =        "String patterns of leading digits",
  journal =      j-APPL-MATH-COMP,
  volume =       "12",
  number =       "4",
  pages =        "321--337",
  month =        jul,
  year =         "1983",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(83)90045-0",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Feb 16 18:02:26 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300383900450",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Montroll:1983:NOD,
  author =       "Elliott W. Montroll and Michael F. Shlesinger",
  title =        "On $ 1 / f $ noise and other distributions with long
                 tails",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "79",
  number =       "10",
  pages =        "3380--3383",
  day =          "15",
  month =        may,
  year =         "1983",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.79.10.3380",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Thu Feb 28 11:03:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.pnas.org/content/79/10/3380.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Orlov:1983:SSZ,
  author =       "Yu. K. Orlov and R. Ya. Chitashvili",
  title =        "The statistical significance of {Zipf}'s
                 distribution",
  journal =      "Soobshch. Akad. Nauk Gruzin. SSR",
  volume =       "109",
  number =       "3",
  pages =        "505--508",
  year =         "1983",
  CODEN =        "????",
  ISSN =         "0132-1447",
  ISSN-L =       "0132-1447",
  MRclass =      "62E99 (62P99)",
  MRnumber =     "723296",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soobshcheniya Akademii Nauk Gruzinsko{\u\i} SSR",
}

@Article{Schatte:1983:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $ \bmod 1 $",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "257--281",
  month =        "????",
  year =         "1983",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19841150121",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Feb 16 19:12:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Schatte:1983:SUD,
  author =       "Peter Schatte",
  title =        "On {$ H_\infty $}-summability and the uniform
                 distribution of sequences",
  journal =      j-MATH-NACHR,
  volume =       "113",
  number =       "1",
  pages =        "237--243",
  month =        "????",
  year =         "1983",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19831130122",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Feb 16 19:13:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19831130122/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Whittaker:1983:SID,
  author =       "James V. Whittaker",
  title =        "On Scale-Invariant Distributions",
  journal =      j-SIAM-J-APPL-MATH,
  volume =       "43",
  number =       "2",
  pages =        "257--267",
  month =        apr,
  year =         "1983",
  CODEN =        "SMJMAP",
  ISSN =         "0036-1399 (print), 1095-712X (electronic)",
  ISSN-L =       "0036-1399",
  MRclass =      "60E05 (10K10 62E10)",
  MRnumber =     "84h:60035",
  MRreviewer =   "K. C. Chanda",
  bibdate =      "Thu Oct 15 18:16:06 MDT 1998",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjapplmath.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of British Columbia, Dep of Mathematics,
                 Vancouver, BC, Can",
  classification = "922",
  fjournal =     "SIAM Journal on Applied Mathematics",
  journal-URL =  "http://epubs.siam.org/siap",
  journalabr =   "SIAM J Appl Math",
  keywords =     "probability",
}

@Article{Bennett:1984:ZLS,
  author =       "J. M. Bennett",
  title =        "{Zipf's Law}, Structured Programming and Creativity",
  journal =      j-AUSTRALIAN-COMP-J,
  volume =       "16",
  number =       "4",
  pages =        "122--129",
  year =         "1984",
  CODEN =        "ACMJB2",
  ISSN =         "0004-8917",
  ISSN-L =       "0004-8917",
  bibdate =      "Fri Mar 9 17:59:26 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "As software projects increase in size, the effort
                 required to implement them increases at a greater rate.
                 The use of higher level languages and adherence to
                 various rules of ``good programming practice'' appear
                 to help only marginally in reducing the impact of this
                 non-linear effect, and progress can only be made by
                 calling on techniques for managing complexity which
                 have emerged in other fields. Hierarchical structures
                 are discussed with particular reference to software as
                 is the effect which appears to be common to a wide
                 range of human activities, and which is known as Zipf's
                 law. The effects of variation in individual programming
                 skills, the roles of creativity, invention and
                 innovation and lessons to be learned from case studies
                 of past failure are also examined.",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Computer Journal",
  keywords =     "creativity; innovation; invention; large software
                 projects; project failures; structured programming;
                 Zipf's law",
}

@Article{Boroda:1984:ZML,
  author =       "M. G. Boroda and A. A. Polikarpov",
  title =        "The {Zipf--Mandelbrot} law and units of different
                 levels of text organization",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "689",
  pages =        "35--60",
  year =         "1984",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "92A25",
  MRnumber =     "781731 (86c:92030)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
                 Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
                 et Commentationes Universitatis Tartuensis",
}

@Article{Brookes:1984:RTE,
  author =       "Bertram C. Brookes",
  title =        "Ranking techniques and the empirical log law",
  journal =      j-INFO-PROC-MAN,
  volume =       "20",
  number =       "1--2",
  pages =        "37--46",
  month =        "????",
  year =         "1984",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(84)90038-4",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Mon Feb 25 10:38:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0306457384900384",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Anomalous Law of Numbers; Benford's Law",
}

@Article{Bunt:1984:MPL,
  author =       "Richard B. Bunt and Jennifer M. Murphy and Shikharesh
                 Majumdar",
  title =        "A measure of program locality and its application",
  journal =      j-SIGMETRICS,
  volume =       "12",
  number =       "3",
  pages =        "28--40",
  month =        aug,
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1031382.809311",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Thu Jun 26 11:00:50 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Although the phenomenon of locality has long been
                 recognized as the single most important characteristic
                 of program behaviour, relatively little work has been
                 done in attempting to measure it. Recent work has led
                 to the development of an intrinsic measure of program
                 locality based on the Bradford--Zipf distribution.
                 Potential applications for such a measure are many, and
                 include the evaluation of program restructuring methods
                 (manual and automatic), the prediction of system
                 performance, the validation of program behaviour
                 models, and the enhanced understanding of the phenomena
                 that characterize program behaviour. A consideration of
                 each of these areas is given in connection with the
                 proposed measure, both to increase confidence in the
                 validity of the measure and to illustrate a methodology
                 for dealing with such problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
}

@Article{Cohen:1984:PNF,
  author =       "D. I. A. Cohen and T. M. Katz",
  title =        "Prime numbers and the first digit phenomenon",
  journal =      j-J-NUMBER-THEORY,
  volume =       "18",
  number =       "3",
  pages =        "261--268",
  month =        jun,
  year =         "1984",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/0022-314X(84)90061-1",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Fri Nov 25 13:58:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
}

@Article{Fedorowicz:1984:DEU,
  author =       "Jane Fedorowicz",
  title =        "Database evaluation using multiple regression
                 techniques",
  journal =      j-SIGMOD,
  volume =       "14",
  number =       "2",
  pages =        "70--76",
  year =         "1984",
  CODEN =        "SRECD8",
  ISBN =         "0-89791-128-8",
  ISBN-13 =      "978-0-89791-128-3",
  ISSN =         "0163-5808 (print), 1943-5835 (electronic)",
  ISSN-L =       "0163-5808",
  bibdate =      "Mon Dec 9 07:58:51 MST 1996",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A model of the inverted file of an automated
                 bibliographic system is constructed using the Zipf
                 distribution of word frequency. By ascertaining the
                 parameters of the Zipfian model of the inverted file
                 system, one can estimate the minimum data storage
                 requirements of the database. In addition, given a few
                 additional system parameters, access time for a
                 specified query can be estimated. The estimation
                 procedures are accomplished using logarithmic
                 transformations and multiple regression techniques.
                 This paper introduces the Zipfian models, their
                 regression formulation, and their results and
                 interpretation for application to database
                 evaluation.",
  acknowledgement = ack-nhfb,
  affiliation =  "Northwestern Univ, Kellogg Graduate Sch of Management,
                 Evanston, IL, USA",
  affiliationaddress = "Northwestern Univ, Kellogg Graduate Sch of
                 Management, Evanston, IL, USA",
  classification = "723; 901; 922",
  conference =   "SIGMOD '84, Proceedings of Annual Meeting (ACM Special
                 Interest Group on Management of Data).",
  fjournal =     "SIGMOD Record (ACM Special Interest Group on
                 Management of Data)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J689",
  keywords =     "access time model; bibliographic techniques; database
                 systems; evaluation; information storage systems;
                 mathematical models; multiple regression techniques;
                 Zipfian model",
  meetingaddress = "Boston, MA, USA",
  sponsor =      "ACM, Special Interest Group on Management of Data, New
                 York, NY, USA",
}

@Article{Friedberg:1984:DFD,
  author =       "Stephen H. Friedberg",
  title =        "The Distribution of First Digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "15",
  number =       "2",
  pages =        "120--125",
  month =        mar,
  year =         "1984",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/00494925.1984.11972760",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:49:53 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.jstor.org/stable/2686516;
                 http://www.tandfonline.com/doi/abs/10.1080/00494925.1984.11972760",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "Benford's Law",
  onlinedate =   "30 Jan 2018",
}

@Article{Fuchs:1984:PDP,
  author =       "A. Fuchs and G. Letta",
  title =        "{Sur le probl{\`e}me du premier chiffre d{\'e}cimal}.
                 ({French}) [{On} the problem of the first decimal
                 digit]",
  journal =      "{Bollettino della Unione Matem{\`a}tica Italiana.
                 Serie VI. B}",
  volume =       "3",
  pages =        "451--461",
  year =         "1984",
  ISSN =         "0392-4041",
  ISSN-L =       "0392-4041",
  bibdate =      "Wed Aug 12 10:09:50 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0557.60011",
  acknowledgement = ack-nhfb,
  ajournal =     "Boll. Unione Mat. Ital., VI. Ser., B",
  keywords =     "analytical density; asymptotic density; first-digit
                 problem",
  language =     "French",
  ZMclass =      "60B99 (Probability theory on general structures)",
  ZMreviewer =   "R. Scozzafava",
}

@Article{Karmeshu:1984:RBL,
  author =       "Karmeshu and N. C. Lind and V. Cano",
  title =        "Rationales for {Bradford's Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "6",
  number =       "4",
  pages =        "233--241",
  month =        jul,
  year =         "1984",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02279358",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:02:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02279358",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Kohyama:1984:TIC,
  author =       "Tamotsu Kohyama and Y{\=o}ji Aizawa",
  title =        "Theory of the intermittent chaos. {$ 1 / f $} spectrum
                 and the {Pareto--Zipf} law",
  journal =      j-PROG-THEOR-PHYS,
  volume =       "71",
  number =       "5",
  pages =        "917--929",
  year =         "1984",
  CODEN =        "PTPKAV",
  DOI =          "https://doi.org/10.1143/PTP.71.917",
  ISSN =         "0033-068X (print), 1347-4081 (electronic)",
  ISSN-L =       "0033-068X",
  MRclass =      "58F13 (76F99)",
  MRnumber =     "756214 (86a:58063)",
  MRreviewer =   "Joseph Ford",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
  journal-URL =  "http://ptp.oxfordjournals.org/content/by/year",
}

@Article{Maia:1984:UBL,
  author =       "M. J. F. Maia and M. D. Maia",
  title =        "On the Unity of {Bradford's Law}",
  journal =      j-J-DOC,
  volume =       "40",
  number =       "3",
  pages =        "206--216",
  month =        "????",
  year =         "1984",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026765",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:11:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{McLaughlin:1984:DFI,
  author =       "William I. McLaughlin and Sylvia A. Lundy",
  title =        "Digit Functions of Integer Sequences",
  journal =      j-FIB-QUART,
  volume =       "22",
  number =       "2",
  pages =        "105--115",
  month =        may,
  year =         "1984",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:30 MDT 2011",
  bibsource =    "http://www.fq.math.ca/22-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/22-2/mclaughlin.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Nagasaka:1984:BL,
  author =       "Kenji Nagasaka",
  title =        "On {Benford}'s law",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "36",
  number =       "1",
  pages =        "337--352",
  month =        "????",
  year =         "1984",
  CODEN =        "AISXAD",
  DOI =          "https://doi.org/10.1007/BF02481974",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  MRclass =      "60F99 (11K06 11K36 62E99)",
  MRnumber =     "758506 (86a:60052)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sat Jan 31 18:19:56 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anninststatmath.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02481974",
  acknowledgement = ack-nhfb,
  ajournal =     "Ann. Inst. Statist. Math.",
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
  journal-URL =  "http://link.springer.com/journal/10463",
}

@Article{Schatte:1984:AUD,
  author =       "Peter Schatte",
  title =        "On the asymptotic uniform distribution of sums reduced
                 $ \bmod 1 $",
  journal =      j-MATH-NACHR,
  volume =       "115",
  number =       "1",
  pages =        "275--281",
  month =        "????",
  year =         "1984",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19841150121",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sat Nov 12 15:54:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19841150121/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Turner:1984:FRD,
  author =       "Peter R. Turner",
  title =        "Further revelations on l.s.d",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "225--231",
  month =        apr,
  year =         "1984",
  CODEN =        "IJNADH",
  DOI =          "https://doi.org/10.1093/imanum/4.2.225",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G10 (11K99)",
  MRnumber =     "85m:65039",
  MRreviewer =   "Calvin T. Long",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  abstract =     "In a recent paper the author showed that the
                 distribution of leading significant digits, l.s.d.,
                 resulting from successive multiplications is
                 logarithmic. In this paper these results are extended
                 by establishing, still without any assumptions of
                 invariance to scaling, that this distribution remains
                 invariant under all further arithmetic operations ---
                 both multiplicative and additive. The fact that 30\% of
                 decimal numbers have l.s.d. 1 persists.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "l. s. d. (leading significant digits)",
}

@Article{Yuan:1984:LOC,
  author =       "Y. Yuan",
  title =        "On the least {$Q$}-order of convergence of variable
                 metric algorithms",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "4",
  number =       "2",
  pages =        "233--239",
  month =        apr,
  year =         "1984",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65K05",
  MRnumber =     "85h:65133",
  MRreviewer =   "A. I. \c Schiop",
  bibdate =      "Sat Dec 23 17:06:35 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajnumeranal.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
}

@Article{Barlow:1985:RED,
  author =       "J. L. Barlow and E. H. Bareiss",
  title =        "On Roundoff Error Distributions in Floating Point and
                 Logarithmic Arithmetic",
  journal =      j-COMPUTING,
  volume =       "34",
  number =       "4",
  pages =        "325--347",
  month =        dec,
  year =         "1985",
  CODEN =        "CMPTA2",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "65G05",
  MRnumber =     "87c:65045",
  MRreviewer =   "N. N. Abdelmalek",
  bibdate =      "Tue Oct 12 16:33:42 MDT 1999",
  bibsource =    "Compendex database;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  acknowledgement = ack-nhfb,
  affiliation =  "Pennsylvania State Univ, Computer Science Dep,
                 University Park, PA, USA",
  affiliationaddress = "USA",
  classification = "723",
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  journalabr =   "Computing (Vienna/New York)",
  keywords =     "computer arithmetic; computer metatheory; floating
                 point arithmetic; logarithmic arithmetic; roundoff
                 error distributions",
}

@Article{Bradford:1985:SIS,
  author =       "Samuel C. Bradford",
  title =        "Sources of Information on Specific Subjects",
  journal =      j-J-INFO-SCI-PRINCIPLES-PRACTICE,
  volume =       "10",
  number =       "4",
  pages =        "173--180",
  month =        oct,
  year =         "1985",
  CODEN =        "JISCDI",
  ISSN =         "0165-5515 (print), 1741-6485 (electronic)",
  ISSN-L =       "0165-5515",
  bibdate =      "Fri Nov 25 11:49:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Bradford:1934:SIS}, the source of
                 Bradford's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Information Science, Principles and
                 Practice",
  journal-URL =  "http://jis.sagepub.com/",
}

@Article{Egghe:1985:CLL,
  author =       "L. Egghe",
  title =        "Consequences of {Lotka's Law} for the {Law of
                 Bradford}",
  journal =      j-J-DOC,
  volume =       "41",
  number =       "3",
  pages =        "173--189",
  month =        "????",
  year =         "1985",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026780",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:23:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  keywords =     "Bradford's Law",
}

@Article{Faber:1985:AML,
  author =       "Vance Faber and Andrew B. {White, Jr.} and G. Milton
                 Wing",
  title =        "Analysis of a model that leads to the {Pareto} law of
                 wealth distribution",
  journal =      j-J-MATH-ANAL-APPL,
  volume =       "112",
  number =       "2",
  pages =        "579--594",
  year =         "1985",
  CODEN =        "JMANAK",
  DOI =          "https://doi.org/10.1016/0022-247X(85)90264-1",
  ISSN =         "0022-247X (print), 1096-0813 (electronic)",
  ISSN-L =       "0022-247X",
  MRclass =      "90A14",
  MRnumber =     "813621 (87b:90027)",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Analysis and Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022247X",
}

@Article{Lagarias:1985:PG,
  author =       "Jeffrey C. Lagarias",
  title =        "The $ 3 x + 1 $ Problem and Its Generalizations",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "92",
  number =       "1",
  pages =        "3--23",
  month =        jan,
  year =         "1985",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K55 (11K31)",
  MRnumber =     "86i:11043",
  MRreviewer =   "A. D. Pollington",
  bibdate =      "Mon Jun 28 12:37:47 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  keywords =     "Benford's Law",
}

@Article{Pao:1985:LLT,
  author =       "Miranda Lee Pao",
  title =        "{Lotka}'s law: a testing procedure",
  journal =      j-INFO-PROC-MAN,
  volume =       "21",
  number =       "4",
  pages =        "305--320",
  month =        "????",
  year =         "1985",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(85)90055-X",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Fri Nov 25 08:41:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
}

@Article{Raimi:1985:FDP,
  author =       "Ralph A. Raimi",
  title =        "The First Digit Phenomenon Again",
  journal =      j-PROC-AMER-PHIL-SOC,
  volume =       "129",
  number =       "2",
  pages =        "211--219",
  month =        jun,
  year =         "1985",
  CODEN =        "PAPCAA",
  ISSN =         "0003-049X (print), 2326-9243 (electronic)",
  ISSN-L =       "0003-049X",
  bibdate =      "Sat Nov 12 16:56:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "This paper contains strong criticism of a derivation
                 of Benford's Law \cite{Logan:1978:FDP}.",
  URL =          "http://www.jstor.org/stable/986989",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the {American Philosophical Society}
                 held at {Philadelphia} for promoting useful knowledge",
  journal-URL =  "http://www.jstor.org/journal/procamerphilsoci",
  remark =       "This paper contains mathematical derivations of both
                 Stigler's Law and Benford's Law. Raimi comments on p.
                 217: ``the Benford law itself as a conclusion to be
                 derived is by no means as firm as Kepler's planetary
                 curves. Indeed, it has been pointed out by Diaconis and
                 Freedman [D-F] [\cite{Diaconis:1979:RP}] that a
                 statistical analysis of Benford's announced data gives
                 a high probability to the conjecture that he did a bit
                 of rounding-off here and there, always in the direction
                 of his law. The license that a physicist often takes on
                 the path from his hypotheses to verified, observable,
                 and repeatable conclusion is not justified here.''.",
}

@Article{Tichy:1985:UDD,
  author =       "Robert F. Tichy",
  title =        "Uniform distribution and diophantine inequalities",
  journal =      j-MONAT-MATH,
  volume =       "99",
  number =       "2",
  pages =        "147--152",
  month =        jun,
  year =         "1985",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01304194",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  bibdate =      "Sun Feb 17 06:26:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01304194",
  ZMnumber =     "0538.10039",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
  keywords =     "diophantine inequalities; discrepancy; Uniformly
                 distributed sequences",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 11D75
                 (Diophantine inequalities)",
}

@Article{Tuldava:1985:FST,
  author =       "Yu. A. Tuldava",
  title =        "The frequency structure of a text and {Zipf}'s law",
  journal =      "Tartu Riikl. {\"U}l. Toimetised",
  volume =       "??",
  number =       "711",
  pages =        "93--116",
  year =         "1985",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "92A25 (94A15)",
  MRnumber =     "836129 (87c:92063)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tartu Riikliku {\"U}likooli Toimetised. Uchenye
                 Zapiski Tartuskogo Gosudarstvennogo Universiteta. Acta
                 et Commentationes Universitatis Tartuensis",
}

@Article{Uppuluri:1985:DFD,
  author =       "V. R. R. Uppuluri and S. A. Patil",
  title =        "The distribution of the first $j$ digits of beta
                 related random variables",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "14",
  number =       "2",
  pages =        "467--472",
  year =         "1985",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610918508812450",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat Jan 30 06:32:23 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput1980.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law",
}

@Article{Chen:1986:RBL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "A relationship between {Lotka's Law}, {Bradford's
                 Law}, and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "5",
  pages =        "307--314",
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Chen:1986:RRB,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "Research: A relationship between {Lotka's Law},
                 {Bradford's Law}, and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "5",
  pages =        "307--314",
  month =        sep,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198609)37:5<307::AID-ASI5>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Egghe:1986:RDB,
  author =       "L. Egghe",
  title =        "Research: The dual of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "4",
  pages =        "246--255",
  month =        jul,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198607)37:4<246::AID-ASI10>3.0.CO%3B2-D",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Feldstein:1986:OUS,
  author =       "Alan Feldstein and Peter Turner",
  title =        "Overflow, underflow, and severe loss of significance
                 in floating-point addition and subtraction",
  journal =      j-IMA-J-NUMER-ANAL,
  volume =       "6",
  number =       "2",
  pages =        "241--251",
  month =        apr,
  year =         "1986",
  CODEN =        "IJNADH",
  ISSN =         "0272-4979 (print), 1464-3642 (electronic)",
  ISSN-L =       "0272-4979",
  MRclass =      "65G05",
  MRnumber =     "89h:65065",
  bibdate =      "Sat Dec 23 14:52:49 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper it is shown that, under the assumption
                 of the logarithmic distribution of numbers,
                 floating-point addition and subtraction can result in
                 overflow or underflow with alarming frequency --- a
                 frequency that increases rapidly with machine speed
                 unless the range of the exponent is also increased. If
                 numbers are assumed to be distributed in accordance
                 with Sweeney's (1965) experiments, then severe loss of
                 significance occurs with large probability in floating
                 point subtraction. These results have implications for
                 computer design and lead to the suggestion of a long
                 word format which will reduce the risks to acceptable
                 levels.",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Numerical Analysis",
  journal-URL =  "http://imajna.oxfordjournals.org/content/by/year",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Article{Green:1986:BRP,
  author =       "M. W. Green",
  title =        "Book Reviews: {{\em Pareto Distributions}}, by {B. C.
                 Arnold}",
  journal =      j-APPL-STAT,
  volume =       "35",
  number =       "2",
  pages =        "215--215",
  year =         "1986",
  CODEN =        "APSTAG",
  ISSN =         "0035-9254 (print), 1467-9876 (electronic)",
  ISSN-L =       "0035-9254",
  bibdate =      "Sat Apr 21 10:24:36 MDT 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Statistics",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9876/issues",
}

@Article{Hoare:1986:DFS,
  author =       "G. T. Q. Hoare and E. Wright",
  title =        "The distribution of first significant digits",
  journal =      j-MATH-GAZ,
  volume =       "70",
  number =       "451",
  pages =        "34--37",
  month =        mar,
  year =         "1986",
  CODEN =        "MAGAAS",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Sat Feb 16 17:57:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3615826",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
}

@Article{Katz:1986:FDP,
  author =       "Talbot M. Katz and Daniel I. A. Cohen",
  title =        "The First Digit Property for Exponential Sequences is
                 Independent of the Underlying Distribution",
  journal =      j-FIB-QUART,
  volume =       "24",
  number =       "1",
  pages =        "2--7",
  month =        feb,
  year =         "1986",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:00:45 MDT 2011",
  bibsource =    "http://www.fq.math.ca/24-1.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/24-1/katz.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Lemons:1986:NTD,
  author =       "Don S. Lemons",
  title =        "On the number of things and the distribution of first
                 digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "54",
  number =       "9",
  pages =        "816--817",
  month =        sep,
  year =         "1986",
  CODEN =        "AJPIAS",
  DOI =          "https://doi.org/10.1119/1.14453",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Wed Nov 23 12:03:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ajp.aapt.org/",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
  keywords =     "Benford's Law",
  remark =       "Lemons gives a derivation of Benford's Law that does
                 not assume scale invariance, unlike other widely-cited
                 derivations
                 \cite{Pinkham:1961:DFS,Raimi:1976:FDP,Raimi:1985:FDP}.",
}

@Book{Lines:1986:NYT,
  author =       "Malcolm E. Lines",
  title =        "A number for your thoughts: facts and speculations
                 about numbers from {Euclid} to the latest computers",
  publisher =    pub-ADAM-HILGER,
  address =      pub-ADAM-HILGER:adr,
  pages =        "vi + 214",
  year =         "1986",
  ISBN =         "0-85274-495-1 (paperback)",
  ISBN-13 =      "978-0-85274-495-6 (paperback)",
  LCCN =         "QA241 .L617 1986",
  bibdate =      "Wed Nov 23 11:34:02 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0668/86183277-d.html",
  acknowledgement = ack-nhfb,
  remark =       "Chapter 7 (pp. 43--52) is entitled: ``The Baffling Law
                 of Benford''.",
  subject =      "number theory",
}

@Article{MacRoberts:1986:QMC,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "Quantitative Measures of Communication in Science: a
                 Study of the Formal Level",
  journal =      j-SOC-STUD-SCI,
  volume =       "16",
  number =       "1",
  pages =        "151--172",
  day =          "1",
  month =        feb,
  year =         "1986",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631286016001008",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:44 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{Stigler:1987:PMF} and reply
                 \cite{MacRoberts:1987:MFU}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631286016001008",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Pao:1986:EEL,
  author =       "Miranda Lee Pao",
  title =        "An empirical examination of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "1",
  pages =        "26--33",
  month =        jan,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/asi.4630370105",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:25 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "24 May 2007",
}

@Article{Pao:1986:REE,
  author =       "Miranda Lee Pao",
  title =        "Research: An empirical examination of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "37",
  number =       "1",
  pages =        "26--33",
  month =        jan,
  year =         "1986",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198601)37:1<26::AID-ASI4>3.0.CO%3B2-Z",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:25 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Patil:1986:DFD,
  author =       "S. A. Patil and V. R. R. Uppuluri",
  title =        "The Distribution of First $j$ Digits",
  journal =      j-COLLEGE-MATH-J,
  volume =       "17",
  number =       "3",
  pages =        "240--243",
  month =        may,
  year =         "1986",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.1986.11972963",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:50:20 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collegemathj.bib",
  URL =          "http://www.jstor.org/stable/2686982;
                 http://www.tandfonline.com/doi/abs/10.1080/07468342.1986.11972963",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  keywords =     "Benford's Law",
  onlinedate =   "30 Jan 2018",
}

@Article{Pontigo:1986:QAB,
  author =       "J. Pontigo and F. W. Lancaster",
  title =        "Qualitative aspects of the {Bradford} distribution",
  journal =      j-SCIENTOMETRICS,
  volume =       "9",
  number =       "1--2",
  pages =        "59--70",
  month =        jan,
  year =         "1986",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016608",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:02:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016608",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Schatte:1986:ALD,
  author =       "Peter Schatte",
  title =        "On the asymptotic logarithmic distribution of the
                 floating-point mantissas of sums",
  journal =      j-MATH-NACHR,
  volume =       "127",
  number =       "1",
  pages =        "7--20",
  month =        "????",
  year =         "1986",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19861270102",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Sun Feb 17 06:04:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/mana.19861270102/abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Article{Tichy:1986:GZU,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung und zahlentheoretische Ungleichungen
                 II}. ({German}) [{Uniform} distribution and
                 number-theoretic inequalities {II}]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "122(1985)",
  number =       "??",
  pages =        "95--99",
  month =        "????",
  year =         "1986",
  CODEN =        "OSAWA8",
  DOI =          "????",
  ISSN =         "0065-535X",
  ISSN-L =       "0065-535X",
  bibdate =      "Sun Feb 17 06:24:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  classmath =    "11K06 (General theory of distribution modulo 1); 11J25
                 (Diophantine inequalities)",
  keywords =     "diophantine inequalities; discrepancy; H infinity;
                 logarithmic mean; summation method; uniform
                 distribution",
  language =     "German",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
}

@Article{Bak:1987:SOC,
  author =       "Per Bak and Chao Tang and Kurt Wiesenfeld",
  title =        "Self-organized criticality: An explanation of the $ 1
                 / f $ noise",
  journal =      j-PHYS-REV-LET,
  volume =       "59",
  number =       "4",
  pages =        "381--384",
  month =        jul,
  year =         "1987",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.59.381",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 10:54:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.59.381",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Chen:1987:AZL,
  author =       "Ye-Sho Chen and Ferdinand F. Leimkuhler",
  title =        "Analysis of {Zipf}'s law: An index approach",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "171--182",
  day =          "1",
  month =        apr,
  year =         "1987",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(87)90002-1",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0306457387900021",
  ZMnumber =     "0614.62150",
  abstract =     "A rigorous analysis of Zipf's law is made using an
                 index for the sequence of observed values of the
                 variables in a Zipf-type relationship. Three important
                 properties relating rank, count, and frequency are
                 identified. Using this approach, the shape of Zipf-type
                 curves can be described in terms of three distinct
                 regions and two parameters of the Mandelbrot--Zipf law.
                 This result has considerable practical significance,
                 since it provides rigorous foundations for the
                 application of Zipf's law.",
  acknowledgement = ack-nhfb,
  classmath =    "62P99 (Appl. of statistics)",
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "index approach; Mandelbrot-Zipf law; Zipf's law",
}

@Article{Chen:1987:BLI,
  author =       "Ye-Sho Chen and F. F. Leimkuhler",
  title =        "{Bradford's Law}: An index approach",
  journal =      j-SCIENTOMETRICS,
  volume =       "11",
  number =       "3--4",
  pages =        "183--198",
  month =        mar,
  year =         "1987",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02016591",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:03 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02016591",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Fedorowicz:1987:DPE,
  author =       "Jane Fedorowicz",
  title =        "Database Performance Evaluation in an Indexed File
                 Environment",
  journal =      j-TODS,
  volume =       "12",
  number =       "1",
  pages =        "85--110",
  month =        mar,
  year =         "1987",
  CODEN =        "ATDSD3",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Compendex database; Database/Graefe.bib;
                 Database/Wiederhold.bib; http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/tods/1987-12-1/p85-fedorowicz/p85-fedorowicz.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1987-12-1/p85-fedorowicz/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/13675.html",
  abstract =     "The use of database systems for managerial decision
                 making often incorporates information-retrieval
                 capabilities with numeric report generation. Of great
                 concern to the user of such a system is the response
                 time associated with issuing a query to the database.
                 This study presents a procedure for estimating response
                 time for one of the most frequently encountered
                 physical storage mechanisms, the indexed file. The
                 model provides a fairly high degree of accuracy, but is
                 simple enough so that the cost of applying the model is
                 not exorbitant. The model incorporates the knowledge
                 that the distribution of access key occurrences is
                 known to follow Zipf's law. It first estimates the
                 access time required to complete the query, which
                 includes the time needed for all input and output
                 transactions, and CPU time used in performing the
                 search. The effects of multiple users on an
                 individual's response time are then assessed using a
                 simple regression estimation technique. The two-step
                 procedure allows for the separation of access time from
                 multiuser influences.",
  acknowledgement = ack-nhfb,
  affiliation =  "Boston Univ, Boston, MA, USA",
  affiliationaddress = "Boston Univ, Boston, MA, USA",
  annote =       "a procedure for estimating response time; distribution
                 of access key occurrences follow Zipf's law. Early
                 version with Kellogg, J. L. Model provides a fairly
                 high degree of accuracy but is simple. The effects of
                 multiple users are assessed using simple regression
                 estimation.",
  classification = "723; 912; 922",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Design; Performance",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "data processing --- File organization; database
                 performance; database systems; indexed file
                 environment; MANAGEMENT --- Information Systems;
                 multiple users, design; Performance; performance;
                 response time; statistical methods --- regression
                 analysis; Zipf's law",
  subject =      "{\bf D.4.3}: Software, OPERATING SYSTEMS, File Systems
                 Management, File organization. {\bf H.2.2}: Information
                 Systems, DATABASE MANAGEMENT, Physical Design, Access
                 methods. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.3.3}: Information Systems,
                 INFORMATION STORAGE AND RETRIEVAL, Information Search
                 and Retrieval, Retrieval models.",
}

@Article{Hosking:1987:PQE,
  author =       "J. R. M. Hosking and J. R. Wallis",
  title =        "Parameter and Quantile Estimation for the Generalized
                 {Pareto} Distribution",
  journal =      j-TECHNOMETRICS,
  volume =       "29",
  number =       "3",
  pages =        "339--349",
  month =        "????",
  year =         "1987",
  CODEN =        "TCMTA2",
  ISSN =         "0040-1706 (print), 1537-2723 (electronic)",
  ISSN-L =       "0040-1706",
  bibdate =      "Fri Nov 25 16:39:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Technometrics",
  journal-URL =  "http://www.jstor.org/journals/00401706.html;
                 http://www.tandfonline.com/loi/utch20",
}

@Article{Kunoff:1987:FDP,
  author =       "Sharon Kunoff",
  title =        "{$ N! $} has the First Digit Property",
  journal =      j-FIB-QUART,
  volume =       "25",
  number =       "4",
  pages =        "365--367",
  month =        nov,
  year =         "1987",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:00 MDT 2011",
  bibsource =    "http://www.fq.math.ca/25-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/25-4/kunoff.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{MacRoberts:1987:MFU,
  author =       "Michael H. MacRoberts and Barbara R. MacRoberts",
  title =        "Measurement in the Face of Universal Uncertainty: a
                 Reply to {Stigler}",
  journal =      j-SOC-STUD-SCI,
  volume =       "17",
  number =       "2",
  pages =        "334--336",
  day =          "1",
  month =        may,
  year =         "1987",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631287017002008",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:46 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{MacRoberts:1986:QMC}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002008",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Nagasaka:1987:BLL,
  author =       "Kenji Nagasaka and Jau-Shyong Shiue",
  title =        "{Benford}'s law for linear recurrence sequences",
  journal =      "Tsukuba J. Math.",
  volume =       "11",
  number =       "2",
  pages =        "341--351",
  year =         "1987",
  CODEN =        "????",
  ISSN =         "0387-4982",
  ISSN-L =       "0387-4982",
  MRclass =      "60E99 (11B37)",
  MRnumber =     "926460 (88m:60047)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Tsukuba Journal of Mathematics",
}

@Article{Nicholls:1987:BCE,
  author =       "Paul Travis Nicholls",
  title =        "Brief Communications: Estimation of {Zipf}
                 parameters",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "38",
  number =       "6",
  pages =        "443--445",
  month =        nov,
  year =         "1987",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:31 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "24 May 2007",
}

@Article{Nicholls:1987:EZP,
  author =       "Paul Travis Nicholls",
  title =        "Estimation of {Zipf} parameters",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "38",
  number =       "6",
  pages =        "443--445",
  year =         "1987",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198711)38:6<443::AID-ASI4>3.0.CO%3B2-E",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
}

@Article{Sanders:1987:PPUa,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Consumer Marketing",
  volume =       "4",
  number =       "1",
  pages =        "47--50",
  month =        "????",
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb008188",
  ISSN =         "0736-3761",
  ISSN-L =       "0736-3761",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sanders:1987:PPUb,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Services Marketing",
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1987",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb024706",
  ISSN =         "0887-6045",
  ISSN-L =       "0887-6045",
  bibdate =      "Fri Nov 25 06:56:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1987:ABM,
  author =       "Peter Schatte",
  title =        "On the asymptotic behaviour of the mantissa
                 distribution of sums",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "23",
  number =       "??",
  pages =        "353--360",
  month =        "????",
  year =         "1987",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  ISSN-L =       "0863-0593",
  bibdate =      "Sat Nov 12 15:58:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Inform. Process. Cybern. EIK",
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
}

@Article{Schatte:1987:SEU,
  author =       "Peter Schatte",
  title =        "Some estimates of the {$ \mathcal {H}_\infty
                 $}-uniform distribution",
  journal =      j-MONAT-MATH,
  volume =       "103",
  number =       "3",
  pages =        "233--249",
  month =        sep,
  year =         "1987",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01364342",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  bibdate =      "Sat Nov 12 15:57:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01364342",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Stigler:1987:PMF,
  author =       "Stephen M. Stigler",
  title =        "Precise Measurement in the Face of Error: a Comment on
                 {MacRoberts} and {MacRoberts}",
  journal =      j-SOC-STUD-SCI,
  volume =       "17",
  number =       "2",
  pages =        "332--334",
  day =          "1",
  month =        may,
  year =         "1987",
  CODEN =        "SSSCDH",
  DOI =          "https://doi.org/10.1177/030631287017002007",
  ISSN =         "0306-3127 (print), 1460-3659 (electronic)",
  ISSN-L =       "0306-3127",
  bibdate =      "Mon Dec 3 09:12:46 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/socstudsci.bib",
  note =         "See \cite{MacRoberts:1986:QMC} and reply
                 \cite{MacRoberts:1987:MFU}.",
  URL =          "https://journals.sagepub.com/doi/pdf/10.1177/030631287017002007",
  acknowledgement = ack-nhfb,
  fjournal =     "Social Studies of Science",
  journal-URL =  "http://sss.sagepub.com/content/by/year",
}

@Article{Tague:1987:MVZ,
  author =       "Jean Tague and Paul Nicholls",
  title =        "The maximal value of a {Zipf} size variable: Sampling
                 properties and relationship to other parameters",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "155--170",
  day =          "7",
  month =        jun,
  year =         "1987",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/0306-4573(87)90001-X",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/030645738790001X",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Zipf's Law",
}

@Article{Tichy:1987:GS,
  author =       "Robert F. Tichy",
  title =        "{Gleichverteilung zum Summierungsverfahren {$ H_\infty
                 $}}. ({German}) [{Uniform} distribution to the {$
                 H_\infty $} summation method]",
  journal =      j-MATH-NACHR,
  volume =       "131",
  number =       "??",
  pages =        "119--125",
  month =        "????",
  year =         "1987",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19871310112",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Mon Feb 18 06:44:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0626.10044",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "$H_\infty$-discrepancy; difference sequences; real
                 sequences; uniform distribution",
  language =     "German",
  ZMclass =      "11K06 (General theory of distribution modulo 1); 40J05
                 (Summability in abstract structures)",
  ZMreviewer =   "D. Leitmann",
}

@Article{Turner:1987:DDI,
  author =       "Peter R. Turner",
  title =        "The Distribution of l.s.d. and Its Implications for
                 Computer Design",
  journal =      j-MATH-GAZ,
  volume =       "71",
  number =       "455",
  pages =        "26--31",
  month =        mar,
  year =         "1987",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.2307/3616283",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue Oct 30 23:36:58 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "[l.s.d. = least significant digits]. The topic is
                 variously known as Benford's Law, the Law of Anomalous
                 Numbers, and Zipf's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  keywords =     "Benford's Law; Law of Anomalous Numbers; logarithmic
                 distribution; overflow; underflow; Zipf's Law",
}

@Article{Belevitch:1988:PQD,
  author =       "Vitold Belevitch",
  title =        "{{\`A}} propos de la queue de la distribution de
                 {Zipf}. ({French}) [{On} the tail of the {Zipf}
                 distribution]",
  journal =      "Ann. Soc. Sci. Bruxelles S{\'e}r. I",
  volume =       "102",
  number =       "3",
  pages =        "73--85 (1989)",
  year =         "1988",
  CODEN =        "ASSBAH",
  ISSN =         "0037-959X",
  ISSN-L =       "0037-959X",
  MRclass =      "92A90",
  MRnumber =     "1016850 (90g:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annales de la Societ{\'e} Scientifique de Bruxelles.
                 S{\'e}rie I. Sciences Math{\'e}matiques, Astronomiques
                 et Physiques",
  language =     "French",
}

@Article{Carslaw:1988:AIN,
  author =       "C. A. Carslaw",
  title =        "Anomalies in Income Numbers: Evidence of Goal-Oriented
                 Behavior",
  journal =      j-ACCOUNT-REV,
  volume =       "63",
  number =       "2",
  pages =        "321--327",
  month =        apr,
  year =         "1988",
  CODEN =        "ACRVAS",
  ISSN =         "0001-4826 (print), 1558-7967 (electronic)",
  ISSN-L =       "0001-4826",
  bibdate =      "Sat Sep 10 11:00:09 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/248109",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  journal-URL =  "https://www.jstor.org/journal/accountingreview",
  keywords =     "Benford's Law; New Zealand firms; second-digit
                 frequency",
  remark-1 =     "This paper references neither Newcomb nor Benford, but
                 it uses their digit-frequency formula from
                 \cite{Feller:1966:IPT} to compare with data on revenues
                 of New Zealand companies.",
  remark-2 =     "According to \cite{Kossovsky:2015:BLT}, this may be
                 the first published serious use of Benford's Law for
                 fraud detection in accounting, although the possibility
                 had been mentioned 16 years earlier
                 \cite{Varian:1972:LEB}, and that earlier paper is not
                 cited in this 1988 paper.",
}

@Article{Hill:1988:RNG,
  author =       "Theodore Hill",
  title =        "Random number guessing and the first digit
                 phenomenon",
  journal =      j-PSYCHOL-REP,
  volume =       "62",
  number =       "3",
  pages =        "967--971",
  month =        jun,
  year =         "1988",
  CODEN =        "PYRTAZ",
  DOI =          "https://doi.org/10.2466/pr0.1988.62.3.967",
  ISSN =         "0033-2941 (print), 1558-691X (electronic)",
  ISSN-L =       "0033-2941",
  bibdate =      "Fri Feb 15 06:41:31 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amsciepub.com/doi/abs/10.2466/pr0.1988.62.3.967",
  acknowledgement = ack-nhfb,
  ajournal =     "Psychol. rep.",
  fjournal =     "Psychological Reports",
}

@InCollection{Kanemitsu:1988:BLF,
  author =       "Shigeru Kanemitsu and Kenji Nagasaka and G{\'e}rard
                 Rauzy and Jau-Shyong Shiue",
  booktitle =    "Probability theory and mathematical statistics
                 ({Kyoto}, 1986)",
  title =        "On {Benford}'s law: the first digit problem",
  volume =       "1299",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "158--169",
  year =         "1988",
  DOI =          "https://doi.org/10.1007/BFb0078471",
  MRclass =      "11K06 (60E99)",
  MRnumber =     "935987 (89d:11059)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Math.",
  acknowledgement = ack-nhfb,
}

@InCollection{Nicolis:1988:PBZ,
  author =       "John S. Nicolis",
  booktitle =    "Synergetics, order and chaos ({Madrid}, 1987)",
  title =        "On the parallel between {Zipf}'s law and {$ 1 / f $}
                 processes in chaotic systems possessing coexisting
                 attractors",
  publisher =    "World Sci. Publ.",
  address =      "Teaneck, NJ, USA",
  pages =        "723--734",
  year =         "1988",
  MRclass =      "58F13 (00A69)",
  MRnumber =     "1115922 (92g:58087)",
  MRreviewer =   "Dieter H. Mayer",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Prather:1988:CET,
  author =       "R. E. Prather",
  title =        "Comparison and Extension of Theories of {Zipf} and
                 {Halstead}",
  journal =      j-COMP-J,
  volume =       "31",
  number =       "3",
  pages =        "248--252",
  month =        jun,
  year =         "1988",
  CODEN =        "CMPJA6",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Mar 25 13:51:56 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/",
  URL =          "http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/248.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/249.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/250.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/251.tif;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_31/Issue_03/tiff/252.tif",
  acknowledgement = ack-nhfb,
  affiliation =  "Trinity Univ, San Antonio, TX, USA",
  affiliationaddress = "Trinity Univ, San Antonio, TX, USA",
  classcodes =   "C6110B (Software engineering techniques)",
  classification = "723",
  corpsource =   "Comput. and Inf. Sci., Trinity Univ., San Antonio, TX,
                 USA",
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
  keywords =     "behavioural psychology; computer programming; computer
                 software; empirical law; Halstead metrics; Halstead's
                 hypothesis; length estimates; Measurements;
                 probabilistic hypothesis; process; programming;
                 software engineering; software metrication; software
                 science; Zipf metrics; Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sanders:1988:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: Its Use and Abuse",
  journal =      "Journal of Business \& Industrial Marketing",
  volume =       "3",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1988",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/eb006057",
  ISSN =         "0885-8624",
  ISSN-L =       "0885-8624",
  bibdate =      "Fri Nov 25 07:04:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Schatte:1988:ASC,
  author =       "Peter Schatte",
  title =        "On the Almost Sure Convergence of Floating-Point
                 Mantissas and {Benford's Law}",
  journal =      j-MATH-NACHR,
  volume =       "135",
  number =       "1",
  pages =        "79--83",
  month =        "????",
  year =         "1988",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19881350108",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "60F15 (11K31)",
  MRnumber =     "944219 (89g:60114)",
  MRreviewer =   "S. A. Book",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  onlinedate =   "12 Nov 2006",
  reviewer =     "S. A. Book",
}

@Article{Schatte:1988:LIL,
  author =       "Peter Schatte",
  title =        "On a law of the iterated logarithm for sums {$ \bmod 1
                 $} with application to {Benford}'s law",
  journal =      j-PROBAB-THEORY-RELAT-FIELDS,
  volume =       "77",
  number =       "2",
  pages =        "167--178",
  month =        feb,
  year =         "1988",
  CODEN =        "PTRFEU",
  DOI =          "https://doi.org/10.1007/BF00334035",
  ISSN =         "0178-8051 (print), 1432-2064 (electronic)",
  ISSN-L =       "0178-8051",
  MRclass =      "60F15 (11K31)",
  MRnumber =     "927235 (89b:60081)",
  MRreviewer =   "L. Kuipers",
  bibdate =      "Sun Apr 27 11:18:06 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/probab-theory-relat-fields.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00334035",
  acknowledgement = ack-nhfb,
  fjournal =     "Probability Theory and Related Fields",
  journal-URL =  "http://link.springer.com/journal/440",
}

@Article{Schatte:1988:MDC,
  author =       "Peter Schatte",
  title =        "On Mantissa Distribution in Computing and {Benford's
                 Law}",
  journal =      j-J-INFO-PROC-CYBERNETICS-EIK,
  volume =       "24",
  number =       "9",
  pages =        "443--455",
  month =        "????",
  year =         "1988",
  CODEN =        "JICYE5",
  ISSN =         "0863-0593",
  ISSN-L =       "0863-0593",
  MRclass =      "60E05 (11K06 11K31 65G99)",
  MRnumber =     "984516 (90g:60016)",
  MRreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/eik/eik24.html#Schatte88",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  dblp-key =     "journals/eik/Schatte88",
  dblp-mdate =   "2020-03-06",
  fjournal =     "Journal of Information Processing and Cybernetics:
                 EIK",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Schatte:1988:UDC,
  author =       "Peter Schatte",
  title =        "On the uniform distribution of certain sequences and
                 {Benford}'s law",
  journal =      j-MATH-NACHR,
  volume =       "136",
  number =       "1",
  pages =        "271--273",
  year =         "1988",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.19881360119",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "11K06 (11K31)",
  MRnumber =     "952478 (89j:11075)",
  MRreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  onlinedate =   "11 Nov 2006",
}

@Article{Tichy:1988:SRC,
  author =       "Robert F. Tichy",
  title =        "{Statistische Resultate {\"u}ber computergerechte
                 Darstellungen von Zahlen}. ({German}) [Statistical
                 results on computer-oriented representations of
                 numbers]",
  journal =      "Anzeiger der {\"O}sterreichischen Akademie der
                 Wissenschaften. Mathematisch-Naturwissenschaftliche
                 Klasse",
  volume =       "1987",
  number =       "??",
  pages =        "1--8",
  month =        "????",
  year =         "1988",
  CODEN =        "OSAWA8",
  DOI =          "????",
  ISSN =         "0065-535X",
  ISSN-L =       "0065-535X",
  bibdate =      "Mon Feb 18 06:45:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0625.10041",
  acknowledgement = ack-nhfb,
  ajournal =     "Anz. {\"O}sterr. Akad. Wiss., Math.-Naturwiss. Kl.",
  language =     "German",
  xxnote =       "Despite repeated searches, I have not found this
                 journal online, not even from links at the Austrian
                 Academy of Sciences, \path=http://www.oeaw.ac.at=.",
  ZMclass =      "11K16 (Normal numbers, etc.); 11J71 (Distribution
                 modulo one); 11K38 (Irregularities of distribution)",
}

@Article{Arnold:1989:BEP,
  author =       "Barry C. Arnold and S. James Press",
  title =        "{Bayesian} estimation and prediction for {Pareto}
                 data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "84",
  number =       "408",
  pages =        "1079--1084",
  month =        "????",
  year =         "1989",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  MRclass =      "62F15 (62F10)",
  MRnumber =     "92f:62034",
  bibdate =      "Mon May 5 12:36:01 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Chen:1989:ZLT,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s laws in text modeling",
  journal =      "International Journal of General Systems. Methodology,
                 Applications, Education",
  volume =       "15",
  number =       "3",
  pages =        "233--252",
  year =         "1989",
  CODEN =        "IJGSAX",
  DOI =          "https://doi.org/10.1080/03081078908935048",
  ISSN =         "0308-1079, 1026-7492, 1563-5104",
  ISSN-L =       "0308-1079",
  MRclass =      "92A90",
  MRnumber =     "1015844",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Internat. J. Gen. Systems",
  fjournal =     "International Journal of General Systems. Methodology,
                 Applications, Education",
}

@Article{Family:1989:KDG,
  author =       "Fereydoon Family and Paul Meakin",
  title =        "Kinetics of droplet growth processes: Simulations,
                 theory, and experiments",
  journal =      j-PHYS-REV-A,
  volume =       "40",
  number =       "7",
  pages =        "3836--3854",
  month =        oct,
  year =         "1989",
  CODEN =        "PLRAAN",
  DOI =          "https://doi.org/10.1103/PhysRevA.40.3836",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Thu Feb 28 10:49:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevA.40.3836",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
}

@InProceedings{Kitsuregawa:1989:EBS,
  author =       "Masaru Kitsuregawa and Masaya Nakayama and Mikio
                 Takagi",
  title =        "The Effect of Bucket Size Tuning in the Dynamic Hybrid
                 {GRACE} Hash Join Method",
  crossref =     "Apers:1989:VLD",
  pages =        "257--266",
  month =        aug,
  year =         "1989",
  CODEN =        "VLDBDP",
  bibdate =      "Sat Jan 25 17:38:12 MST 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib",
  abstract =     "In this paper, we show detailed analysis and
                 performance evaluation of the Dynamic Hybrid GRACE Hash
                 Join Method (DHGH Method) when the tuple distribution
                 in buckets is unbalanced. The conventional Hash Join
                 Methods specify the tuple distribution in buckets
                 statically. However it may differ from estimation since
                 join operations are applied with selection operations.
                 When the tuple distribution in buckets is unbalanced,
                 the processing cost of join operation becomes more
                 costly than the ideal case when you use Hybrid Hash
                 Join Method (HH Method). On the other hand, when you
                 use the DHGH Method, the destaging buckets are selected
                 dynamically, gives the same performance as the ideal
                 case even if the tuple distribution in buckets is
                 unbalanced such as Zipf-like distributions.",
  acknowledgement = ack-nhfb,
  affiliation =  "Univ of Tokyo",
  affiliationaddress = "Tokyo, Jpn",
  classification = "723",
  journalabr =   "Very Large Data Bases Int Conf Very Large Data Bases",
  keywords =     "Computer Metatheory --- Programming Theory; Computer
                 Programming --- Algorithms; Database Systems; Query
                 Processing; Relational; Relational Algebra; VLDB",
}

@Article{Lang:1989:UAB,
  author =       "Sheau-Dong Lang and James R. Driscoll and Jiann H.
                 Jou",
  title =        "A Unified Analysis of Batched Searching of Sequential
                 and Tree-Structured Files",
  journal =      j-TODS,
  volume =       "14",
  number =       "4",
  pages =        "604--618",
  month =        dec,
  year =         "1989",
  CODEN =        "ATDSD3",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  MRclass =      "68P10 (68P20)",
  MRnumber =     "1 073 204",
  bibdate =      "Sat Apr 14 10:34:48 MDT 2001",
  bibsource =    "Database/Graefe.bib; Database/Wiederhold.bib;
                 http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/tods/1989-14-4/p604-lang/p604-lang.pdf;
                 http://www.acm.org/pubs/citations/journals/tods/1989-14-4/p604-lang/;
                 http://www.acm.org/pubs/toc/Abstracts/tods/76908.html",
  abstract =     "A direct and unified approach is used to analyze the
                 efficiency of batched searching of sequential and
                 tree-structured files. The analysis is applicable to
                 arbitrary search distributions, and closed-form
                 expressions are obtained for the expected batched
                 searching cost and savings. In particular, we consider
                 a search distribution satisfying Zipf's law for
                 sequential files and four types of uniform (random)
                 search distribution for sequential and tree-structured
                 files. These results unify and extend earlier research
                 on batched searching and estimating block accesses for
                 database systems.",
  acknowledgement = ack-nhfb,
  affiliation =  "Central Florida Univ., Orlando, FL, USA",
  annote =       "closed-form expressions for the number of accesses
                 needed given arbitrary search distributions.",
  fjournal =     "ACM Transactions on Database Systems",
  generalterms = "Algorithms; Design; Performance; Theory",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf H.3.3}: Information Systems, INFORMATION STORAGE
                 AND RETRIEVAL, Information Search and Retrieval, Search
                 process. {\bf H.3.2}: Information Systems, INFORMATION
                 STORAGE AND RETRIEVAL, Information Storage, File
                 organization. {\bf H.2.2}: Information Systems,
                 DATABASE MANAGEMENT, Physical Design, Access methods.",
}

@Article{Nicholls:1989:RBM,
  author =       "Paul Travis Nicholls",
  title =        "Research: Bibliometric modeling processes and the
                 empirical validity of {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "40",
  number =       "6",
  pages =        "379--385",
  month =        nov,
  year =         "1989",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(198911)40:6<379::AID-ASI1>3.0.CO%3B2-Q",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:37 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "27 May 2007",
}

@Article{Nicolis:1989:CDM,
  author =       "G. Nicolis and C. Nicolis and John S. Nicolis",
  title =        "Chaotic dynamics, {Markov} partitions, and {Zipf}'s
                 law",
  journal =      j-J-STAT-PHYS,
  volume =       "54",
  number =       "3--4",
  pages =        "915--924",
  month =        feb,
  year =         "1989",
  CODEN =        "JSTPSB",
  DOI =          "https://doi.org/10.1007/BF01019781",
  ISSN =         "0022-4715 (print), 1572-9613 (electronic)",
  ISSN-L =       "0022-4715",
  MRclass =      "58F13 (58F14 58F20)",
  MRnumber =     "988565 (90b:58184)",
  MRreviewer =   "Shi Hai Li",
  bibdate =      "Thu Aug 28 18:40:55 MDT 2014",
  bibsource =    "http://link.springer.com/journal/10955;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0022-4715&volume=54&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatphys1980.bib",
  URL =          "http://link.springer.com/article/10.1007/BF01019781",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
  journal-URL =  "http://link.springer.com/journal/10955",
}

@Article{Nicolis:1989:PBZ,
  author =       "John S. Nicolis and Ichiro Tsuda",
  title =        "On the parallel between {Zipf}'s law and {$ 1 / f $}
                 processes in chaotic systems possessing coexisting
                 attractors",
  journal =      j-PROG-THEOR-PHYS,
  volume =       "82",
  number =       "2",
  pages =        "254--274",
  year =         "1989",
  CODEN =        "PTPKAV",
  ISSN =         "0033-068X (print), 1347-4081 (electronic)",
  ISSN-L =       "0033-068X",
  MRclass =      "58F13 (92K20)",
  MRnumber =     "1023357 (91d:58165)",
  MRreviewer =   "Nima Geffen",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Progress of Theoretical Physics",
  journal-URL =  "http://ptp.oxfordjournals.org/content/by/year",
}

@Article{Schatte:1989:MUD,
  author =       "Peter Schatte",
  title =        "On measures of uniformly distributed sequences and
                 {Benford}'s law",
  journal =      j-MONAT-MATH,
  volume =       "107",
  number =       "3",
  pages =        "245--256",
  year =         "1989",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01300347",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  MRclass =      "11K36 (60F99)",
  MRnumber =     "1008683 (90k:11097)",
  MRreviewer =   "Kazuo Goto",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Monatshefte f{\"u}r Mathematik",
}

@Article{Shanbhag:1989:BRBa,
  author =       "D. N. Shanbhag",
  title =        "Book Review: {{\booktitle{Pareto Distributions}}, by
                 B. C. Arnold}",
  journal =      j-J-R-STAT-SOC-SER-A-STAT-SOC,
  volume =       "152",
  number =       "2",
  pages =        "253--254",
  month =        "????",
  year =         "1989",
  CODEN =        "JSSAEF",
  DOI =          "https://doi.org/10.2307/2982920",
  ISSN =         "0964-1998 (print), 1467-985X (electronic)",
  ISSN-L =       "0964-1998",
  bibdate =      "Sat Jan 24 15:13:38 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349642;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-a-1980.bib",
  URL =          "http://www.jstor.org/stable/2982920",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series A
                 (Statistics in Society)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-985X;
                 http://www.jstor.org/journals/09641998.html",
}

@Article{Shieh:1989:BZE,
  author =       "Yeung-Nan Shieh",
  title =        "The {Beckmann--Zipf} effect and plant location under
                 uniform pricing",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "89--92",
  day =          "1",
  month =        jan,
  year =         "1989",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/0165-1765(89)90162-6",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "90A12 (90B05)",
  MRnumber =     "1010312",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0165176589901626",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Thomas:1989:UPR,
  author =       "Jacob K. Thomas",
  title =        "Unusual patterns in reported earnings",
  journal =      j-ACCOUNT-REV,
  volume =       "59",
  number =       "4",
  pages =        "773--787",
  month =        oct,
  year =         "1989",
  CODEN =        "ACRVAS",
  ISSN =         "0001-4826 (print), 1558-7967 (electronic)",
  ISSN-L =       "0001-4826",
  bibdate =      "Fri Feb 15 06:49:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/247861",
  acknowledgement = ack-nhfb,
  fjournal =     "The Accounting Review",
  keywords =     "Benford's Law; distribution of first digits;
                 distribution of second digits",
}

@Article{Xekalaki:1989:APY,
  author =       "E. Xekalaki and J. Panaretos",
  title =        "On the Association of the {Pareto} and the {Yule}
                 Distribution",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "33",
  number =       "1",
  pages =        "191--195",
  month =        "????",
  year =         "1989",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/1133028",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Tue Apr 1 10:40:04 MDT 2014",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/33/1;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/theoryprobabappl.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and its Applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  onlinedate =   "January 1989",
}

@Article{Egghe:1990:RAT,
  author =       "L. Egghe",
  title =        "Research: Applications of the theory of {Bradford}'s
                 {Law} to the calculation of {Leimkuhler's Law} and to
                 the completion of bibliographies",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "41",
  number =       "7",
  pages =        "469--492",
  month =        oct,
  year =         "1990",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199010)41:7<469::AID-ASI1>3.0.CO%3B2-P",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:41 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Egghe:1990:RND,
  author =       "L. Egghe",
  title =        "Research: A note on different {Bradford} multipliers",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "41",
  number =       "3",
  pages =        "204--209",
  month =        apr,
  year =         "1990",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199004)41:3<204::AID-ASI7>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:39 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Jan 1999",
}

@Article{Katsikas:1990:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic dynamics of generating {Markov} partitions and
                 linguistic sequences mimicking {Zipf}'s law",
  journal =      "Nuovo Cimento D (1)",
  volume =       "12",
  number =       "2",
  pages =        "177--195",
  year =         "1990",
  CODEN =        "NCSDDN",
  DOI =          "https://doi.org/10.1007/BF02450454",
  ISSN =         "0392-6737 (print), 1826-9893 (electronic)",
  ISSN-L =       "0392-6737",
  MRclass =      "92A90 (58F13 92A08 94A15)",
  MRnumber =     "1049338 (90m:92114)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Societ{\`a} Italiana di Fisica. Il Nuovo Cimento. D.
                 Serie 1",
}

@InCollection{Nagasaka:1990:BLL,
  author =       "Kenji Nagasaka and Shigeru Kanemitsu and Jau-Shyong
                 Shiue",
  booktitle =    "Number theory, {Vol}.\ {I} ({Budapest}, 1987)",
  title =        "{Benford}'s law: the logarithmic law of first digit",
  volume =       "51",
  publisher =    pub-NORTH-HOLLAND,
  address =      pub-NORTH-HOLLAND:adr,
  pages =        "361--391",
  year =         "1990",
  MRclass =      "11K06",
  MRnumber =     "1058225 (92b:11048)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Colloq. Math. Soc. J{\'a}nos Bolyai",
  acknowledgement = ack-nhfb,
}

@Article{Peritz:1990:BDB,
  author =       "Bluma C. Peritz",
  title =        "A {Bradford} distribution for bibliometrics",
  journal =      j-SCIENTOMETRICS,
  volume =       "18",
  number =       "5--6",
  pages =        "323--329",
  month =        may,
  year =         "1990",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02020148",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:16 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02020148",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Schatte:1990:BLC,
  author =       "Peter Schatte",
  title =        "On {Benford}'s law for continued fractions",
  journal =      j-MATH-NACHR,
  volume =       "148",
  pages =        "137--144",
  year =         "1990",
  CODEN =        "MTMNAQ",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  MRclass =      "11K50 (11K06)",
  MRnumber =     "1127337 (92m:11077)",
  MRreviewer =   "Harald Niederreiter",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
}

@Book{Szekely:1990:PKN,
  author =       "G{\'a}bor J. Sz{\'e}kely",
  title =        "{Paradoxa: klassische und neue {\"U}berraschungen aus
                 Wahrscheinlichkeitsrechnung und mathematischer
                 Statistik}. (German) [{Paradoxes}: traditional and new
                 surprises in probability and mathematical statistics]",
  publisher =    "Deutsch",
  address =      "Thun, Switzerland",
  pages =        "239",
  year =         "1990",
  ISBN =         "3-87144-850-8",
  ISBN-13 =      "978-3-87144-850-8",
  LCCN =         "????",
  bibdate =      "Thu Nov 17 19:26:05 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  note =         "Translation by Ulrike Leitner from the Hungarian
                 original.",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht003363686.pdf;
                 http://www.zentralblatt-math.org/zmath/en/search/?an=0743.60004",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{VandenBroeck:1990:LFB,
  author =       "C. {Van den Broeck} and R. Kawai",
  title =        "Learning in feedforward {Boolean} networks",
  journal =      j-PHYS-REV-A,
  volume =       "42",
  number =       "??",
  pages =        "6210--??",
  day =          "15",
  month =        nov,
  year =         "1990",
  CODEN =        "PLRAAN",
  DOI =          "https://doi.org/10.1103/PhysRevA.42.6210",
  ISSN =         "1050-2947 (print), 1094-1622, 1538-4446, 1538-4519",
  ISSN-L =       "1050-2947",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevA.42.6210",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review A (Atomic, Molecular, and Optical
                 Physics)",
  journal-URL =  "http://pra.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Yeh:1990:ODT,
  author =       "Hsiaw-Chan Yeh",
  title =        "One discrete time series model for fat-tailed integer
                 random variables: {Zipf} process",
  journal =      "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
  volume =       "18",
  number =       "1",
  pages =        "19--33",
  year =         "1990",
  CODEN =        "BIMSDG",
  ISSN =         "0304-9825",
  ISSN-L =       "0304-9825",
  MRclass =      "60J10 (62M10)",
  MRnumber =     "1072827 (91i:60175)",
  MRreviewer =   "Ed McKenzie",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Math. Acad. Sinica",
  fjournal =     "Bulletin of the Institute of Mathematics. Academia
                 Sinica",
}

@Article{Antonini:1991:NUD,
  author =       "Rita Giuliano Antonini",
  title =        "On the Notion of Uniform Distribution Mod $1$",
  journal =      j-FIB-QUART,
  volume =       "29",
  number =       "3",
  pages =        "230--234",
  month =        aug,
  year =         "1991",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:01:34 MDT 2011",
  bibsource =    "http://www.fq.math.ca/29-3.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/29-3/antonini.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
  keywords =     "Benford's Law",
}

@Article{Burke:1991:BLP,
  author =       "John Burke and Eric Kincanon",
  title =        "{Benford}'s law and physical constants: The
                 distribution of initial digits",
  journal =      j-AMER-J-PHYSICS,
  volume =       "59",
  number =       "10",
  pages =        "952--952",
  month =        oct,
  year =         "1991",
  CODEN =        "AJPIAS",
  DOI =          "https://doi.org/10.1119/1.16838",
  ISSN =         "0002-9505 (print), 1943-2909 (electronic)",
  ISSN-L =       "0002-9505",
  bibdate =      "Mon Nov 14 17:31:11 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/1991AmJPh..59..952B;
                 http://ajp.aapt.org/resource/1/ajpias/v59/i10/p952_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Physics",
  journal-URL =  "http://scitation.aip.org/content/aapt/journal/ajp",
}

@Article{Burrell:1991:BDG,
  author =       "Q. L. Burrell",
  title =        "The {Bradford} distribution and the {Gini} index",
  journal =      j-SCIENTOMETRICS,
  volume =       "21",
  number =       "2",
  pages =        "181--194",
  month =        jun,
  year =         "1991",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02017568",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:22 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02017568",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Chen:1991:ZLN,
  author =       "Ye-Sho Chen",
  title =        "{Zipf}'s law in natural languages, programming
                 languages, and command languages: the {Simon--Yule}
                 approach",
  journal =      j-INT-J-SYST-SCI,
  volume =       "22",
  number =       "11",
  pages =        "2299--2312",
  year =         "1991",
  CODEN =        "IJSYA9",
  DOI =          "https://doi.org/10.1080/00207729108910791",
  ISSN =         "0020-7721 (print), 1464-5319 (electronic)",
  ISSN-L =       "0020-7721",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0793.68020",
  abstract =     "Zipf's law and issues in natural languages,
                 programming languages and command languages related to
                 it, are reviewed. We point out the need for a unified
                 theory to resolve the issues. Based on Herbert Simon's
                 creative process for scientific discovery, we evaluate
                 four leading theories of language generation. As a
                 result, the Simon--Yule model of text generation is
                 selected as a promising theory. The implications of the
                 theory related to the issues in natural languages,
                 programming languages and command languages are
                 discussed.",
  acknowledgement = ack-nhfb,
  classmath =    "68N15 (Programming languages) 68T50 (Natural language
                 processing)",
  fjournal =     "International Journal of Systems Science",
  keywords =     "command languages; natural languages; programming
                 languages; Simon-Yule model; text generation; Zipf's
                 law",
}

@Book{Durrett:1991:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Wadsworth and Brooks\slash Cole Advanced Books and
                 Software",
  address =      "Pacific Grove, CA, USA",
  pages =        "ix + 453",
  year =         "1991",
  ISBN =         "0-534-13206-5",
  ISBN-13 =      "978-0-534-13206-4",
  LCCN =         "QA273 .D865 1991",
  bibdate =      "Mon Nov 21 10:06:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$49.95",
  series =       "The Wadsworth and Brooks\slash Cole statistics\slash
                 probability series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 300ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that Durrett has a proof
                 that the $k$-th digit of powers of integers follows
                 Benford's Law.",
  subject =      "Probabilities",
}

@Book{Hardy:1991:DS,
  author =       "G. H. (Godfrey Harold) Hardy",
  title =        "Divergent series",
  publisher =    "Chelsea Pub. Co.",
  address =      "New York, NY, USA",
  edition =      "Second",
  pages =        "xvi + 396",
  year =         "1991",
  ISBN =         "0-8284-0334-1",
  ISBN-13 =      "978-0-8284-0334-4",
  LCCN =         "QA295 .H29 1991",
  bibdate =      "Wed Nov 16 08:17:27 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1877--1947",
  remark =       "Unaltered reprint of \cite{Hardy:1949:DS}, despite
                 label of second edition.",
  subject =      "Divergent series",
}

@Article{Katsikas:1991:CDG,
  author =       "A. A. Katsikas and J. S. Nicolis",
  title =        "Chaotic Dynamics of Generating {Markov} Partitions,
                 and Linguistic Sequences Mimicking {Zipf}'s Law",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "565",
  pages =        "335--??",
  year =         "1991",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon May 13 08:51:55 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Schatte:1991:NBL,
  author =       "P. Schatte and K. Nagasaka",
  title =        "A note on {Benford}'s law for second order linear
                 recurrences with periodical coefficients",
  journal =      j-Z-ANAL-ANWEND,
  volume =       "10",
  number =       "2",
  pages =        "251--254",
  year =         "1991",
  CODEN =        "????",
  ISSN =         "0232-2064 (print), 1661-4534 (electronic)",
  ISSN-L =       "0232-2064",
  MRclass =      "11K31",
  MRnumber =     "1155374 (93b:11101)",
  MRreviewer =   "F. Schweiger",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Analysis und ihre Anwendungen}",
}

@Article{Schatte:1991:ULI,
  author =       "P. Schatte",
  title =        "On a uniform law of the iterated logarithm for sums
                 mod {$1$} and {Benford}'s law",
  journal =      "Litovsk. Mat. Sb.",
  volume =       "31",
  number =       "1",
  pages =        "205--217",
  year =         "1991",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/BF00972327",
  ISSN =         "0132-2818",
  ISSN-L =       "0132-2818",
  MRclass =      "60F15 (11K99)",
  MRnumber =     "1161363 (93g:60067)",
  MRreviewer =   "O. P. Stackelberg",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Lietuvos TSR Moksl\polhk u Akademija. Lietuvos TSR
                 Auk\v stosios Mokyklos. Lietuvos Matematikos Rinkinys.
                 Akademiya Nauk Litovsko{\u\i} SSR. Vysshie Uchebnye
                 Zavedeniya Litovsko{\u\i} SSR. Litovski\u\i\
                 Matematicheski{\u\i} Sbornik",
  xxnote =       "Check pages: reprinted in two version of this
                 journal??",
}

@Book{Schroeder:1991:FCP,
  author =       "Manfred Schroeder",
  title =        "Fractals, Chaos, Power Laws",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  pages =        "xviii + 429",
  year =         "1991",
  ISBN =         "0-671-74217-5, 0-7167-2136-8, 0-7167-2357-3",
  ISBN-13 =      "978-0-671-74217-1, 978-0-7167-2136-9,
                 978-0-7167-2357-8",
  LCCN =         "QD921 .S3 1990",
  bibdate =      "Wed Dec 15 10:41:35 1993",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/shannon-claude-elwood.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "Reveals the extraordinary dimensions of new
                 mathematical insights about the nature of physical
                 reality; explores the powerful applications of these
                 symmetry concepts in physics, chemistry, music, and the
                 visual arts. Includes such areas as deterministic chaos
                 and strange attractors, iterated mappings, nonlinear
                 dynamics, Cayley trees, cellular automata, random
                 fractals and related topics.",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Introduction \\
                 Similarity and dissimilarity \\
                 Self-similarity --- discrete, continuous, strict, and
                 otherwise \\
                 Power laws: endless sources of self-similarity \\
                 Noises: white, pink, brown, and black \\
                 Brownian motion, gambling losses, and intergalactic
                 voids: random fractals par excellence \\
                 Cantor sets: self-similarity and arithmetic dust \\
                 Fractals in higher dimensions and a digital sundial \\
                 Multifractals: intimately intertwined fractals \\
                 Some practical fractals and their measurement \\
                 Iteration, strange mappings, and a billion digits for
                 $\pi$ \\
                 A self-similar sequence, the logistic parabola, and
                 symbolic dynamics \\
                 A forbidden symmetry, Fibonacci's rabbits, and a new
                 state of matter \\
                 Periodic and quasiperiodic structures in space --- the
                 route to spatial chaos \\
                 Percolation: from forest fires to epidemics \\
                 Phase transitions and renormalization \\
                 Cellular automata",
  tableofcontents = "Preface / xiii \\
                 1: Introduction / 1 \\
                 Einstein, Pythagoras, and Simple Similarity / 3 \\
                 A Self-Similar Array of Self-Preserving Queens / 4 \\
                 A Self-Similar Snowflake / 7 \\
                 A New Dimension for Fractals / 9 \\
                 A Self-Similar Tiling and a ``Non-Euclidean'' Paradox /
                 13 \\
                 At the Gates of Cantor's Paradise / 15 \\
                 The Sierpinski Gasket / 17 \\
                 Sir Pinski's Game and Deterministic Chaos / 20 \\
                 Three Bodies Cause Chaos / 25 \\
                 Strange Attractors, Their Basins, and a Chaos Game 2 /
                 7 \\
                 Percolating Random Fractals / 30 \\
                 Power Laws: from Alvarez to Zipf / 33 \\
                 Newton's Iteration and How to Abolish Two-Nation
                 Boundaries / 38 \\
                 Could Minkowski Hear the Shape of a Drum? / 40 \\
                 Discrete Self-Similarity: Creases and Center Folds / 45
                 \\
                 Golden and Silver Means and Hyperbolic Chaos / 49 \\
                 Winning at Fibonacci Nim / 53 \\
                 Self-Similar Sequences from Square Lattices / 55 \\
                 John Horton Conway's ``Death Bet'' / 57 \\
                 2: Similarity and Dissimilarity / 61 \\
                 More Than One Scale / 61 \\
                 To Scale or Not to Scale: A Bit of Biology and
                 Astrophysics / 63 \\
                 Similarity in Physics: Some Astounding Consequences /
                 66 \\
                 Similarity in Concert Halls, Microwaves, and
                 Hydrodynamics / 68 \\
                 Scaling in Psychology / 70 \\
                 Acousticians, Alchemy, and Concert Halls / 72 \\
                 Preference and Dissimilarity: Concert Halls Revisited /
                 74 \\
                 3: Self-Similarity --- Discrete, Continuous, Strict,
                 and Otherwise / 81 \\
                 The Logarithmic Spiral, Cutting Knives, and Wideband
                 Antennas / 89 \\
                 Some Simple Cases of Self-Similarity / 93 \\
                 Weierstrass Functions and a Musical Paradox / 96 \\
                 More Self-Similarity in Music: The Tempered Scales of
                 Bach / 99 \\
                 The Excellent Relations between the Primes 3, 5, and 7
                 / 102 \\
                 4: Power Laws: Endless Sources of Self-Similarity / 103
                 \\
                 The Sizes of Cities and Meteorites / 103 \\
                 A Fifth Force of Attraction / 105 \\
                 Free of Natural Scales / 107 \\
                 Bach Composing on All Scales / 107 \\
                 Birkhoff's Aesthetic Theory / 109 \\
                 Heisenberg's Hyperbolic Uncertainty Principle / 112 \\
                 Fractional Exponents / 115 \\
                 The Peculiar Distribution of the First Digit / 116 \\
                 The Diameter Exponents of Trees, Rivers, Arteries, and
                 Lungs / 117 \\
                 5: Noises: White, Pink, Brown, and Black / 121 \\
                 Pink Noise / 122 \\
                 Self-Similar Trends on the Stock Market / 126 \\
                 Black Noises and Nile Floods / 129 \\
                 Warning: World Warming / 131 \\
                 Fractional Integration: A Modem Tool / 131 \\
                 Brownian Mountains / 133 \\
                 Radon Transform and Computer Tomography / 134 \\
                 Fresh and Tired Mountains / 135 \\
                 6: Brownian Motion, Gambling Losses, and Intergalactic
                 Voids: Random Fractals Par Excellence / 139 \\
                 The Brownian Beast Tamed / 140 \\
                 Brownian Motion as a Fractal / 141 \\
                 How Many Molecules? / 143 \\
                 The Spectrum of Brownian Motion / 144 \\
                 The Gambler's Ruin, Random Walks, and Information
                 Theory / 145 \\
                 Counterintuition Runs Rampant in Random Runs / 146 \\
                 More Food for Fair Thought / 147 \\
                 The St. Petersburg Paradox / 148 \\
                 Shannon's Outguessing Machine / 149 \\
                 The Classical Mechanics of Roulette and Shannon's
                 Channel Capacity / 150 \\
                 The Clustering of Poverty and Galaxies / 152 \\
                 Levy Flights through the Universe / 155 \\
                 Paradoxes from Probabilistic Power Laws / 155 \\
                 Invariant Distributions: Gauss, Cauchy, and Beyond /
                 157 \\
                 7: Cantor Sets: Self-Similarity and Arithmetic Dust /
                 161 \\
                 A Comer of Cantor's Paradise / 161 \\
                 Cantor Sets as Invariant Sets / 165 \\
                 Symbolic Dynamics and Deterministic Chaos / 166 \\
                 Devil's Staircases and a Pinball Machine / 167 \\
                 Mode Locking in Swings and Clocks / 171 \\
                 The Frustrated Manhattan Pedestrian / 172 \\
                 Arnold Tongues 17 / 4 \\
                 8: Fractals in Higher Dimensions and a Digital Sundial
                 / 177 \\
                 Cartesian Products of Cantor Sets / 177 \\
                 A Leaky Gasket, Soft Sponges, and Swiss Cheeses / 178
                 \\
                 A Cantor-Set Sundial / 181 \\
                 Fat Fractals / 183 \\
                 9: Multifractals: Intimately Intertwined Fractals / 187
                 \\
                 The Distributions of People and Ore / 187 \\
                 Self-Affine Fractals without Holes / 190 \\
                 The Multifractal Spectrum: Turbulence and
                 Diffusion-Limited Aggregation / 193 \\
                 Viscous Fingering / 199 \\
                 Multifractals on Fractals / 200 \\
                 Fractal Dimensions from Generalized Entropies / 203 \\
                 The Relation between the Multifractal Spectrum
                 $f(\alpha)$ and the Mass Exponents $(q)$ / 205 \\
                 Strange Attractors as Multifractals / 206 \\
                 A Greedy Algorithm for Unfavorable Odds / 207 \\
                 10: Some Practical Fractals and Their Measurement / 211
                 \\
                 Dimensions from Box Counting / 213 \\
                 The Mass Dimension / 215 \\
                 The Correlation Dimension / 220 \\
                 Infinitely Many Dimensions / 220 \\
                 The Determination of Fractal Dimensions from Time
                 Series / 223 \\
                 Abstract Concrete / 224 \\
                 Fractal Interfaces Enforce Fractional Frequency
                 Exponents / 225 \\
                 The Fractal Dimensions of Fracture Surfaces / 230 \\
                 The Fractal Shapes of Clouds and Rain Areas / 231 \\
                 Cluster Agglomeration / 232 \\
                 Diffraction from Fractals / 233 \\
                 11: Iteration, Strange Mappings, and a Billion Digits
                 for Pi / 237 \\
                 Looking for Zeros and Encountering Chaos / 239 \\
                 The Strange Sets of Julia / 243 \\
                 A Multifractal Julia Set / 245 \\
                 The Beauty of Broken Linear Relationships / 249 \\
                 The Baker's Transformation and Digital Musical Chairs /
                 251 \\
                 Arnol'd's Cat Map / 253 \\
                 A Billion Digits for $\pi$ / 257 \\
                 Bushes and Flowers from Iterations / 259 \\
                 12: A Self-Similar Sequence, the Logistic Parabola, and
                 Symbolic Dynamics / 263 \\
                 Self-Similarity from the Integers / 264 \\
                 The Logistic Parabola and Period Doubling / 268 \\
                 Self-Similarity in the Logistic Parabola / 272 \\
                 The Scaling of the Growth Parameter / 274 \\
                 Self-Similar Symbolic Dynamics / 277 \\
                 Periodic Windows Embedded in Chaos / 279 \\
                 The Parenting of New Orbits / 282 \\
                 The Calculation of the Growth Parameters for Different
                 Orbits / 286 \\
                 Tangent Bifurcations, Intermittency, and I/f Noise /
                 289 \\
                 A Case of Complete Chaos / 291 \\
                 The Mandelbrot Set / 295 \\
                 The Julia Sets of the Complex Quadratic Map / 297 \\
                 13: A Forbidden Symmetry, Fibonacci's Rabbits, and a
                 New State of Matter / 301 \\
                 The Forbidden Fivefold Symmetry / 301 \\
                 Long-Range Order from Neighborly Interactions / 304 \\
                 Generation of the Rabbit Sequence from the Fibonacci
                 Number System / 307 \\
                 The Self-Similar Spectrum of the Rabbit Sequence / 308
                 \\
                 Self-Similarity in the Rabbit Sequence / 310 \\
                 A One-Dimensional Quasiperiodic Lattice / 310 \\
                 Self-Similarity from Projections / 311 \\
                 More Forbidden Symmetries / 315 \\
                 14: Periodic and Quasiperiodic Structures in Space ---
                 The route to Spatial Chaos / 319 \\
                 Periodicity and Quasiperiodicity in Space / 320 \\
                 The Devil's Staircase for Ising Spins / 321 \\
                 Quasiperiodic Spatial Distributions / 322 \\
                 Beatty Sequence Spins / 325 \\
                 The Scaling Laws for Quasiperiodic Spins / 329 \\
                 Self-Similar Winding Numbers / 330 \\
                 Circle Maps and Arnold Tongues / 331 \\
                 Mediants, Farey Sequences, and the Farey Tree / 334 \\
                 The Golden-Mean Route to Chaos / 340 \\
                 15: Percolation: From Forest Fires to Epidemics / 345
                 \\
                 Critical Conflagration on a Square Lattice / 346 \\
                 Universality / 350 \\
                 The Critical Density / 353 \\
                 The Fractal Perimeters of Percolation / 353 \\
                 Finite-Size Scaling / 354 \\
                 16: Phase Transitions and Renormalization / 357 \\
                 A First-Order Markov Process / 357 \\
                 Self-Similar and Non-Self-Similar Markov Processes /
                 358 \\
                 The Scaling of Markov Output's / 360 \\
                 Renormalization and Hierarchical Lattices / 362 \\
                 The Percolation Threshold of the Bethe Lattice / 363
                 \\
                 A Simple Renormalization / 367 \\
                 17: Cellular Automata / 371 \\
                 The Game of Life / 373 \\
                 Cellular Growth and Decay / 375 \\
                 Biological Pattern Formation / 382 \\
                 Self-Similarity from a Cellular Automaton / 383 \\
                 A Catalytic Converter as a Cellular Automaton / 386 \\
                 Pascal's Triangle Modulo $N$ / 387 \\
                 Bak's Self-Organized Critical Sandpiles / 389 \\
                 Appendix / 391 \\
                 References / 395 \\
                 Author Index / 411 \\
                 Subject Index / 417",
}

@Article{Trubnikov:1991:SDZ,
  author =       "B. A. Trubnikov and I. A. Rumynski{\u\i}",
  title =        "A simple derivation of the {Zipf--Krylov} law for
                 words and the possibility of its ``evolution''
                 interpretation",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "321",
  number =       "2",
  pages =        "270--275",
  year =         "1991",
  CODEN =        "DANKAS",
  ISSN =         "0002-3264",
  ISSN-L =       "0002-3264",
  MRclass =      "00A69 (92K20)",
  MRnumber =     "1153554",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Doklady Akademii Nauk SSSR",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}

@Article{Basu:1992:RHD,
  author =       "Aparna Basu",
  title =        "Research: Hierarchical distributions and {Bradford's
                 Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "7",
  pages =        "494--500",
  month =        aug,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<494::AID-ASI4>3.0.CO%3B2-F",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:51 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@TechReport{Busta:1992:TRN,
  author =       "B. Busta and R. Sundheim",
  title =        "Tax return numbers tend to obey {Benford}'s law",
  type =         "Working Paper",
  number =       "W93-106-94",
  institution =  "Center for Business Research, St. Cloud State
                 University",
  address =      "St. Cloud, MN, USA",
  year =         "1992",
  bibdate =      "Sat Feb 16 17:29:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Dehaene:1992:CLR,
  author =       "Stanislas Dehaene and Jacques Mehler",
  title =        "Cross-linguistic regularities in the frequency of
                 number words",
  journal =      j-COGNITION,
  volume =       "43",
  number =       "1",
  pages =        "1--29",
  year =         "1992",
  CODEN =        "CGTNAU",
  DOI =          "https://doi.org/10.1016/0010-0277(92)90030-L",
  ISSN =         "0010-0277 (print), 1873-7838 (electronic)",
  ISSN-L =       "0010-0277",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/001002779290030L",
  abstract =     "We examine the frequency of numerals and ordinals in
                 seven different languages and/or cultures. Many
                 cross-cultural and cross-linguistic patterns are
                 identified. The most striking is a decrease of
                 frequency with numerical magnitude, with local
                 increases for reference numerals such as 10, 12, 15,
                 20, 50 or 100. Four explanations are considered for
                 this effect: sampling artifacts, notational
                 regularities, environmental biases and psychological
                 limitations on number representations. The
                 psychological explanation, which appeals to a
                 Fechnerian encoding of numerical magnitudes and to the
                 existence of numerical points of reference, accounts
                 for most of the data. Our finding also has practical
                 importance since it reveals the frequent confound of
                 two experimental variables: numerical magnitude and
                 numeral frequency.",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognition",
  keywords =     "Benford's Law",
}

@Article{Goto:1992:SEB,
  author =       "Kazuo Got{\^o}",
  title =        "Some examples of {Benford} sequences",
  journal =      "Math. J. Okayama Univ.",
  volume =       "34",
  pages =        "225--232 (1994)",
  year =         "1992",
  CODEN =        "MJOKAP",
  ISSN =         "0030-1566",
  ISSN-L =       "0030-1566",
  MRclass =      "11K36",
  MRnumber =     "1272624 (95c:11097)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Journal of Okayama University",
}

@Article{Gunther:1992:PCZ,
  author =       "R. G{\"u}nther and B. Schapiro and P. Wagner",
  title =        "Physical complexity and {Zipf}'s law",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "31",
  number =       "3",
  pages =        "525--543",
  year =         "1992",
  CODEN =        "IJTPBM",
  DOI =          "https://doi.org/10.1007/BF00740003",
  ISSN =         "0020-7748 (print), 1572-9575 (electronic)",
  ISSN-L =       "0020-7748",
  MRclass =      "58F40",
  MRnumber =     "1154668 (92k:58252)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Theoretical Physics",
  journal-URL =  "http://link.springer.com/journal/10773",
}

@Article{Jech:1992:LDL,
  author =       "Thomas Jech",
  title =        "The logarithmic distribution of leading digits and
                 finitely additive measures",
  journal =      j-DISCRETE-MATH,
  volume =       "108",
  number =       "1--3",
  pages =        "53--57",
  month =        "????",
  year =         "1992",
  CODEN =        "DSMHA4",
  ISSN =         "0012-365X (print), 1872-681X (electronic)",
  ISSN-L =       "0012-365X",
  bibdate =      "Fri Nov 18 12:12:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete Mathematics",
}

@Article{Lagarias:1992:PTS,
  author =       "J. C. Lagarias and A. Weiss",
  title =        "The $ 3 x + 1 $ Problem: Two Stochastic Models",
  journal =      j-ANN-APPL-PROBAB,
  volume =       "2",
  number =       "1",
  pages =        "229--261",
  month =        feb,
  year =         "1992",
  CODEN =        "????",
  ISSN =         "1050-5164",
  ISSN-L =       "1050-5164",
  bibdate =      "Fri Jun 6 11:35:34 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/annapplprobab.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.aoap/1177005779",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Applied Probability",
  journal-URL =  "http://projecteuclid.org/all/euclid.aoap/;
                 http://www.jstor.org/journals/10505164.html",
}

@Article{Li:1992:RTE,
  author =       "W. Li",
  title =        "Random texts exhibit {Zipf}'s-law-like word frequency
                 distribution",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "38",
  number =       "6",
  pages =        "1842--1845",
  month =        "????",
  year =         "1992",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.165464",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Fri Nov 18 12:32:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
}

@Article{Longfellow:1992:LER,
  author =       "Charles A. {Longfellow, Jr.}",
  title =        "Letters to the {Editor}: Regarding {``Lotka's Law and
                 the Kolmogorov--Smirnov Test: An Error in
                 Calculation''}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "7",
  pages =        "518--518",
  month =        aug,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199208)43:7<518::AID-ASI7>3.0.CO%3B2-#",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:51 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  note =         "See \cite{Loughner:1992:BCL}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Loughner:1992:BCL,
  author =       "William Loughner",
  title =        "Brief Communications: {Lotka's Law} and the
                 {Kolmogorov--Smirnov} test: an error in calculation",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "2",
  pages =        "149--150",
  month =        mar,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199203)43:2<149::AID-ASI4>3.0.CO%3B2-Y",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  note =         "See comment \cite{Longfellow:1992:LER}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@PhdThesis{Nigrini:1992:DIE,
  author =       "Mark John Nigrini",
  title =        "The detection of income tax evasion through an
                 analysis of digital distributions",
  type =         "{Ph.D.} Dissertation",
  school =       "Department of Accounting\slash Business Law,
                 University of Cincinnati",
  address =      "Cincinnati, OH, USA",
  pages =        "xvi + 309",
  day =          "28",
  month =        aug,
  year =         "1992",
  bibdate =      "Sat Nov 12 15:47:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/docview/304052348",
  acknowledgement = ack-nhfb,
  advisor =      "Wallace R. Wood",
  remark =       "There are more than 230 mentions of Frank Benford, and
                 8 of Simon Newcomb, but no mention of Pareto or Zipf.",
}

@Article{Rousseau:1992:RBR,
  author =       "Ronald Rousseau",
  title =        "Research: Breakdown of the robustness property of
                 {Lotka's Law}: the case of adjusted counts for
                 multiauthorship attribution",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "43",
  number =       "10",
  pages =        "645--647",
  month =        dec,
  year =         "1992",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199212)43:10<645::AID-ASI1>3.0.CO%3B2-X",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:48 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Sanders:1992:PPU,
  author =       "Robert Sanders",
  title =        "The {Pareto Principle}: its Use and Abuse",
  journal =      j-J-PROD-BRAND-MANAG,
  volume =       "1",
  number =       "2",
  pages =        "37--40",
  month =        "????",
  year =         "1992",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/10610429210036762",
  ISSN =         "1061-0421",
  ISSN-L =       "1061-0421",
  bibdate =      "Fri Nov 25 06:50:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Product \& Brand Management",
  keywords =     "80/20 rule",
}

@Article{Too:1992:UDM,
  author =       "Yeu-Hua Too",
  title =        "On the uniform distribution modulo one of some
                 log-like sequences",
  journal =      "Proceedings of the Japan Academy, Series A.
                 Mathematical Sciences",
  volume =       "68",
  number =       "9",
  pages =        "269--272",
  month =        "????",
  year =         "1992",
  DOI =          "https://doi.org/10.3792/pjaa.68.269",
  ISSN =         "0021-4280",
  ISSN-L =       "0021-4280",
  bibdate =      "Mon Feb 18 06:55:06 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.pja/1195511634",
  acknowledgement = ack-nhfb,
}

@Article{Trachtenberg:1992:WFR,
  author =       "M. Trachtenberg",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software",
  journal =      j-IEEE-TRANS-RELIAB,
  volume =       "41",
  number =       "3",
  pages =        "386--389",
  year =         "1992",
  CODEN =        "IEERAJ",
  DOI =          "https://doi.org/10.1109/24.159803",
  ISSN =         "0018-9529 (print), 1558-1721 (electronic)",
  ISSN-L =       "0018-9529",
  bibdate =      "Sat Nov 12 10:50:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0825.68222",
  acknowledgement = ack-nhfb,
  classmath =    "68M15 (Reliability and testing of computer systems)
                 68N01 (General)",
  fjournal =     "IEEE Transactions on Reliability",
}

@Article{Anonymous:1993:WFR,
  author =       "Anonymous",
  title =        "Why failure rates observe {Zipf}'s law in operational
                 software: {M. Trachtenberg. IEEE Transactions on
                 Reliability, {\bf 41}(3), 386 (1992)}",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "33",
  number =       "13",
  pages =        "2062--2062",
  month =        oct,
  year =         "1993",
  CODEN =        "MCRLAS",
  DOI =          "https://doi.org/10.1016/0026-2714(93)90406-O",
  ISSN =         "0026-2714 (print), 1872-941X (electronic)",
  ISSN-L =       "0026-2714",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/002627149390406O",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Zipf's Law",
}

@Article{Buck:1993:IBF,
  author =       "B. Buck and A. C. Merchant and S. M. Perez",
  title =        "An illustration of {Benford}'s first digit law using
                 alpha decay half lives",
  journal =      j-EUR-J-PHYS,
  volume =       "14",
  number =       "2",
  pages =        "59--63",
  month =        "????",
  year =         "1993",
  CODEN =        "EJPHD4",
  DOI =          "https://doi.org/10.1088/0143-0807/14/2/003",
  ISSN =         "0143-0807 (print), 1361-6404 (electronic)",
  ISSN-L =       "0143-0807",
  bibdate =      "Mon Nov 14 17:32:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/1993EJPh...14...59B",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/0143-0807/",
}

@Article{Christian:1993:NES,
  author =       "C. W. Christian and S. Gupta",
  title =        "New Evidence on ``Secondary Evasion''",
  journal =      "Journal of the {American Taxation Association}",
  volume =       "15",
  number =       "??",
  pages =        "72--93",
  month =        "????",
  year =         "1993",
  ISSN =         "0198-9073 (print), 1558-8017 (electronic)",
  ISSN-L =       "0198-9073",
  bibdate =      "Thu Oct 13 06:50:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Amer. Tax. Assoc.",
  fjournal =     "Journal of the {American Taxation Association}",
  journal-URL =  "http://aaajournals.org/loi/atax",
  remark =       "No journal issues online before 1999.",
}

@Article{Deakin:1993:ADB,
  author =       "Michael A. B. Deakin",
  title =        "Another derivation of {Benford}'s law",
  journal =      j-AUSTRALIAN-MATH-SOC-GAZ,
  volume =       "20",
  number =       "5",
  pages =        "162--163",
  year =         "1993",
  CODEN =        "????",
  ISSN =         "0311-0729 (print), 1326-2297 (electronic)",
  ISSN-L =       "0311-0729",
  MRclass =      "11K36",
  MRnumber =     "1268513 (95j:11072)",
  MRreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Australian Mathematical Society Gazette",
  journal-URL =  "http://www.austms.org.au/gazette",
}

@Article{Nigrini:1993:CBL,
  author =       "Mark Nigrini",
  title =        "Can {Benford's Law} be used in Forensic Accounting?",
  journal =      "The Balance Sheet",
  volume =       "??",
  number =       "??",
  pages =        "7--8",
  month =        jun,
  year =         "1993",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 21 22:03:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Oluic-Vukovic:1993:LEW,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "Letters to the {Editor}: Why has {Bradford's Law} been
                 an elusive phenomenon so far?",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "44",
  number =       "3",
  pages =        "182--183",
  month =        apr,
  year =         "1993",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199304)44:3<182::AID-ASI9>3.0.CO%3B2-S",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:54 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@TechReport{Stewart:1993:LAN,
  author =       "Ian Stewart",
  title =        "The law of anomalous numbers",
  type =         "Working paper",
  institution =  "Mathematics Institute, University of Warwick",
  address =      "Warwick, UK",
  year =         "1993",
  bibdate =      "Fri Mar 22 09:15:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Published in Spektrum der Wissenschaft (April 1994)",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@TechReport{Sundheim:1993:FNT,
  author =       "R. Sundheim and B. Busta",
  title =        "{Fibonacci} numbers tend to obey {Benford's Law}: an
                 extension of {Wlodarski} and {Sentance}",
  type =         "Working Paper",
  institution =  "St. Cloud State University",
  address =      "St. Cloud, MN, USA",
  month =        "????",
  year =         "1993",
  bibdate =      "Mon Feb 18 06:37:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sury:1993:FPD,
  author =       "B. Sury",
  title =        "Fractional parts of $ \log p $ and a digit function",
  journal =      j-EXPO-MATH,
  volume =       "11",
  number =       "4",
  pages =        "381--384",
  month =        "????",
  year =         "1993",
  DOI =          "????",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  bibdate =      "Mon Feb 18 06:39:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  ZMnumber =     "0787.11003",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
  keywords =     "decimal expansion; sum of digits",
  ZMclass =      "11A63 (Radix representation; digital problems)",
  ZMreviewer =   "G. Larcher (Salzburg)",
}

@Article{Wolf:1993:PHJ,
  author =       "Joel L. Wolf and Philip S. Yu and John Turek and
                 Daniel M. Dias",
  title =        "A parallel hash join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "12",
  pages =        "1355--1371",
  month =        dec,
  year =         "1993",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.250117",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM T. J. Watson Research Cent",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "721.1; 722.4; 723.1; 723.2; 723.3; 921.4; C4240P
                 (Parallel programming and algorithm theory); C4250
                 (Database theory); C6160D (Relational DBMS)",
  corpsource =   "IBM Thomas J. Watson Res. Center, Yorktown Heights,
                 NY, USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; combinatorial; Combinatorial mathematics;
                 Combinatorial optimization; Complex queries; complex
                 queries; Computational complexity; Data handling; Data
                 skew; data skew; database theory; hash; Hash joins;
                 hashing; heuristic optimization; hierarchical; join
                 column; joins; load balancing; Load balancing;
                 optimization; parallel algorithms; parallel hash join
                 algorithm; Parallel processing systems; Program
                 processors; Query languages; query processing;
                 Relational database systems; relational databases;
                 resource allocation; scheduling; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Wolf:1993:PSM,
  author =       "Joel L. Wolf and Daniel M. Dias and Philip S. Yu",
  title =        "Parallel sort merge join algorithm for managing data
                 skew",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "4",
  number =       "1",
  pages =        "70--86",
  month =        jan,
  year =         "1993",
  CODEN =        "ITDSEO",
  DOI =          "https://doi.org/10.1109/71.205654",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Fri Apr 11 15:20:39 MDT 1997",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "IBM",
  affiliationaddress = "Yorktown Heights, NY, USA",
  classification = "723.1; 723.3; 921.5; C4240P (Parallel programming
                 and algorithm theory); C4250 (Database theory); C6130
                 (Data handling techniques); C6160B (Distributed DBMS);
                 C6160D (Relational DBMS)",
  corpsource =   "IBM T. J. Watson Res. Center. Yorktown Heights, NY,
                 USA",
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
  journalabr =   "IEEE Trans Parallel Distrib Syst",
  keywords =     "Algorithms; Computer systems programming; Data skew;
                 data skew management; distributed databases; Divide and
                 conquer approach; divide-and-conquer; join phases; load
                 balancing; merging; multiple processors;
                 Multiprocessing programs; Optimization; parallel;
                 Parallel algorithms; parallel algorithms; Parallel sort
                 merge join algorithm; parallelizable optimization
                 algorithm; phase; Query processing; relational algebra;
                 Relational database systems; relational databases;
                 scheduling; Scheduling; sort merge join algorithm; sort
                 phase; sorting; Sorting; transfer phase; Zipf-like
                 distribution",
  treatment =    "T Theoretical or Mathematical",
}

@Book{Arthur:1994:IRP,
  author =       "W. Brian Arthur",
  title =        "Increasing returns and path dependence in the
                 economy",
  publisher =    pub-U-MICHIGAN,
  address =      pub-U-MICHIGAN:adr,
  pages =        "xx + 201",
  year =         "1994",
  ISBN =         "0-472-09496-3, 0-472-06496-7 (paperback)",
  ISBN-13 =      "978-0-472-09496-7, 978-0-472-06496-0 (paperback)",
  LCCN =         "HD69.S5 A77 1994",
  bibdate =      "Wed Feb 27 07:08:40 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "With a foreword by Kenneth J. Arrow.",
  series =       "Economics, cognition, and society",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economies of scale; Mathematical models; Economic
                 development; Economics, Mathematical",
}

@Article{Basu:1994:LEE,
  author =       "Aparna Basu",
  title =        "Letters to the {Editor}: The elusive phenomenon of
                 {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "45",
  number =       "1",
  pages =        "59--60",
  month =        jan,
  year =         "1994",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199401)45:1<59::AID-ASI8>3.0.CO%3B2-F",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:03:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Bookstein:1994:TMD,
  author =       "A. Bookstein",
  title =        "Towards a multi-disciplinary {Bradford Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "30",
  number =       "1",
  pages =        "353--361",
  month =        may,
  year =         "1994",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02017233",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Thu Sep 3 07:35:17 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02017233",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Boyle:1994:AFS,
  author =       "Jeff Boyle",
  title =        "An application of {Fourier} series to the most
                 significant digit problem",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "101",
  number =       "9",
  pages =        "879--886",
  month =        nov,
  year =         "1994",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "60F99",
  MRnumber =     "1 300 493",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Egghe:1994:RSF,
  author =       "L. Egghe",
  title =        "Research: Special features of the author--publication
                 relationship and a new explanation of {Lotka's Law}
                 based on convolution theory",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "45",
  number =       "6",
  pages =        "422--427",
  month =        jul,
  year =         "1994",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199407)45:6<422::AID-ASI8>3.0.CO%3B2-C",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:01 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Fuchs:1994:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers]",
  journal =      "Rendiconti della Accademia Nazionale delle Scienze
                 detta dei XL. Serie V. Memorie di Matem{\`a}tica",
  volume =       "18",
  number =       "1",
  pages =        "81--87",
  month =        "????",
  year =         "1994",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  ZMnumber =     "0838.11004",
  acknowledgement = ack-nhfb,
  ajournal =     "Rend. Accad. Naz. Sci. XL, V. Ser., Mem. Mat.",
  keywords =     "asymptotic densities; logarithmic density; primes;
                 relative densities",
  language =     "French",
  xxjournal =    "Rend. Acad. Naz. Sci. Detta",
  xxvolume =     "XL",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K16
                 (Normal numbers, etc.)",
  ZMreviewer =   "I. Z. Ruzsa (Budapest)",
}

@Article{Ley:1994:TPB,
  author =       "Eduadro Ley and Hal R. Varian",
  title =        "Are there psychological barriers in the {Dow--Jones}
                 index?",
  journal =      j-APPL-FINANC-ECON,
  volume =       "4",
  number =       "3",
  pages =        "217--224",
  month =        "????",
  year =         "1994",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/758526902",
  ISSN =         "0960-3107 (print), 1466-4305 (electronic)",
  ISSN-L =       "0960-3107",
  bibdate =      "Sat Feb 16 18:29:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/758526902",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Financial Economics",
}

@Article{Mantegna:1994:LFN,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C. K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Linguistic Features of Noncoding {DNA} Sequences",
  journal =      j-PHYS-REV-LET,
  volume =       "73",
  number =       "??",
  pages =        "3169--??",
  day =          "5",
  month =        dec,
  year =         "1994",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.73.3169",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comment \cite{Voss:1996:CLF} and reply
                 \cite{Mantegna:1996:MAR}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.73.3169",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Nigrini:1994:UDF,
  author =       "Mark J. Nigrini",
  title =        "Using digital frequencies to detect fraud",
  journal =      "The White Paper",
  volume =       "??",
  number =       "2",
  pages =        "3--6",
  month =        apr # "\slash " # may,
  year =         "1994",
  bibdate =      "Sat Feb 16 18:53:08 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "The White Paper is the precursor to Fraud Magazine; I
                 cannot find it in the Library of Congress catalog.",
}

@Article{Pedrotti:1994:ALU,
  author =       "A. Pedrotti",
  title =        "Analysis of a list-update strategy",
  journal =      j-INFO-PROC-LETT,
  volume =       "52",
  number =       "3",
  pages =        "115--121",
  day =          "11",
  month =        nov,
  year =         "1994",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "Compendex database;
                 http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  affiliation =  "Scuola Normale Superiore",
  affiliationaddress = "Pisa, Italy",
  classification = "721.1; 723.2; 921.6; 922.1; 922.2; C4240C
                 (Computational complexity); C6130 (Data handling
                 techniques)",
  corpsource =   "Scuola Normale Superiore, Pisa, Italy",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  journalabr =   "Inf Process Lett",
  keywords =     "Algorithms; analysis of algorithms; average-case
                 complexity; BIT; competitive algorithms; Computational
                 complexity; computational complexity; convergence;
                 Convergence of numerical methods; Data handling;
                 Function evaluation; Heuristic methods; list
                 processing; list update; Markov chains; Move to front
                 algorithm; move-to-front; Probability; Random number
                 generation; searching; Theorem proving; transpose;
                 Zipf's law",
  treatment =    "T Theoretical or Mathematical",
}

@Article{Sheppard:1994:TNA,
  author =       "Lee A. Sheppard",
  title =        "{Tax Notes} audits the {Clintons}",
  journal =      "Tax Notes Today",
  volume =       "??",
  number =       "??",
  pages =        "18--23",
  day =          "4",
  month =        apr,
  year =         "1994",
  bibdate =      "Fri Mar 22 09:13:48 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.bankler.com/docs/Tax_Notes_Audits_the_Clintons.pdf",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Tritch:1994:MAC,
  author =       "Teresa Tritch and Mary L. Sprouse",
  title =        "{Money} audits the {Clintons}",
  journal =      "Money Magazine",
  volume =       "??",
  number =       "??",
  pages =        "84--98",
  day =          "1",
  month =        apr,
  year =         "1994",
  bibdate =      "Fri Mar 22 09:16:28 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://money.cnn.com/magazines/moneymag/moneymag_archive/1994/04/01/88775/index.htm",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Berton:1995:HGT,
  author =       "L. Berton",
  title =        "He's Got their Number. {Scholar} Uses Math to Foil
                 Financial Fraud",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        jul,
  year =         "1995",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  ISSN-L =       "0099-9660",
  bibdate =      "Sat Dec 10 11:17:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Wall Street Journal",
}

@Book{Bologna:1995:FAF,
  author =       "Jack Bologna and Robert J. Lindquist",
  title =        "Fraud auditing and forensic accounting: new tools and
                 techniques",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "xv + 249",
  year =         "1995",
  ISBN =         "0-471-10646-1 (hardcover)",
  ISBN-13 =      "978-0-471-10646-3 (hardcover)",
  LCCN =         "HV8079.W47 B65 1995",
  bibdate =      "Tue Nov 22 10:31:53 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/wiley042/95005510.html;
                 http://www.loc.gov/catdir/description/wiley033/95005510.html;
                 http://www.loc.gov/catdir/toc/onix04/95005510.html",
  acknowledgement = ack-nhfb,
  remark =       "This book does not discuss Benford's Law, but may be
                 helpful background for application of that law to the
                 detection of fraud.",
  subject =      "white collar crime investigation; United States;
                 forensic accounting; fraud investigation",
}

@Article{Chen:1995:LED,
  author =       "Ye-Sho Chen",
  title =        "Letters to the {Editor}: On the dynamic behavior of
                 {Bradford's Law} --- response",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "10",
  pages =        "799--800",
  month =        dec,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<799::AID-ASI19>3.0.CO%3B2-P",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Chen:1995:RDB,
  author =       "Ye-Sho Chen and P. Pete Chong and Morgan Y. Tong",
  title =        "Research: Dynamic behavior of {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "5",
  pages =        "370--383",
  month =        jun,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<370::AID-ASI7>3.0.CO%3B2-J",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Czirok:1995:CBS,
  author =       "Andras Czir{\'o}k and Rosario N. Mantegna and Shlomo
                 Havlin and H. Eugene Stanley",
  title =        "Correlations in binary sequences and a generalized
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "446--??",
  day =          "1",
  month =        jul,
  year =         "1995",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.52.446",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.52.446",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Filipponi:1995:SPA,
  author =       "Piero Filipponi and Renato Menicocci",
  title =        "Some Probabilistic Aspects of the Terminal Digits of
                 {Fibonacci} Numbers",
  journal =      j-FIB-QUART,
  volume =       "33",
  number =       "4",
  pages =        "325--331",
  month =        aug,
  year =         "1995",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:19 MDT 2011",
  bibsource =    "http://www.fq.math.ca/33-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/33-4/filipponi.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Havlin:1995:DBZ,
  author =       "Shlomo Havlin",
  title =        "The distance between {Zipf} plots",
  journal =      j-PHYSICA-A,
  volume =       "216",
  number =       "1--2",
  pages =        "148--150",
  day =          "1",
  month =        jun,
  year =         "1995",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/0378-4371(95)00069-J",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/037843719500069J",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Hill:1995:BII,
  author =       "Theodore P. Hill",
  title =        "Base-invariance implies {Benford's Law}",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "123",
  number =       "3",
  pages =        "887--895",
  month =        mar,
  year =         "1995",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.2307/2160815",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "60A10 (28D05)",
  MRnumber =     "1233974 (95d:60006)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/2160815",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Hill:1995:SDP,
  author =       "Theodore P. Hill",
  title =        "The significant-digit phenomenon",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "102",
  number =       "4",
  pages =        "322--327",
  month =        apr,
  year =         "1995",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2974952",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K99 (60E99)",
  MRnumber =     "96f:11101",
  MRreviewer =   "Jean-Loup Mauclaire",
  bibdate =      "Wed Dec 3 17:17:33 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Hill:1995:SDS,
  author =       "Theodore P. Hill",
  title =        "A statistical derivation of the significant-digit
                 law",
  journal =      j-STAT-SCI,
  volume =       "10",
  number =       "4",
  pages =        "354--363",
  year =         "1995",
  CODEN =        "STSCEP",
  ISSN =         "0883-4237 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  MRclass =      "60E99 (60A10 62E99)",
  MRnumber =     "1421567 (98a:60021)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 10:09:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "2-P&origin=MSN;
                 http://links.jstor.org/sici?sici=0883-4237(199511)10:4<354:ASDOTS>2.0.CO",
  ZMnumber =     "Zbl 0955.60509",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science. A Review Journal of the Institute
                 of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
}

@Article{Kanter:1995:MPL,
  author =       "I. Kanter and D. A. Kessler",
  title =        "{Markov} Processes: Linguistics and {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "74",
  number =       "??",
  pages =        "4559--??",
  day =          "29",
  month =        may,
  year =         "1995",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.74.4559",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.74.4559",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Koenig:1995:BCL,
  author =       "Michael Koenig and Toni Harrell",
  title =        "Brief Communications: {Lotka's Law}, {Price}'s urn,
                 and electronic publishing",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "5",
  pages =        "386--388",
  month =        jun,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199506)46:5<386::AID-ASI9>3.0.CO%3B2-V",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Makse:1995:MUG,
  author =       "Hern{\'a}n A. Makse and Shlomo Havlin and H. Eugene
                 Stanley",
  title =        "Modelling urban growth patterns",
  journal =      j-NATURE,
  volume =       "377",
  number =       "6550",
  pages =        "608--612",
  day =          "19",
  month =        oct,
  year =         "1995",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/377608a0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Feb 27 06:06:25 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v377/n6550/abs/377608a0.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Berlin (Germany) population; London (UK) population;
                 Zipf's Law",
}

@Article{Mantegna:1995:SAC,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C.-K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "Systematic analysis of coding and noncoding {DNA}
                 sequences using methods of statistical linguistics",
  journal =      j-PHYS-REV-E,
  volume =       "52",
  number =       "??",
  pages =        "2939--??",
  day =          "1",
  month =        sep,
  year =         "1995",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.52.2939",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.52.2939",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Mosimann:1995:DFC,
  author =       "James E. Mosimann and Claire V. Wiseman and Ruth E.
                 Edelman",
  title =        "Data Fabrication: Can People Generate Random Digits?",
  journal =      j-ACCOUNT-RES,
  volume =       "4",
  number =       "1",
  pages =        "31--55",
  month =        "????",
  year =         "1995",
  CODEN =        "ARQAEZ",
  DOI =          "https://doi.org/10.1080/08989629508573866",
  ISSN =         "0898-9621 (print), 1545-5815 (electronic)",
  ISSN-L =       "0898-9621",
  bibdate =      "Sat Dec 10 11:56:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/08989629508573866",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountability in Research",
  journal-URL =  "http://www.tandfonline.com/toc/gacr20",
  keywords =     "Benford's Law",
  remark =       "The abstract ends with: ``The difficulty that people
                 have in creating random error digits supports the
                 utility of examining such digits in investigations of
                 scientific misconduct.''",
}

@Article{Oluic-Vukovic:1995:LED,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "Letters to the {Editor}: On the dynamic behavior of
                 {Bradford's Law}",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "46",
  number =       "10",
  pages =        "798--799",
  month =        dec,
  year =         "1995",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199512)46:10<798::AID-ASI18>3.0.CO%3B2-T",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:04 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "4 Jan 1999",
}

@Article{Stanley:1995:ZPS,
  author =       "Michael H. R. Stanley and Sergey V. Buldyrev and
                 Shlomo Havlin and Rosario N. Mantegna and Michael A.
                 Salinger and H. Eugene Stanley",
  title =        "{Zipf} plots and the size distribution of firms",
  journal =      j-ECONOM-LETT,
  volume =       "49",
  number =       "4",
  pages =        "453--457",
  day =          "15",
  month =        oct,
  year =         "1995",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/0165-1765(95)00696-D",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/016517659500696D",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Wagner-Dobler:1995:DLL,
  author =       "Roland Wagner-D{\"o}bler and Jan Berg",
  title =        "The Dependence of {Lotka's Law} on the Selection of
                 Time Periods in the Development of Scientific Areas and
                 Authors",
  journal =      j-J-DOC,
  volume =       "51",
  number =       "1",
  pages =        "28--43",
  month =        "????",
  year =         "1995",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/eb026941",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:29:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Zornig:1995:URZ,
  author =       "Peter Z{\"o}rnig and Gabriel Altmann",
  title =        "Unified representation of {Zipf} distributions",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "461--473",
  day =          "1",
  month =        apr,
  year =         "1995",
  CODEN =        "CSDADW",
  DOI =          "https://doi.org/10.1016/0167-9473(94)00009-8",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  MRclass =      "62E10 (62F10)",
  MRnumber =     "1333065 (96f:62029)",
  MRreviewer =   "Friedrich Liese",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0167947394000098",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
  keywords =     "Zipf's Law",
}

@Book{Bak:1996:HNW,
  author =       "Per Bak",
  title =        "How nature works: the science of self-organized
                 criticality",
  publisher =    "Copernicus",
  address =      "New York, NY, USA",
  pages =        "xiii + 212 + 8",
  year =         "1996",
  ISBN =         "0-387-94791-4 (hardcover)",
  ISBN-13 =      "978-0-387-94791-4 (hardcover)",
  LCCN =         "QC173.4.C74 B34 1996",
  bibdate =      "Thu Nov 24 13:34:22 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Critical phenomena (Physics); Complexity (Philosophy);
                 Physics; Philosophy",
}

@Article{Beirlant:1996:TIE,
  author =       "Jan Beirlant and Petra Vynckier and Jozef L. Teugels",
  title =        "Tail Index Estimation, {Pareto} Quantile Plots, and
                 Regression Diagnostics",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "91",
  number =       "436",
  pages =        "1659--??",
  month =        "????",
  year =         "1996",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon May 5 08:26:17 MDT 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Bonhoeffer:1996:NSH,
  author =       "Sebastian Bonhoeffer and Andreas V. M. Herz and
                 Maarten C. Boerlijst and Sean Nee and Martin A. Nowak
                 and Robert M. May",
  title =        "No Signs of Hidden Language in Noncoding {DNA}",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "11",
  pages =        "1977--1977",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1977",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 17:27:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1977",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Burgos:1996:ZSB,
  author =       "Javier D. Burgos and Pedro Moreno-Tovar",
  title =        "{Zipf}-scaling behavior in the immune system",
  journal =      j-BIOSYSTEMS,
  volume =       "39",
  number =       "3",
  pages =        "227--232",
  day =          "15",
  month =        nov,
  year =         "1996",
  CODEN =        "BSYMBO",
  DOI =          "https://doi.org/10.1016/0303-2647(96)01618-8",
  ISSN =         "0303-2647 (print), 1872-8324 (electronic)",
  ISSN-L =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0303264796016188",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03032647",
  keywords =     "Zipf's Law",
}

@Article{Campanino:1996:IIM,
  author =       "Massimo Campanino and Stefano Isola",
  title =        "Infinite invariant measures for non-uniformly
                 expanding transformations of $ [0, 1] $: Weak law of
                 large numbers with anomalous scaling",
  journal =      j-FORUM-MATH,
  volume =       "8",
  number =       "1",
  pages =        "71--92",
  year =         "1996",
  CODEN =        "FOMAEF",
  DOI =          "https://doi.org/10.1515/form.1996.8.71",
  ISSN =         "0933-7741 (print), 1435-5337 (electronic)",
  ISSN-L =       "0933-7741",
  bibdate =      "Sat Nov 12 10:33:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0837.60022",
  abstract =     "We consider a class of maps of $ [0, 1] $ with an
                 indifferent fixed point at 0 and expanding everywhere
                 else. Using the invariant ergodic probability measure
                 of a suitable, everywhere expanding, induced
                 transformation we are able to study the infinite
                 invariant measure of the original map in some detail.
                 Given a continuous function with compact support in
                 $]0, 1]$, we prove that its time averages satisfy a
                 `weak law of large numbers' with anomalous scaling $ n
                 / \log n $ and give an upper bound for the decay of
                 correlations.",
  acknowledgement = ack-nhfb,
  ajournal =     "Forum Math.",
  classmath =    "60F05 (Weak limit theorems) 28D05 (Measure-preserving
                 transformations) 37A99 (Ergodic theory)",
  fjournal =     "Forum Mathematicum",
  keywords =     "decay of correlations; invariant ergodic probability
                 measure; weak law of large numbers",
}

@Article{Czirok:1996:POP,
  author =       "Andr{\'a}s Czir{\'o}k and H. Eugene Stanley and
                 Tam{\'a}s Vicsek",
  title =        "Possible origin of power-law behavior in $n$-tuple
                 {Zipf} analysis",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "6371--??",
  day =          "1",
  month =        jun,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.53.6371",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.53.6371",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Fuchs:1996:PDP,
  author =       "Aim{\'e} Fuchs and Giorgio Letta",
  title =        "Le probl{\`e}me du premier chiffre d{\'e}cimal pour
                 les nombres premiers. ({French}) [The problem for the
                 first decimal digit of prime numbers]",
  journal =      j-ELECT-J-COMB,
  volume =       "3",
  number =       "2",
  pages =        "R25:1--R25:7",
  month =        "????",
  year =         "1996",
  ISSN =         "1077-8926 (print), 1097-1440 (electronic)",
  ISSN-L =       "1077-8926",
  bibdate =      "Sat Feb 16 17:40:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The Foata Festschrift volume.",
  URL =          "http://www.combinatorics.org/ojs/index.php/eljc/article/download/v3i2r25/pdf",
  ZMnumber =     "0853.11006",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Combinatorics",
  language =     "French",
  xxpages =      "601--607",
}

@Article{Gunther:1996:ZLE,
  author =       "R. G{\"u}nther and L. Levitin and B. Schapiro and P.
                 Wagner",
  title =        "{Zipf}'s law and the effect of ranking on probability
                 distributions",
  journal =      j-INT-J-THEOR-PHYS,
  volume =       "35",
  number =       "2",
  pages =        "395--417",
  year =         "1996",
  CODEN =        "IJTPBM",
  DOI =          "https://doi.org/10.1007/BF02083823",
  ISSN =         "0020-7748 (print), 1572-9575 (electronic)",
  ISSN-L =       "0020-7748",
  bibdate =      "Sat Nov 12 10:53:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0843.60002",
  abstract =     "Ranking procedures are widely used in the description
                 of many different types of complex systems. Zipf's law
                 is one of the most remarkable frequency-rank
                 relationships and has been observed independently in
                 physics, linguistics, biology, demography, etc. We show
                 that ranking plays a crucial role in making it possible
                 to detect empirical relationships in systems that exist
                 in one realization only, even when the statistical
                 ensemble to which the systems belong has a very broad
                 probability distribution. Analytical results and
                 numerical simulations are presented which clarify the
                 relations between the probability distributions and the
                 behavior of expected values for unranked and ranked
                 random variables. This analysis is performed, in
                 particular, for the evolutionary model presented in our
                 previous papers which leads to Zipf's law and reveals
                 the underlying mechanism of this phenomenon in terms of
                 a system with interdependent and interacting components
                 as opposed to the ``ideal gas'' models suggested by
                 previous researchers. The ranking procedure applied to
                 this model leads to a new, unexpected phenomenon: a
                 characteristic ``staircase'' behavior of the mean
                 values of the ranked variables (ranked occupation
                 numbers). This result is due to the broadness of the
                 probability distributions for the occupation numbers
                 and does not follow from the ``ideal gas'' model. Thus,
                 it provides an opportunity, by comparison with
                 empirical data, to obtain evidence as to which model
                 relates to reality.",
  acknowledgement = ack-nhfb,
  classmath =    "60A99 (Foundations of probability theory)",
  fjournal =     "International Journal of Theoretical Physics",
  journal-URL =  "http://link.springer.com/journal/10773",
  keywords =     "numerical simulations; ranking procedures; Zipf's
                 law",
}

@TechReport{Hill:1996:NDT,
  author =       "Theodore P. Hill",
  title =        "A note on distributions of true versus fabricated
                 data",
  type =         "Preprint",
  institution =  "Department of Mathematics, Georgia Institute of
                 Technology",
  address =      "Atlanta, GA, USA",
  pages =        "4",
  year =         "1996",
  bibdate =      "Sat Feb 16 17:47:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1046&context=rgp_rsr",
  acknowledgement = ack-nhfb,
}

@Article{Israeloff:1996:CZD,
  author =       "N. E. Israeloff and M. Kagalenko and K. Chan",
  title =        "Can {Zipf} Distinguish Language From Noise in
                 Noncoding {DNA}?",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "11",
  pages =        "1976--??",
  day =          "11",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1976",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1976",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Krugman:1996:CMU,
  author =       "Paul Krugman",
  title =        "Confronting the Mystery of Urban Hierarchy",
  journal =      j-J-JPN-INT-ECON,
  volume =       "10",
  number =       "4",
  pages =        "399--418",
  month =        dec,
  year =         "1996",
  CODEN =        "JJIEBD",
  DOI =          "https://doi.org/10.1006/jjie.1996.0023",
  ISSN =         "0889-1583 (print), 1095-8681 (electronic)",
  ISSN-L =       "0889-1583",
  bibdate =      "Wed Feb 27 06:15:55 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0889158396900234",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the {Japanese} and International
                 Economies",
  keywords =     "Zipf's Law",
}

@Book{Krugman:1996:SOE,
  author =       "Paul R. Krugman",
  title =        "The Self-Organizing Economy",
  publisher =    "Blackwell Publishers",
  address =      "Cambridge, MA, USA",
  pages =        "vi + 122",
  year =         "1996",
  ISBN =         "1-55786-699-6 (paperback)",
  ISBN-13 =      "978-1-55786-699-8 (paperback)",
  LCCN =         "HB199 .K75 1996",
  bibdate =      "Wed Feb 27 07:08:14 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Zipf's Law",
  subject =      "Economics; Self-organizing systems",
}

@Article{Ley:1996:PDU,
  author =       "Eduardo Ley",
  title =        "On the Peculiar Distribution of the {U.S.} Stock
                 Indexes' Digits",
  journal =      j-AMER-STAT,
  volume =       "50",
  number =       "4",
  pages =        "311--313",
  month =        nov,
  year =         "1996",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Nov 14 15:09:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.jstor.org/stable/2684926",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Mantegna:1996:MAR,
  author =       "R. N. Mantegna and S. V. Buldyrev and A. L. Goldberger
                 and S. Havlin and C.-K. Peng and M. Simons and H. E.
                 Stanley",
  title =        "{Mantegna} {\em et al.} Reply",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  pages =        "1979--1981",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1979",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 17:28:12 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mantegna:1994:LFN,Voss:1996:CLF}",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1979",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  issue =        "11",
  journal-URL =  "http://prl.aps.org/browse",
}

@Article{Newman:1996:ASC,
  author =       "M. E. J. Newman and Kim Sneppen",
  title =        "Avalanches, scaling, and coherent noise",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "6",
  pages =        "6226--6231",
  month =        dec,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.6226",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:44:51 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.6226",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@InProceedings{Nigrini:1996:DAR,
  author =       "Mark J. Nigrini",
  editor =       "M. Ettredge",
  booktitle =    "{Proceedings of the 1996 Deloitte \& Touche I
                 University of Kansas Symposium on Auditing Problems}",
  title =        "Digital Analysis and the Reduction of Auditor
                 Litigation Risk",
  publisher =    "University of Kansas",
  address =      "Lawrence, KS, USA",
  pages =        "69--81",
  year =         "1996",
  bibdate =      "Sat Sep 10 15:20:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Nigrini:1996:TCA,
  author =       "Mark J. Nigrini",
  title =        "A Taxpayer Compliance Application of {Benford's Law}",
  journal =      "Journal of the {American Taxation Association}",
  volume =       "18",
  number =       "1",
  pages =        "72--91",
  month =        "????",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "0198-9073 (print), 1558-8017 (electronic)",
  ISSN-L =       "0198-9073",
  bibdate =      "Mon Nov 14 16:30:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Amer. Tax. Assoc.",
  fjournal =     "Journal of the {American Taxation Association}",
  journal-URL =  "http://aaajournals.org/loi/atax",
  remark =       "No journal issues online before 1999.",
}

@Article{Perline:1996:ZLC,
  author =       "Richard Perline",
  title =        "{Zipf}'s law, the {Central Limit Theorem}, and the
                 random division of the unit interval",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "220--223",
  day =          "1",
  month =        jul,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.220",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.220",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Mandelbrot's monkey-at-the-typewriter model of Zipf's
                 inverse power law; Zipf's Law",
}

@Article{Sole:1996:ESO,
  author =       "Ricard V. Sol{\'e} and Susanna C. Manrubia",
  title =        "Extinction and self-organized criticality in a model
                 of large-scale evolution",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "1",
  pages =        "R42--R45",
  month =        jul,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.R42",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:32:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.R42",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Solomon:1996:SSE,
  author =       "Sorin Solomon and Moshe Levy",
  title =        "Spontaneous Scaling Emergence in Generic Stochastic
                 Systems",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "7",
  number =       "5",
  pages =        "745--752",
  month =        oct,
  year =         "1996",
  CODEN =        "IJMPEO",
  DOI =          "https://doi.org/10.1142/S0129183196000624",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  bibdate =      "Thu Feb 28 10:20:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.worldscientific.com/doi/abs/10.1142/S0129183196000624",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
}

@Article{Voss:1996:CLF,
  author =       "Richard F. Voss",
  title =        "Comment on {``Linguistic Features of Noncoding DNA
                 Sequences''}",
  journal =      j-PHYS-REV-LET,
  volume =       "76",
  number =       "11",
  pages =        "1978--1978",
  month =        mar,
  year =         "1996",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.76.1978",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mantegna:1994:LFN} and reply
                 \cite{Mantegna:1996:MAR}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.76.1978",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Benford's Law",
}

@Article{Watanabe:1996:EZL,
  author =       "Makoto S. Watanabe",
  title =        "Erratum: {Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "54",
  number =       "??",
  pages =        "4483--4483",
  day =          "1",
  month =        oct,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.54.4483",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite {Watanabe:1996:ZLP}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.54.4483",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Watanabe:1996:ZLP,
  author =       "Makoto S. Watanabe",
  title =        "{Zipf}'s law in percolation",
  journal =      j-PHYS-REV-E,
  volume =       "53",
  number =       "??",
  pages =        "4187--4190",
  day =          "1",
  month =        apr,
  year =         "1996",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.53.4187",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See erratum \cite {Watanabe:1996:EZL}.",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.53.4187",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Allaart:1997:ISC,
  author =       "Pieter C. Allaart",
  title =        "An Invariant-Sum Characterization of {Benford's Law}",
  journal =      j-J-APPL-PROBAB,
  volume =       "34",
  number =       "1",
  pages =        "288--291",
  month =        mar,
  year =         "1997",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.2307/3215195",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "60E05",
  MRnumber =     "1429075 (98d:60029)",
  MRreviewer =   "Peter Schatte",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3215195",
  abstract =     "The accountant Nigrini remarked that in tables of data
                 distributed according to Benford's law, the sum of all
                 elements with first digit $ d (d = 1, 2, \ldots, 9) $
                 is approximately constant. In this note, a mathematical
                 formulation of Nigrini's observation is given and it is
                 shown that Benford's law is the unique probability
                 distribution such that the expected sum of all elements
                 with first digits $ d_1, \ldots, d_k $ is constant for
                 every fixed $k$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Castillo:1997:FGP,
  author =       "Enrique Castillo and Ali S. Hadi",
  title =        "Fitting the Generalized {Pareto} Distribution to
                 Data",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "92",
  number =       "440",
  pages =        "1609--1620",
  month =        dec,
  year =         "1997",
  CODEN =        "JSTNAL",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Mon Oct 30 06:57:36 MST 2000",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc.bib",
  URL =          "http://www.amstat.org/publications/jasa/abstracts_97/december/CASTILLO.HTM;
                 http://www.jstor.org/stable/2965432",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Chen:1997:NHS,
  author =       "Weishing Chen and Tai-Hsi Wu",
  title =        "A non-homogeneous software reliability model based on
                 {Zipf}'s law",
  journal =      "International Journal of Quality \& Reliability
                 Management",
  volume =       "14",
  number =       "4",
  pages =        "409--431",
  month =        "????",
  year =         "1997",
  DOI =          "https://doi.org/10.1108/02656719710170666",
  ISSN =         "0265-671X (print), 1758-6682 (electronic)",
  ISSN-L =       "0265-671X",
  bibdate =      "Fri Nov 25 07:08:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Denisov:1997:FBS,
  author =       "S. Denisov",
  title =        "Fractal binary sequences: {Tsallis} thermodynamics and
                 the {Zipf} law",
  journal =      j-PHYS-LET-A,
  volume =       "235",
  number =       "5",
  pages =        "447--451",
  day =          "17",
  month =        nov,
  year =         "1997",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/S0375-9601(97)00688-9",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960197006889",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Zipf's Law",
}

@InCollection{Gell-Mann:1997:ETZ,
  author =       "Murray Gell-Mann",
  title =        "Empirical Theory --- {Zipf}'s Law",
  crossref =     "Gell-Mann:1997:QJA",
  pages =        "92--97",
  year =         "1997",
  bibdate =      "Mon Sep 01 10:20:00 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Hill:1997:BL,
  author =       "Theodore Hill",
  editor =       "Michiel Hazewinkel",
  booktitle =    "Encyclopedia of Mathematics, Supplement {I}",
  title =        "{Benford's Law}",
  volume =       "1",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "102--103",
  year =         "1997",
  ISBN =         "90-481-4896-0",
  ISBN-13 =      "978-90-481-4896-7",
  LCCN =         "????",
  bibdate =      "Wed Nov 16 10:29:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Irmay:1997:RBZ,
  author =       "Shragga Irmay",
  title =        "The relationship between {Zipf}'s law and the
                 distribution of first digits",
  journal =      j-J-APPL-STAT,
  volume =       "24",
  number =       "4",
  pages =        "383--393",
  day =          "1",
  month =        aug,
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "62E15",
  MRnumber =     "1491308 (98h:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.catchword.co.uk/titles/carfax/02664763/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/02664769723594",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; Zipf's Law",
  xxpages =      "383--394",
}

@Article{Jeevanand:1997:BEB,
  author =       "E. S. Jeevanand",
  title =        "{Bayes} Estimation of {$ P(X_2 < X_1) $} for a
                 Bivariate {Pareto} Distribution",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "46",
  number =       "1",
  pages =        "93--99",
  month =        "????",
  year =         "1997",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2988496",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:24 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i349996;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-1990.bib",
  URL =          "http://www.jstor.org/stable/2988496",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@Manual{Nigrini:1997:DAT,
  author =       "Mark J. Nigrini",
  title =        "Digital Analysis Tests and Statistics",
  organization = "The Nigrini Institute, Inc.",
  address =      "Allen, TX, USA",
  month =        "????",
  year =         "1997",
  bibdate =      "Sat Feb 16 18:55:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nigrini.com/data_software/Program_Details_2009.docx",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1997:UBL,
  author =       "Mark J. Nigrini and L. J. Mittermaier",
  title =        "The Use of {Benford's Law} as an Aid in Analytical
                 Procedures",
  journal =      j-AUDITING,
  volume =       "16",
  number =       "2",
  pages =        "52--67",
  month =        "????",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Sun Nov 13 11:37:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaapubs.org/loi/ajpt",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
  remark =       "No journal issues online before 1999.",
}

@Article{Oluic-Vukovic:1997:BDC,
  author =       "Vesna Olui{\'c}-Vukovi{\'c}",
  title =        "{Bradford}'s distribution: {From} the classical
                 bibliometric ``law'' to the more general stochastic
                 models",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "48",
  number =       "9",
  pages =        "833--842",
  month =        sep,
  year =         "1997",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(199709)48:9<833::AID-ASI7>3.0.CO%3B2-S",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:21 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "7 Dec 1998",
}

@Book{Robertson:1997:FEM,
  author =       "Jack C. Robertson",
  title =        "Fraud Examination for Managers and Auditors",
  publisher =    "Viesca Books",
  address =      "Austin, TX, USA",
  edition =      "1997",
  pages =        "vii + 564",
  year =         "1997",
  ISBN =         "0-9656785-0-4",
  ISBN-13 =      "978-0-9656785-0-6",
  LCCN =         "HV8079.F7 R63 1997",
  bibdate =      "Thu Oct 13 09:04:19 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Fraud investigation",
}

@Article{Salsburg:1997:DPB,
  author =       "David Salsburg",
  title =        "Digit Preferences in the {Bible}",
  journal =      j-CHANCE,
  volume =       "10",
  number =       "4",
  pages =        "46--48",
  month =        "????",
  year =         "1997",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.1997.10542065",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Sat Feb 16 19:08:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amstat.tandfonline.com/doi/full/10.1080/09332480.1997.10542065",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
}

@InCollection{Smith:1997:EBL,
  author =       "Steven W. Smith",
  booktitle =    "The Scientist and Engineer's Guide to Digital Signal
                 Processing",
  title =        "Explaining {Benford's Law}",
  chapter =      "34",
  publisher =    "California Technical Publishing",
  address =      "San Diego, CA, USA",
  bookpages =    "xiv + 626",
  pages =        "701--722",
  year =         "1997",
  ISBN =         "0-9660176-3-3",
  ISBN-13 =      "978-0-9660176-3-2",
  LCCN =         "TK5102.9 .S57 1997",
  bibdate =      "Sat Sep 10 16:54:35 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.dspguide.com/ch34.htm",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "Chapters appear to stop at 31 in 1997 edition
                 (according to Amazon book preview), so a later addition
                 should have a new ISBN (the 2002 edition from Newnes is
                 \booktitle{Digital Signal Processing: A Practical Guide
                 for Engineers and Scientists}, with ISBN
                 0-7506-7444-X). However, the Web site says it is the
                 same book. The Web edition has 34 chapters, and all are
                 freely downloadable.",
}

@Article{Tsonis:1997:ZLS,
  author =       "A. A. Tsonis and C. Schultz and P. A. Tsonis",
  title =        "{Zipf's Law} and the structure and evolution of
                 languages",
  journal =      j-COMPLEXITY,
  volume =       "2",
  number =       "5",
  pages =        "12--13",
  year =         "1997",
  CODEN =        "COMPFS",
  DOI =          "https://doi.org/10.1002/(SICI)1099-0526(199705/06)2:5<12::AID-CPLX3>3.0.CO%3B2-C",
  ISSN =         "1076-2787 (print), 1099-0526 (electronic)",
  ISSN-L =       "1076-2787",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Complexity",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1099-0526",
}

@Article{Zanette:1997:RIU,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Role of Intermittency in Urban Development: A Model of
                 Large-Scale City Formation",
  journal =      j-PHYS-REV-LET,
  volume =       "79",
  number =       "3",
  pages =        "523--526",
  day =          "3",
  month =        jul,
  year =         "1997",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.79.523",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 10:40:44 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.79.523",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Bach:1998:EPM,
  author =       "Eric Bach",
  title =        "Efficient prediction of {Marsaglia--Zaman} random
                 number generators",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "44",
  number =       "3",
  pages =        "1253--1257",
  year =         "1998",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.669305",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  MRclass =      "65C10",
  MRnumber =     "99b:65007",
  bibdate =      "Thu Dec 22 07:42:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  ZMnumber =     "0915.65003",
  abstract =     "This paper presents two properties of the random
                 number generator by {\em G. Marsaglia} and {\em A.
                 Zaman} [Ann. Appl. Probab. 1, No. 3, 462-480 (1991; Zbl
                 0733.65005)]. First, it is shown that its successive
                 digits are digits of certain rational $b$-adic numbers.
                 Then, an efficient algorithm is derived to predict an
                 unknown pseudorandom sequence of this type. Two
                 examples of the prediction are given.",
  acknowledgement = ack-nhfb,
  classmath =    "*65C10 Random number generation 11K45 Pseudo-random
                 numbers, etc.",
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  keywords =     "$b$-adic number; algorithm; continued fraction;
                 pseudo-random number generator",
  ZMreviewer =   "K. Uosaki (Tottori)",
}

@Article{Browne:1998:FBL,
  author =       "Malcolm W. Browne",
  title =        "Following {Benford's Law}, or Looking Out for {No.
                 1}",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "F4--F4",
  day =          "4",
  month =        aug,
  year =         "1998",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibdate =      "Sat Feb 16 14:29:48 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Science section.",
  URL =          "http://search.proquest.com/hnpnewyorktimes/docview/109868161/13C4AACC02923FE97A/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
}

@Article{Busta:1998:UBL,
  author =       "Bruce Busta and Randy Weinberg",
  title =        "Using {Benford's Law} and Neural Networks as a Review
                 Procedure",
  journal =      "Managerial Auditing Journal",
  volume =       "13",
  number =       "6",
  pages =        "356--366",
  month =        "????",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1108/02686909810222375",
  ISSN =         "0268-6902 (print), 1758-7735 (electronic)",
  ISSN-L =       "0268-6902",
  bibdate =      "Tue Nov 22 18:50:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chongde:1998:EMB,
  author =       "Wang Chongde and Wang Zhe",
  title =        "Evaluation of the models for {Bradford's Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "42",
  number =       "1",
  pages =        "89--95",
  month =        may,
  year =         "1998",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/BF02465014",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:03:59 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics1990.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02465014",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{DeCeuster:1998:HPB,
  author =       "Marc J. K. {De Ceuster} and Geert Dhaene and Tom
                 Schatteman",
  title =        "On the hypothesis of psychological barriers in stock
                 markets and {Benford's Law}",
  journal =      j-J-EMPIR-FINANCE,
  volume =       "5",
  number =       "3",
  pages =        "263--279",
  month =        sep,
  year =         "1998",
  CODEN =        "JEFIEC",
  DOI =          "https://doi.org/10.1016/S0927-5398(97)00024-8",
  ISSN =         "0927-5398 (print), 1879-1727 (electronic)",
  ISSN-L =       "0927-5398",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927539897000248",
  abstract =     "We consider the hypothesis of psychological barriers
                 at round numbers of a stock index. This hypothesis is
                 often examined by testing the uniformity of the
                 distribution of the trailing digits in the stock index,
                 a rejection being interpreted as evidencing the
                 existence of psychological barriers. By virtue of
                 Benford's Law, we show that the uniform distribution is
                 not the right benchmark against which to test. As an
                 alternative we propose a test based on the cyclical
                 permutations of the actual returns. Applying this test
                 to the Dow Jones 30 Industrial Average, the Financial
                 Times Stock Exchange 100 and the Nikkei Stock Average
                 225, we find no convincing evidence of psychological
                 barriers, contrary to previous findings.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Empirical Finance",
  keywords =     "Benford's Law; Psychological barriers",
}

@Article{Herman:1998:TRI,
  author =       "Tom Herman",
  title =        "Tax report: An {IRS} blooper startles thousands of
                 taxpayers",
  journal =      j-WALL-ST-J,
  volume =       "??",
  number =       "??",
  pages =        "1--1",
  day =          "18",
  month =        feb,
  year =         "1998",
  CODEN =        "WSJOAF",
  ISSN =         "0099-9660",
  bibdate =      "Fri Mar 22 09:17:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://online.wsj.com/article/SB887753996209804500.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Wall Street Journal",
  keywords =     "Benford's Law",
  remark =       "From the article: ``[a taxpayer] was expecting a \$513
                 tax refund. Instead, he recently received a letter from
                 the Internal Revenue Service informing him that he owes
                 the government \$300,000,007.57. \ldots{} about 3,000
                 other people around the nation got similar erroneous
                 notices, each showing a balance due of `three hundred
                 million dollars and change.'\,''",
}

@Article{Hill:1998:FDP,
  author =       "Theodore P. Hill",
  title =        "The First Digit Phenomenon",
  journal =      j-AM-SCI,
  volume =       "86",
  number =       "4",
  pages =        "358--363",
  month =        jul # "\slash " # aug,
  year =         "1998",
  CODEN =        "AMSCAC",
  DOI =          "https://doi.org/10.1511/1998.4.358",
  ISSN =         "0003-0996 (print), 1545-2786 (electronic)",
  ISSN-L =       "0003-0996",
  bibdate =      "Sat Dec 10 11:54:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://people.math.gatech.edu/~hill/publications/PAPER%20PDFS/TheFirstDigitPhenomenonAmericanScientist1996.pdf;
                 http://www.math.gatech.edu/~hill/publications/cv.dir/1st-dig.pdf",
  abstract =     "A century ago, Simon Newcomb observed an unexpected
                 pattern in the first digits of logarithm tables: The
                 digit $1$ is significantly more likely to occur than
                 $2$, $2$ than $3$, and so on. More than a half-century
                 later, Frank Benford rediscovered the first-digit
                 phenomenon and found that it applied to many tables of
                 numerical data, including the stock market, census
                 statistics and accounting figures. New mathematical
                 insights establish the empirical law developed by
                 Newcomb and Benford as part of modern probability
                 theory, and recent applications include testing of
                 mathematical models, design of computers and detection
                 of fraud in accounting.",
  acknowledgement = ack-nhfb,
  fjournal =     "American Scientist",
  journal-URL =  "http://www.americanscientist.org/issues/past.aspx",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Book{Knuth:1998:SA,
  author =       "Donald E. Knuth",
  title =        "Seminumerical Algorithms",
  volume =       "2",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  edition =      "Third",
  pages =        "xiii + 762",
  year =         "1998",
  ISBN =         "0-201-89684-2",
  ISBN-13 =      "978-0-201-89684-8",
  LCCN =         "QA76.6 .K64 1997",
  bibdate =      "Fri Jul 11 15:41:22 1997",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/css.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
  note =         "See section 4.2.4V, The Fraction Parts, pages
                 254--262, for a discussion of Benford's Law.",
  price =        "US\$52.75",
  series =       "The Art of Computer Programming",
  acknowledgement = ack-nhfb,
  remark =       "Knuth comments on page 255: ``The fact that the
                 leading digits tend to be small makes the most obvious
                 techniques of ``average error'' estimation for floating
                 point calculations invalid. The relative error due to
                 rounding is usually a little more than expected.",
  tableofcontents = "3: Random Numbers / 1 \\
                 3.1. Introduction / 1 \\
                 3.2. Generating Uniform Random Numbers / 10 \\
                 3.2.1. The Linear Congruential Method / 10 \\
                 3.2 1.1. Choice of modulus / 12 \\
                 3.2.1.2 Choice of multiplier / 16 \\
                 3.2.1.3. Potency / 23 \\
                 3.2.2. Other Methods / 26 \\
                 3.3. Statistical Tests / 41 \\
                 3.3.1. General Test Procedures for Studying Random Data
                 / 41 \\
                 3.3.2. Empirical Tests / 61 \\
                 *3.3.3. Theoretical Tests / 80 \\
                 3.3.4. The Spectral Test / 93 \\
                 3.4. Other Types of Random Quantities / 119 \\
                 3.4 1. Numerical Distributions / 119 \\
                 3.4.2. Random Sampling and Shuffling / 142 \\
                 *3.5. What Is a Random Sequence? / 149 \\
                 3.6. Summary / 184 \\
                 4: Arithmetic / 194 \\
                 4.1. Positional Number Systems / 195 \\
                 4.2. Floating Point Arithmetic / 214 \\
                 4.2.1. Single-Precision Calculations / 214 \\
                 4.2 2. Accuracy of Floating Point Arithmetic / 229 \\
                 *4.2.3. Double-Precision Calculations / 246 \\
                 4.2.4. Distribution of Floating Point Numbers / 253 \\
                 4.3 Multiple Precision Arithmetic / 265 \\
                 4.3.1. The Classical Algorithms / 265 \\
                 *4.3.2. Modular Arithmetic / 284 \\
                 *4.3.3. How Fast Can We Multiply? / 294 \\
                 4.4. Radix Conversion / 319 \\
                 4.5. Rational Arithmetic / 330 \\
                 4.5.1. Fractions / 330 \\
                 4.5.2. The Greatest Common Divisor / 333 \\
                 *4.5.3. Analysis of Euclid's Algorithm / 356 \\
                 4.5.4. Factoring into Primes / 379 \\
                 4.6. Polynomial Arithmetic / 418 \\
                 4.6.1. Division of Polynomials / 420 \\
                 *4.6.2. Factorization of Polynomials / 439 \\
                 4.6.3. Evaluation of Powers / 461 \\
                 4.6.4. Evaluation of Polynomials / 485 \\
                 *4.7. Manipulation of Power Series / 525 \\
                 Answers to Exercises / 538 \\
                 Appendix A: Tables of Numerical Quantities / 726 \\
                 1. Fundamental Constants (decimal) / 726 \\
                 2; Fundamental Constants ( octal) / 727 \\
                 3. Harmonic Numbers, Bernoulli Numbers, Fibonacci
                 Numbers / 728 \\
                 Appendix B: Index to Notations / 730 \\
                 Index and Glossary / 735",
}

@Article{Manrubia:1998:IMU,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Intermittency model for urban development",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "1",
  pages =        "295--302",
  month =        jul,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.58.295",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:42:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.58.295",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Marsili:1998:IIL,
  author =       "Matteo Marsili and Yi-Cheng Zhang",
  title =        "Interacting Individuals Leading to {Zipf's Law}",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "??",
  pages =        "2741--??",
  day =          "23",
  month =        mar,
  year =         "1998",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.80.2741",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.2741",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Nigrini:1998:DIB,
  author =       "Mark J. Nigrini",
  title =        "{Dow} Illustrates {Benford's Law}",
  journal =      j-NY-TIMES,
  volume =       "??",
  number =       "??",
  pages =        "F4--F4",
  day =          "4",
  month =        aug,
  year =         "1998",
  CODEN =        "NYTIAO",
  ISSN =         "0362-4331 (print), 1542-667X, 1553-8095",
  ISSN-L =       "0362-4331",
  bibdate =      "Sat Feb 16 15:46:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://search.proquest.com/hnpnewyorktimes/docview/109901848/13C4AB0BB5661D397CE/1",
  acknowledgement = ack-nhfb,
  fjournal =     "New York Times",
  journal-URL =  "http://www.nytimes.com/",
}

@Article{NunesAmaral:1998:PLS,
  author =       "Lu{\'\i}s A. {Nunes Amaral} and Sergey V. Buldyrev and
                 Shlomo Havlin and Michael A. Salinger and H. Eugene
                 Stanley",
  title =        "Power Law Scaling for a System of Interacting Units
                 with Complex Internal Structure",
  journal =      j-PHYS-REV-LET,
  volume =       "80",
  number =       "7",
  pages =        "1385--1388",
  day =          "16",
  month =        feb,
  year =         "1998",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.80.1385",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Thu Feb 28 11:09:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.80.1385",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Pietronero:1998:UDN,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "The Uneven Distribution of Numbers in Nature",
  journal =      "ArXiv e-prints",
  pages =        "9",
  day =          "27",
  month =        aug,
  year =         "1998",
  bibdate =      "Mon Nov 21 06:58:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/cond-mat/9808305",
  abstract =     "Suppose you look at today's stock prices and bet on
                 the value of the first digit. One could guess that a
                 fair bet should correspond to the frequency of $ 1 / 9
                 = 11.11 \% $ for each digit from 1 to 9. This is by no
                 means the case, and one can easily observe a strong
                 prevalence of the small values over the large ones. The
                 first three integers 1, 2 and 3 alone have globally a
                 frequency of 60\% while the other six values 4, 5, 6,
                 7, 8 and 9 appear only in 40\% of the cases. This
                 situation is actually much more general than the stock
                 market and it occurs in a variety of number catalogs
                 related to natural phenomena. The first observation of
                 this property traces back to S. Newcomb in 1881 but a
                 more precise account was given by F. Benford in 1938.
                 In this note we illustrate these observations with the
                 enlightening specific example of the stock market. We
                 also identify the general mechanism for the origin of
                 this uneven distribution in the multiplicative nature
                 of fluctuations in economics and in many natural
                 phenomena. This provides a natural explanation for the
                 ubiquitous presence of the Benford's law in many
                 different phenomena with the common element that their
                 fluctuations refer to a fraction of their values. This
                 brings us close to the problem of the spontaneous
                 origin of scale invariant properties in various
                 phenomena which is a debated question at the frontier
                 of different fields.",
  acknowledgement = ack-nhfb,
}

@Article{Pocheau:1998:SRS,
  author =       "A. Pocheau",
  title =        "Scale ratios, statistical symmetries and
                 intermittency",
  journal =      j-EUROPHYS-LETT,
  volume =       "43",
  number =       "4",
  pages =        "410--415",
  month =        aug,
  year =         "1998",
  CODEN =        "EULEEJ",
  DOI =          "https://doi.org/10.1209/epl/i1998-00103-6",
  ISSN =         "0295-5075 (print), 1286-4854 (electronic)",
  ISSN-L =       "0295-5075",
  bibdate =      "Sat Feb 16 16:02:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Europhysics Letters",
  journal-URL =  "http://iopscience.iop.org/0295-5075",
}

@Article{Ramsden:1998:ZLB,
  author =       "J. J. Ramsden and J. Vohradsk{\'y}",
  title =        "{Zipf}-like behavior in procaryotic protein
                 expression",
  journal =      j-PHYS-REV-E,
  volume =       "58",
  number =       "??",
  pages =        "7777--??",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.58.7777",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.58.7777",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Rousset:1998:CPV,
  author =       "Olivier G. Rousset and Yilong Ma and Alan C. Evans",
  title =        "Correction for Partial Volume Effects in {PET}:
                 Principle and Validation",
  journal =      j-NUCL-MED,
  volume =       "39",
  number =       "5",
  pages =        "904--911",
  month =        may,
  year =         "1998",
  CODEN =        "JNMEAQ",
  ISSN =         "0161-5505 (print), 1535-5667 (electronic)",
  ISSN-L =       "0161-5505",
  bibdate =      "Sat Sep 10 16:10:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jnm.snmjournals.org/content/39/5/904.full.pdf+html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Nuclear Medicine",
  journal-URL =  "http://jnm.snmjournals.org/content/by/year",
  keywords =     "Benford's Law",
}

@Article{Schatte:1998:BLV,
  author =       "P. Schatte",
  title =        "On {Benford's law} to variable base",
  journal =      j-STAT-PROB-LETT,
  volume =       "37",
  number =       "4",
  pages =        "391--397",
  day =          "30",
  month =        mar,
  year =         "1998",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/S0167-7152(97)00142-9",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60F05 (60E15)",
  MRnumber =     "1624423 (99e:60072)",
  MRreviewer =   "Theodore P. Hill",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715297001429",
  abstract =     "Benford's law is studied in dependence on the base $ b
                 > 1 $. It can hold to large bases $b$ only
                 approximately. The quality of approximation is
                 estimated in cases of products and sums of random
                 variables, respectively, and in case of some
                 deterministic sequences. Always the approximation by
                 Benford's law becomes worse as $ b \to \infty $, but as
                 a rule also as $ b \to 1 + 0 $",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Discrepancy; First-digit problem;
                 Mantissa distribution; Products of random variables;
                 Sums of random variables",
}

@Article{Simon:1998:ADC,
  author =       "Jonathan Simon",
  title =        "An Analysis of the Distribution of Combinations Chosen
                 by {UK National Lottery} Players",
  journal =      j-J-RISK-UNCERT,
  volume =       "17",
  number =       "3",
  pages =        "243--277",
  year =         "1998",
  CODEN =        "JRUNEN",
  DOI =          "https://doi.org/10.1023/A:1007786901776",
  ISSN =         "0895-5646 (print), 1573-0476 (electronic)",
  ISSN-L =       "0895-5646",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Risk and Uncertainty",
  journal-URL =  "http://link.springer.com/journal/11166",
  keywords =     "Benford's Law",
}

@Article{Slijepcevic:1998:NID,
  author =       "Sini{\v{s}}a Slijep{\v{c}}evi{\'c}",
  title =        "A Note on Initial Digits of Recurrence Sequences",
  journal =      j-FIB-QUART,
  volume =       "36",
  number =       "4",
  pages =        "305--308",
  month =        aug,
  year =         "1998",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  bibdate =      "Thu Oct 20 18:02:49 MDT 2011",
  bibsource =    "http://www.fq.math.ca/36-4.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Scanned/36-4/slijepcevic.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Troll:1998:ZLC,
  author =       "G. Troll and P. beim Graben",
  title =        "{Zipf}'s law is not a consequence of the {Central
                 Limit Theorem}",
  journal =      j-PHYS-REV-E,
  volume =       "57",
  number =       "3",
  pages =        "1347--1355",
  day =          "1",
  month =        feb,
  year =         "1998",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.57.1347",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.57.1347;
                 http://pre.aps.org/abstract/PRE/v57/i2/p1347_1",
  abstract =     "It has been observed that the rank statistics of
                 string frequencies of many symbolic systems (e.g., word
                 frequencies of natural languages) follows Zipf's law in
                 good approximation. We show that, contrary to claims in
                 the literature, Zipf's law cannot be realized by the
                 central limit theorem(s). The observation that a
                 log-normal distribution of string frequencies yields an
                 approximately Zipf-like rank statistics is actually
                 misleading. Indeed, Zipf's law for the rank statistics
                 is strictly equivalent to a power law distribution of
                 frequencies. There are two natural ways to perform the
                 infinite size limit for the vocabulary. The first one
                 is the method of choice in the literature; it makes the
                 upper word length bound tend to infinity and leads in
                 the case of a multistate Bernoulli process via a
                 central limit theorem to a log-normal frequency
                 distribution. An alternative and for text samples
                 actually better realizable way is to make the lower
                 frequency bound tend to zero. This limit procedure
                 leads to a power law distribution and hence to Zipf's
                 law --- at least for Bernoulli processes and to a very
                 good approximation for natural languages where it
                 passes the $ \chi^2 $ test. For the Bernoulli case we
                 will give a heuristic proof.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Book{Wirsching:1998:DSG,
  author =       "G{\"u}nther J. Wirsching",
  title =        "The dynamical system generated by the $ 3 n + 1 $
                 function",
  volume =       "1681",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vii + 158",
  year =         "1998",
  ISBN =         "3-540-63970-5 (softcover)",
  ISBN-13 =      "978-3-540-63970-1 (softcover)",
  ISSN =         "0075-8434 (print), 1617-9692 (electronic)",
  LCCN =         "QA3 .L28 no. 1681",
  bibdate =      "Mon Nov 21 08:00:54 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNM,
  URL =          "http://www.loc.gov/catdir/enhancements/fy0818/97051329-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0818/97051329-t.html",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Sequences (Mathematics); Combinatorial probabilities;
                 Convergence",
}

@Article{Ausloos:1999:PMK,
  author =       "M. Ausloos and K. Ivanova",
  title =        "Precise $ (m, k) $-{Zipf} diagram analysis of
                 mathematical and financial time series when $ m = 6 $,
                 $ k = 2 $",
  journal =      j-PHYSICA-A,
  volume =       "270",
  number =       "3--4",
  pages =        "526--542",
  day =          "15",
  month =        aug,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(99)00178-8",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437199001788",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{AyllonBurguillo:1999:PDS,
  author =       "Juan David {Ayll{\'o}n Burguillo} and Manuel {Perera
                 Dom{\'\i}nguez}",
  title =        "El primer d{\'\i}gito significativo. ({Spanish}) [The
                 first significant digit]",
  journal =      "{Epsilon}: Revista de la {Sociedad Andaluza de
                 Educaci{\'o}n Matem{\'a}tica ``Thales''}",
  volume =       "15",
  number =       "3(45)",
  pages =        "339--352",
  month =        "????",
  year =         "1999",
  ISSN =         "1131-9321",
  ISSN-L =       "1131-9321",
  MRnumber =     "K60xx",
  bibdate =      "Sat Feb 16 14:32:14 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "MATHEDUC.02332710",
  acknowledgement = ack-nhfb,
  ajournal =     "{Rev. Epsil{\'o}n SAEM `Thales'}",
  journal-URL =  "http://thales.cica.es/epsilon/;
                 http://dialnet.unirioja.es/servlet/revista?codigo=504",
  language =     "Spanish",
  remark =       "Reported in \cite{Torres:2007:HDN} to contain an
                 extensive bibliography on Benford's Law. The publisher
                 does not have issues before 2003, and no electronic
                 copy has yet been found on the Internet. Attempts to
                 get this paper via Interlibrary Loan failed on the
                 grounds that ``We are unable to verify any owning
                 libraries within the United States or those that we
                 have ILL privileges.''",
  xxauthor =     "Manuel {Perera Dom{\'\i}nguez} and Juan David
                 {Ayll{\'o}n Burguillo}",
}

@Article{Barabasi:1999:ESR,
  author =       "Albert-L{\'a}szl{\'o} Barab{\'a}si and R{\'e}ka
                 Albert",
  title =        "Emergence of scaling in random networks",
  journal =      j-SCIENCE,
  volume =       "286",
  number =       "5439",
  pages =        "509--512",
  day =          "15",
  month =        oct,
  year =         "1999",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.286.5439.509",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Tue Nov 15 09:57:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/286/5439/509",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "power-law distribution; Zipf's Law",
}

@Article{Brakman:1999:RZT,
  author =       "Steven Brakman and Harry Garretsen and Charles {Van
                 Marrewijk} and Marianne {Van Den Berg}",
  title =        "The Return of {Zipf}: Towards a Further Understanding
                 of the Rank--Size Distribution",
  journal =      j-J-REG-SCI,
  volume =       "39",
  number =       "1",
  pages =        "183--213",
  year =         "1999",
  DOI =          "https://doi.org/10.1111/1467-9787.00129",
  ISSN =         "0022-4146 (print), 1467-9787 (electronic)",
  ISSN-L =       "0022-4146",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Regional Science",
}

@Article{Coderre:1999:FDU,
  author =       "David Coderre",
  title =        "Fraud Detection Using Digital Analysis",
  journal =      j-EDPACS,
  volume =       "27",
  number =       "3",
  pages =        "1--8",
  month =        "????",
  year =         "1999",
  CODEN =        "EDPCDF",
  DOI =          "https://doi.org/10.1201/1079/43249.27.3.19990901/30268.1",
  ISSN =         "0736-6981 (print), 1936-1009 (electronic)",
  ISSN-L =       "0736-6981",
  bibdate =      "Sat Jan 07 09:20:49 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43249.27.3.19990901/30268.1",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  keywords =     "Benford's Law",
  onlinedate =   "21 Dec 2006",
}

@Article{Egghe:1999:LZM,
  author =       "L. Egghe",
  title =        "On the law of {Zipf--Mandelbrot} for multi-word
                 phrases",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "50",
  number =       "3",
  pages =        "233--241",
  month =        "????",
  year =         "1999",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Mon Sep 10 06:09:31 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "17 Feb 1999",
}

@Article{Egghe:1999:RLZ,
  author =       "L. Egghe",
  title =        "Research: On the law of {Zipf--Mandelbrot} for
                 multi-word phrases",
  journal =      j-J-AM-SOC-INF-SCI,
  volume =       "50",
  number =       "3",
  pages =        "233--241",
  month =        "????",
  year =         "1999",
  CODEN =        "AISJB6",
  DOI =          "https://doi.org/10.1002/(SICI)1097-4571(1999)50:3<233::AID-ASI6>3.0.CO%3B2-8",
  ISSN =         "0002-8231 (print), 1097-4571 (electronic)",
  ISSN-L =       "0002-8231",
  bibdate =      "Fri Sep 11 09:04:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasis.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "17 Feb 1999",
}

@Article{Gabaix:1999:ZLC,
  author =       "Xavier Gabaix",
  title =        "{Zipf}'s law for cities: An explanation",
  journal =      j-Q-J-ECON,
  volume =       "114",
  number =       "3",
  pages =        "739--767",
  year =         "1999",
  CODEN =        "QJECAT",
  DOI =          "https://doi.org/10.1162/003355399556133",
  ISSN =         "0033-5533 (print), 1531-4650 (electronic)",
  ISSN-L =       "0033-5533",
  bibdate =      "Sat Nov 12 10:57:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0952.91059",
  abstract =     "Zipf's law is a very tight constraint on the class of
                 admissible models of local growth. It says that for
                 most countries the size distribution of cities
                 strikingly fits a power law: the number of cities with
                 populations greater than $S$ is proportional to $ 1 / S
                 $. Suppose that, at least in the upper tail, all cities
                 follow some proportional growth process (this appears
                 to be verified empirically). This automatically leads
                 their distribution to converge to Zipf's law.",
  acknowledgement = ack-nhfb,
  ajournal =     "Q. J. Econ.",
  classmath =    "91B62 (Dynamic economic models etc.) 91B72 (Spatial
                 models)",
  fjournal =     "The Quarterly Journal of Economics",
  keywords =     "local growth; Zipf's law",
}

@Book{Gigerenzer:1999:SHM,
  author =       "Gerd Gigerenzer and Peter M. Todd",
  title =        "Simple heuristics that make us smart",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xv + 416",
  year =         "1999",
  ISBN =         "0-19-512156-2",
  ISBN-13 =      "978-0-19-512156-8",
  LCCN =         "BD260 .G54 1999",
  bibdate =      "Sat Sep 10 11:19:26 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Evolution and cognition",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0640/98051084-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0640/98051084-t.html;
                 http://www.loc.gov/catdir/enhancements/fy0726/98051084-b.html",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Heuristic",
  tableofcontents = "The ABC Research Group \\
                 I. The Research Agenda \\
                 1. Fast and Frugal Heuristics: The Adaptive Toolbox /
                 Gerd Gigerenzer and Peter M. Todd \\
                 II. Ignorance-Based Decision Making \\
                 2. The Recognition Heuristic: How Ignorance Makes Us
                 Smart / Daniel G. Goldstein and Gerd Gigerenzer \\
                 3. Can Ignorance Beat the Stock Market? / Bernhard
                 Borges et al. \\
                 III. One-Reason Decision Making \\
                 4. Betting on One Good Reason: The Take The Best
                 Heuristic / Gerd Gigerenzer and Daniel G. Goldstein \\
                 5. How Good Are Simple Heuristics? / Jean Czerlinski,
                 Gerd Gigerenzer, and Daniel G. Goldstein \\
                 6. Why Does One-Reason Decision Making Work? A Case
                 Study in Ecological Rationality / Laura Martignon and
                 Ulrich Hoffrage \\
                 7. When Do People Use Simple Heuristics, and How Can We
                 Tell? / J{\"o}rg Rieskamp and Ulrich Hoffrage \\
                 8. Bayesian Benchmarks for Fast and Frugal Heuristics /
                 Laura Martignon and Kathryn Blackmond Laskey \\
                 IV. Beyond Choice: Memory, Estimation, and
                 Categorization \\
                 9. Hindsight Bias: A Price Worth Paying for Fast and
                 Frugal Memory / Ulrich Hoffrage and Ralph Hertwig \\
                 10. Quick Estimation: Letting the Environment Do the
                 Work / Ralph Hertwig, Ulrich Hoffrage, and Laura
                 Martignon \\
                 11. Categorization by Elimination: Using Few Cues to
                 Choose / Patricia M. Berretty, Peter M. Todd, and Laura
                 Martignon \\
                 V. Social Intelligence \\
                 12. How Motion Reveals Intention: Categorizing Social
                 Interactions / Philip W. Blythe, Peter M. Todd, and
                 Geoffrey F. Miller \\
                 13. From Pride and Prejudice to Persuasion: Satisficing
                 in Mate Search / Peter M. Todd and Geoffrey F. Miller
                 \\
                 14. Parental Investment by Simple Decision Rules /
                 Jennifer Nerissa Davis and Peter M. Todd \\
                 VI. A Look Around, A Look Back, A Look Ahead \\
                 15. Demons versus Heuristics in Artificial
                 Intelligence, Behavioral Ecology, and Economics / Adam
                 S. Goodie et al. \\
                 16. What We Have Learned (So Far) / Peter M. Todd and
                 Gerd Gigerenzer \\
                 References \\
                 Name Index \\
                 Subject Index",
}

@Article{Hill:1999:DFD,
  author =       "Theodore P. Hill",
  title =        "The Difficulty of Faking Data",
  journal =      j-CHANCE,
  volume =       "12",
  number =       "3",
  pages =        "27--31",
  month =        "????",
  year =         "1999",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.1999.10542154",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Tue Nov 22 18:54:44 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amstat.tandfonline.com/doi/abs/10.1080/09332480.1999.10542154",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
  keywords =     "Benford's Law",
  xxnote =       "Check: Hurlimann bibliography says v26 pp. 8--13??;
                 that is wrong!",
}

@Article{Hill:1999:PCS,
  author =       "Theodore P. Hill",
  title =        "Le premier chiffre significatif fait sa loi.
                 ({French}) [{The} first significant digit makes its
                 law]",
  journal =      "La Recherche: L'actualit{\'e} des sciences",
  volume =       "2",
  number =       "316",
  pages =        "72--76",
  month =        jan,
  year =         "1999",
  CODEN =        "RCCHBV",
  ISSN =         "0029-5671 (print), 1625-9955 (electronic)",
  ISSN-L =       "0029-5671",
  bibdate =      "Sat Feb 16 17:51:25 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.larecherche.fr/savoirs/autre/premier-chiffre-significatif-fait-sa-loi-01-01-1999-70970",
  acknowledgement = ack-nhfb,
  language =     "French",
  xxjournal =    "La Recherche Hors S{\'e}rie",
}

@Article{Huberman:1999:IGD,
  author =       "Bernardo A. Huberman and Lada A. Adamic",
  title =        "{Internet}: Growth dynamics of the {World-Wide Web}",
  journal =      j-NATURE,
  volume =       "401",
  number =       "6749",
  pages =        "131--131",
  day =          "9",
  month =        sep,
  year =         "1999",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/43604",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Tue Nov 15 09:52:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Zipf's Law",
}

@TechReport{Lowe:1999:FDL,
  author =       "Tomas Lowe and Sally Murphy and Justin Hayward",
  title =        "The First Digit Law",
  type =         "Report",
  number =       "??",
  institution =  "Department of Computing, Imperial College",
  address =      "London, UK",
  month =        jun,
  year =         "1999",
  bibdate =      "Wed Nov 23 16:59:50 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://users.isr.ist.utl.pt/~jmrs/research/TopicsLinks/Benford/hayward.pdf;
                 http://www.doc.ic.ac.uk/~jjh97/suprema/main_page.html",
  acknowledgement = ack-nhfb,
  lastaccess =   "23 November 2011",
}

@Article{Malcai:1999:PLD,
  author =       "Ofer Malcai and Ofer Biham and Sorin Solomon",
  title =        "Power-law distributions and {L{\'e}vy}-stable
                 intermittent fluctuations in stochastic systems of many
                 autocatalytic elements",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "2",
  pages =        "1299--1303",
  month =        aug,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.60.1299",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 10:25:38 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.60.1299",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
}

@Article{Manrubia:1999:SMP,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette",
  title =        "Stochastic multiplicative processes with reset
                 events",
  journal =      j-PHYS-REV-E,
  volume =       "59",
  number =       "5",
  pages =        "4945--4948",
  month =        may,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.59.4945",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:25:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.59.4945",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "5",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's law",
}

@Article{Manrubia:1999:TDS,
  author =       "Susanna C. Manrubia and Dami{\'a}n H. Zanette and
                 Ricard V. Sol{\'e}",
  title =        "Transient Dynamics and Scaling Phenomena in Urban
                 Growth",
  journal =      j-FRACTALS,
  volume =       "7",
  number =       "1",
  pages =        "1--8",
  month =        mar,
  year =         "1999",
  CODEN =        "FRACEG",
  DOI =          "https://doi.org/10.1142/S0218348X99000025",
  ISSN =         "0218-348X",
  ISSN-L =       "0218-348X",
  bibdate =      "Wed Feb 27 07:11:42 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.worldscientific.com/doi/abs/10.1142/S0218348X99000025",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals",
  journal-URL =  "http://www.worldscientific.com/loi/fractals",
  keywords =     "Zipf's Law",
}

@Article{Matthews:1999:PO,
  author =       "Robert Matthews",
  title =        "The Power of One",
  journal =      j-NEW-SCIENTIST,
  volume =       "163",
  number =       "2194",
  pages =        "27--30",
  day =          "10",
  month =        jul,
  year =         "1999",
  CODEN =        "NWSCAL",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Mon Nov 14 16:04:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fortunecity.com/emachines/e11/86/one.html;
                 http://www.newscientist.com/article/mg16321944.600-the-power-of-one.html",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  xxISSN =       "0262-4079, 0028-6664",
}

@Article{Mercik:1999:SAI,
  author =       "Szymon Mercik and Karina Weron and Zuzanna Siwy",
  title =        "Statistical analysis of ionic current fluctuations in
                 membrane channels",
  journal =      j-PHYS-REV-E,
  volume =       "60",
  number =       "6",
  pages =        "7343--7348",
  day =          "1",
  month =        dec,
  year =         "1999",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.60.7343",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.60.7343",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Book{Miller:1999:JFM,
  author =       "Irwin Miller and Marylees Miller",
  title =        "{John E. Freund}'s mathematical statistics",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Sixth",
  pages =        "xii + 624",
  year =         "1999",
  ISBN =         "0-13-123613-X",
  ISBN-13 =      "978-0-13-123613-4",
  LCCN =         "QA276 .M4726 1999",
  bibdate =      "Thu Oct 13 07:00:13 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1928--",
  remark =       "Revised edition of John E. Freund,
                 \booktitle{Mathematical statistics}, 5th edition,
                 1992.",
  subject =      "Mathematical statistics",
}

@Article{Nigrini:1999:AVD,
  author =       "Mark J. Nigrini",
  title =        "Adding value with digital analysis",
  journal =      "The Internal Auditor: Journal of the {Institute of
                 Internal Auditors}",
  volume =       "56",
  number =       "1",
  pages =        "21--23",
  month =        "????",
  year =         "1999",
  CODEN =        "ITAUAB",
  ISSN =         "0020-5745",
  ISSN-L =       "0020-5745",
  bibdate =      "Sat Feb 16 18:56:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Nigrini:1999:IGY,
  author =       "Mark J. Nigrini",
  title =        "{I've} Got Your Number: How a Mathematical Phenomenon
                 Can Help {CPAs} Uncover Fraud and Other
                 Irregularities",
  journal =      j-J-ACCOUNTANCY,
  volume =       "187",
  number =       "2",
  pages =        "79--83",
  month =        may,
  year =         "1999",
  CODEN =        "JACYAD",
  ISSN =         "0021-8448 (print), 1945-0729 (electronic)",
  ISSN-L =       "0021-8448",
  bibdate =      "Mon Nov 14 16:31:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.aicpa.org/pubs/jofa/may1999/nigrini.htm;
                 http://www.journalofaccountancy.com/issues/1999/may/nigrini.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
  journal-URL =  "http://www.journalofaccountancy.com/",
}

@Article{Nigrini:1999:PPF,
  author =       "Mark J. Nigrini",
  title =        "Peculiar patterns of first digits",
  journal =      j-IEEE-POT,
  volume =       "18",
  number =       "2",
  pages =        "24--27",
  month =        apr # "\slash " # may,
  year =         "1999",
  CODEN =        "IEPTDF",
  DOI =          "https://doi.org/10.1109/45.755849",
  ISSN =         "0278-6648 (print), 1558-1772 (electronic)",
  ISSN-L =       "0278-6648",
  bibdate =      "Mon Nov 21 22:18:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Despite seeing numbers all the time only occasionally
                 would one say that a list of numbers seems odd. For
                 this to occur, the numbers are typically highly rounded
                 or implausible (too much of a coincidence). However
                 digit pattern analysis, using a computer, can produce
                 valuable findings not revealed at a mere glance. The
                 most widely cited paper on digit frequencies was
                 published by Frank Benford in 1938. With powerful,
                 low-cost personal computers, Benford's law can help us
                 to efficiently test the integrity of data. The first
                 step is to assess whether Benford's law should apply to
                 the data. If the data is expected to conform, then
                 Benford's law becomes the expected distribution.
                 Conformity means that the actual distribution closely
                 approximates the expected distribution",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Potentials",
}

@Article{Okuyama:1999:ZLI,
  author =       "K. Okuyama and M. Takayasu and H. Takayasu",
  title =        "{Zipf}'s law in income distribution of companies",
  journal =      j-PHYSICA-A,
  volume =       "269",
  number =       "1",
  pages =        "125--131",
  day =          "1",
  month =        jul,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(99)00086-2",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437199000862",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Growth rate of assets; Income distribution; Zipf's
                 Law",
}

@Article{Piqueira:1999:ZLO,
  author =       "J. R. C. Piqueira and L. H. A. Monteiro and T. M. C.
                 de Magalh{\~a}es and R. T. Ramos and R. B. Sassi and E.
                 G. Cruz",
  title =        "{Zipf's Law} Organizes a Psychiatric Ward",
  journal =      j-J-THEOR-BIOL,
  volume =       "198",
  number =       "3",
  pages =        "439--443",
  day =          "7",
  month =        jun,
  year =         "1999",
  CODEN =        "JTBIAP",
  DOI =          "https://doi.org/10.1006/jtbi.1999.0923",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022519399909232",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@Article{Stanley:1999:SUR,
  author =       "H. Eugene Stanley",
  title =        "Scaling, universality, and renormalization: Three
                 pillars of modern critical phenomena",
  journal =      j-REV-MOD-PHYS,
  volume =       "71",
  number =       "2",
  pages =        "S358--S366",
  month =        mar,
  year =         "1999",
  CODEN =        "RMPHAT",
  DOI =          "https://doi.org/10.1103/RevModPhys.71.S358",
  ISSN =         "0034-6861 (print), 1538-4527 (electronic), 1539-0756",
  ISSN-L =       "0034-6861",
  bibdate =      "Wed May 23 10:16:18 MDT 2012",
  bibsource =    "http://rmp.aps.org/toc/RMP/v71/i2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/revmodphys1990.bib",
  URL =          "http://link.aps.org/doi/10.1103/RevModPhys.71.S358;
                 http://rmp.aps.org/abstract/RMP/v71/i2/pS358_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Reviews of Modern Physics",
  journal-URL =  "http://rmp.aps.org/browse",
}

@Article{Vandewalle:1999:ZAF,
  author =       "N. Vandewalle and M. Ausloos",
  title =        "The $n$-{Zipf} analysis of financial data series and
                 biased data series",
  journal =      j-PHYSICA-A,
  volume =       "268",
  number =       "1--2",
  pages =        "240--249",
  day =          "1",
  month =        jun,
  year =         "1999",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(99)00031-X",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037843719900031X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Vardi:1999:PCS,
  author =       "Ilan Vardi",
  title =        "Premiers chiffres significatifs et nombres
                 alg{\'e}briques. ({French}) [Significant leading digits
                 and algebraic numbers]",
  journal =      j-C-R-ACAD-SCI-I,
  volume =       "328",
  number =       "9",
  pages =        "749--754",
  month =        may,
  year =         "1999",
  CODEN =        "CASMEI",
  DOI =          "https://doi.org/10.1016/S0764-4442(99)80265-1",
  ISSN =         "0764-4442 (print), 1778-3577 (electronic)",
  ISSN-L =       "0764-4442",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0764444299802651",
  abstract =     "I show that there is a meromorphic continuation of $
                 \sigma \log_\beta n / a < \log_\beta a n^{-s} $ to the
                 whole plane if and only if $ \beta $ is a Pisot number,
                 $ \alpha \in Q(\beta) $, and either the second largest
                 conjugate of $ \beta $ is real or the conjugate of $
                 \alpha $ corresponding to the second largest conjugate
                 of $ \beta $ is positive.",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes rendus de l'Acad{\'e}mie des sciences.
                 S{\'e}rie I, Math{'e}matique",
  keywords =     "Benford's Law",
  language =     "French",
}

@Article{Walthoe:1999:LNO,
  author =       "Jon Walthoe and Robert Hunt and Mike Pearson",
  title =        "Looking out for number one",
  journal =      "Plus Magazine",
  volume =       "??",
  number =       "??",
  pages =        "1--9",
  month =        sep,
  year =         "1999",
  DOI =          "????",
  bibdate =      "Mon Feb 18 06:59:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Published by the University of Cambridge Millennium
                 Mathematics Project.",
  URL =          "http://plus.maths.org/issue9/features/benford/2pdf/index.html/op.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Banyard:2000:NAF,
  author =       "Peter Banyard",
  title =        "A New Aid for Fraud Detection",
  journal =      "Credit Management: journal of the {Institute of Credit
                 Management}",
  volume =       "??",
  number =       "??",
  address =      "Stamford College, UK",
  pages =        "32--33",
  month =        mar,
  year =         "2000",
  DOI =          "",
  ISSN =         "0265-2099",
  ISSN-L =       "0265-2099",
  bibdate =      "Thu Oct 13 08:34:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  abstract =     "A simple mathematical curiosity, discovered about a
                 century ago, may well prove a surefire way of sniffing
                 out swindlers. Benford's Law was just an observation
                 until the theory that proved it was discovered 3 years
                 ago. It seems unlikely, but about 30\% of numbers start
                 with the digit one. Another 18\% start with the digit 2
                 and only 4.6\% start with 9. It would be quite easy to
                 build a Benford fraud buster into any analysis of
                 figures, while it remains extremely difficult to
                 produce an artificial set of figures that will comply
                 with the law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "I cannot find a Web site for this journal, or for its
                 archives, despite extensive searching.",
}

@Article{Blank:2000:PLC,
  author =       "Aharon Blank and Sorin Solomon",
  title =        "Power laws in cities population, financial markets and
                 {Internet} sites (scaling in systems with a variable
                 number of components)",
  journal =      j-PHYSICA-A,
  volume =       "287",
  number =       "1--2",
  pages =        "279--288",
  day =          "15",
  month =        nov,
  year =         "2000",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00464-7",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 06:24:21 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437100004647",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@InProceedings{Burns:2000:SSR,
  author =       "B. D. Burns",
  editor =       "Niels A. Taatgen and Hedderik van Rijn",
  booktitle =    "{Proceedings of the 31st Annual Conference of the
                 Cognitive Science Society 2009 (CogSci 2009):
                 Amsterdam, Netherlands, 29 July--1 August 2009}",
  title =        "Sensitivity to Statistical Regularities: People
                 (Largely) Follow {Benford's Law}",
  publisher =    "Cognitive Science Society",
  address =      "Austin, TX, USA",
  pages =        "2872--2877",
  year =         "2010",
  ISBN =         "1-61567-407-1",
  ISBN-13 =      "978-1-61567-407-7",
  LCCN =         "????",
  bibdate =      "Sat Sep 10 10:53:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Drake:2000:CAA,
  author =       "Philip D. Drake and Mark J. Nigrini",
  title =        "Computer assisted analytical procedures using
                 {Benford's Law}",
  journal =      j-J-ACCOUNT-EDUC,
  volume =       "18",
  number =       "2",
  pages =        "127--146",
  month =        "Spring",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S0748-5751(00)00008-7",
  ISSN =         "0748-5751 (print), 1873-1996 (electronic)",
  ISSN-L =       "0748-5751",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0748575100000087;
                 http://www.sciencedirect.com/science/journal/07485751",
  abstract =     "This case introduces students to Benford's Law and
                 Digital Analysis, which can be used as an analytical
                 procedure and fraud detection tool. Digital Analysis
                 (DA) is the analysis of digit and number patterns of a
                 data set. Actual digit frequencies in a data set are
                 compared to the expected frequencies according to
                 Benford's Law [Benford, F. (1938). The law of the
                 anomalous numbers, Proceedings of the American
                 Philosophical Society, 78, 551 572.]. Minor differences
                 suggest that the data have passed a reasonableness
                 test, while major differences signal possible financial
                 statement mis-statements. After describing Benford's
                 Law and the basic {DA} tests, the case requires
                 auditing students to download {DA} software and the
                 actual accounts payable file of a software company from
                 a designated Internet site. Students then, (1) analyse
                 the data using three {DA} tests as an analytical
                 procedure in an external audit context, and (2) graph
                 and a report the results and audit-related conclusions.
                 The teaching note includes the actual findings from the
                 audit of that data set and guidance on using the case
                 in an auditing course.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accounting Education",
  keywords =     "Benford's Law",
}

@Article{Lanza:2000:UDA,
  author =       "R. B. Lanza",
  title =        "Using digital analysis to detect fraud: Review of the
                 {DATAS\reg} statistical analysis tool",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "1",
  number =       "??",
  pages =        "291--296",
  month =        "????",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "1524-5586",
  bibdate =      "Tue Nov 22 10:47:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.rtedwards.com/journals/JFA/",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Leemis:2000:SDS,
  author =       "Lawrence M. Leemis and Bruce W. Schmeiser and Diane L.
                 Evans",
  title =        "Survival Distributions Satisfying {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "54",
  number =       "4",
  pages =        "236--241",
  month =        nov,
  year =         "2000",
  CODEN =        "ASTAAJ",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRclass =      "62E15 (62N05)",
  MRnumber =     "1803620",
  bibdate =      "Fri Jan 27 18:16:34 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326510;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/publications/tas/Leemis.htm;
                 http://www.jstor.org/stable/2685773",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@InProceedings{Lei:2000:EIN,
  author =       "Skylar Lei and Michael Smith and Giancarlo Succi",
  title =        "Empirical investigation of a novel approach to check
                 the integrity of software engineering measuring
                 processes",
  crossref =     "ACM:2000:PIC",
  pages =        "773--773",
  year =         "2000",
  DOI =          "https://doi.org/10.1145/337180.337629",
  bibdate =      "Sat Feb 16 18:28:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Lowe:2000:BLF,
  author =       "R. Lowe",
  title =        "{Benford's Law} and fraud detection",
  journal =      "Chartered Accountants Journal of New Zealand",
  volume =       "79",
  number =       "10",
  pages =        "32--36",
  month =        "????",
  year =         "2000",
  DOI =          "",
  ISSN =         "1172-9929",
  ISSN-L =       "1172-9929",
  bibdate =      "Thu Oct 13 08:55:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.nzica.com/journalarchive.aspx",
  remark =       "No archives online before 2012. Library of Congress
                 says that publication ceased in July 2005 at volume 84,
                 number 6.",
}

@Article{Lowe:2000:WBL,
  author =       "R. Lowe",
  title =        "When {Benford's Law} is broken",
  journal =      "Chartered Accountants Journal of New Zealand",
  volume =       "79",
  number =       "11",
  pages =        "24--27",
  month =        "????",
  year =         "2000",
  DOI =          "",
  ISSN =         "1172-9929",
  ISSN-L =       "1172-9929",
  bibdate =      "Thu Oct 13 08:55:37 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.nzica.com/journalarchive.aspx",
  remark =       "No archives online before 2012. Library of Congress
                 says that publication ceased in July 2005 at volume 84,
                 number 6.",
}

@TechReport{Nigrini:2000:CA,
  author =       "Mark J. Nigrini",
  title =        "Continuous Auditing",
  type =         "Preprint",
  institution =  "Ernst \& Young Center for Auditing Research and
                 Advanced Technology, University of Kansas",
  address =      "Lawrence, KS, USA",
  pages =        "23",
  day =          "30",
  month =        aug,
  year =         "2000",
  bibdate =      "Sat Feb 16 18:57:40 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://aaahq.org/audit/midyear/01midyear/papers/nigrini_continuous_audit.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Book{Nigrini:2000:DAT,
  author =       "Mark J. Nigrini",
  title =        "Digital analysis tests and statistics: using digit and
                 number patterns and Benford's law to detect errors,
                 biases, fraud, irregularities, and processing
                 inefficiencies",
  publisher =    "Nigrini Institute Inc.",
  address =      "Allen, TX, USA",
  pages =        "242",
  year =         "2000",
  LCCN =         "????",
  bibdate =      "Sat Jan 23 07:53:08 MST 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Nigrini:2000:DAU,
  author =       "Mark John Nigrini",
  title =        "Digital analysis using {Benford}'s law: tests and
                 statistics for auditors",
  publisher =    "Global Audit Publications",
  address =      "Vancouver, BC, Canada",
  edition =      "Second",
  pages =        "xvii + 278",
  year =         "2000",
  ISBN =         "189449709 (??invalid ISBN??)",
  ISBN-13 =      "189449709 (??invalid ISBN??)",
  LCCN =         "????",
  bibdate =      "Tue Nov 22 20:48:29 MST 2011",
  bibsource =    "amicus.nlc-bnc.ca:210/NL;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  subject =      "Numerical analysis; Data processing; Auditing;
                 Statistical methods; Analyse num{\'e}rique;
                 Informatique; V{\'e}rification comptable; M{\'e}thodes
                 statistiques",
}

@Article{Padmanabhan:2000:CAD,
  author =       "Venkata N. Padmanabhan and Lili Qiu",
  title =        "The content and access dynamics of a busy {Web} server
                 (poster session)",
  journal =      j-SIGMETRICS,
  volume =       "28",
  number =       "1",
  pages =        "122--123",
  month =        jun,
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/339331.339405",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Thu Jun 26 11:31:11 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "We study the MSNBC Web site, one of the busiest in the
                 Internet today. We analyze the dynamics of content
                 creation and modification as well as client accesses.
                 Our key findings are (a) files tend to change little
                 upon modification, (b) a small set of files get
                 modified repeatedly, (c) file popularity follows a
                 Zipf-like distribution with an $ \alpha $ much larger
                 than reported in previous, proxy-based studies, and (d)
                 there is significant temporal stability in file
                 popularity but not much stability in the domains from
                 which popular content is accessed. We discuss
                 implications of these findings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
}

@Book{Sole:2000:SLH,
  author =       "Ricard Vicente Sol{\'e} and Brian Goodwin",
  title =        "Signs of Life: How Complexity Pervades Biology",
  publisher =    pub-BASIC-BOOKS,
  address =      pub-BASIC-BOOKS:adr,
  pages =        "xi + 322",
  year =         "2000",
  ISBN =         "0-465-01927-7, 0-465-01928-5 (paperback)",
  ISBN-13 =      "978-0-465-01927-4, 978-0-465-01928-1 (paperback)",
  LCCN =         "QH501 .S65 2000",
  bibdate =      "Thu Feb 28 09:59:50 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Mandelbrot; Zipf's law",
  tableofcontents = "Nonlinearity, chaos, and emergence \\
                 Order, complexity, disorder \\
                 Genetic networks, cell differentiation, and development
                 \\
                 Physiology on the edge of chaos \\
                 Brain dynamics \\
                 Ants, brains, and chaos \\
                 The Baroque of nature \\
                 Life on the edge of catastrophe \\
                 Evolution and extinction \\
                 Fractal cities and market crashes",
}

@Article{Soliman:2000:BPP,
  author =       "Ahmed A. Soliman",
  title =        "{Bayes} Prediction in a {Pareto} Lifetime Model with
                 Random Sample Size",
  journal =      j-J-R-STAT-SOC-SER-D-STATISTICIAN,
  volume =       "49",
  number =       "1",
  pages =        "51--62",
  month =        "????",
  year =         "2000",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2307/2681255",
  ISSN =         "0039-0526 (print), 1467-9884 (electronic)",
  ISSN-L =       "0039-0526",
  bibdate =      "Thu Jan 22 18:10:23 MST 2015",
  bibsource =    "http://www.jstor.org/stable/i326257;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jrss-d-2000.bib",
  URL =          "http://www.jstor.org/stable/2681255",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Royal Statistical Society. Series D
                 (The Statistician)",
  journal-URL =  "http://www.jstor.org/journals/00390526.html",
}

@Article{Stanley:2000:SIU,
  author =       "H. E. Stanley and L. A. N. Amaral and P. Gopikrishnan
                 and P. Ch. Ivanov and T. H. Keitt and V. Plerou",
  title =        "Scale invariance and universality: organizing
                 principles in complex systems",
  journal =      j-PHYSICA-A,
  volume =       "281",
  number =       "1--4",
  pages =        "60--68",
  day =          "15",
  month =        jun,
  year =         "2000",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00195-3",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu Feb 28 09:52:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437100001953",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "power law; scale invariance; Zipf's law",
}

@Article{Tapp:2000:UTD,
  author =       "D. J. Tapp and D. B. Burg",
  title =        "Using technology to detect fraud",
  journal =      "{Pennsylvania CPA} Journal",
  volume =       "71",
  number =       "4",
  pages =        "20--23",
  month =        "????",
  year =         "2000",
  ISSN =         "0746-1062",
  ISSN-L =       "0746-1062",
  bibdate =      "Thu Oct 13 09:05:22 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.picpa.org/keep-informed/pennsylvania-cpa-journal",
  keywords =     "Benford's Law",
  remark =       "No archives online before 2014.",
}

@Article{Tolle:2000:DDS,
  author =       "Charles R. Tolle and Joanne L. Budzien and Randall A.
                 Laviolette",
  title =        "Do dynamical systems follow {Benford}'s law?",
  journal =      j-CHAOS,
  volume =       "10",
  number =       "2",
  pages =        "331--336",
  month =        "????",
  year =         "2000",
  CODEN =        "CHAOEH",
  DOI =          "https://doi.org/10.1063/1.166498",
  ISSN =         "1054-1500",
  ISSN-L =       "1054-1500",
  bibdate =      "Mon Nov 14 17:35:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2000Chaos..10..331T;
                 http://link.aip.org/link/chaoeh/v10/i2/p331/s1;
                 http://link.aip.org/link/doi/10.1063/1.166498",
  abstract =     "Data compiled from a variety of sources follow
                 Benford's law, which gives a monotonically decreasing
                 distribution of the first digit (1 through 9). We
                 examine the frequency of the first digit of the
                 coordinates of the trajectories generated by some
                 common dynamical systems. One-dimensional cellular
                 automata fulfill the expectation that the frequency of
                 the first digit is uniform. The molecular dynamics of
                 fluids, on the other hand, provides trajectories that
                 follow Benford's law. Finally, three chaotic systems
                 are considered: Lorenz, H{\'e}non, and R{\"o}ssler. The
                 Lorenz system generates trajectories that follow
                 Benford's law. The H{\'e}non system generates
                 trajectories that resemble neither the uniform
                 distribution nor Benford's law. Finally, the
                 R{\"o}ssler system generates trajectories that follow
                 the uniform distribution for some parameters choices,
                 and Benford's law for others.",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos (Woodbury, NY)",
  journal-URL =  "http://scitation.aip.org/content/aip/journal/chaos",
  xxpages =      "331--337",
}

@Article{Urzua:2000:SET,
  author =       "Carlos M. Urz{\'u}a",
  title =        "A simple and efficient test for {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "66",
  number =       "3",
  pages =        "257--260",
  day =          "1",
  month =        mar,
  year =         "2000",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/S0165-1765(99)00215-3",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176599002153",
  ZMnumber =     "0951.91059",
  abstract =     "This paper presents a simple and locally optimal test
                 for Zipf's law. Its use is illustrated in the case of
                 the largest US metropolitan areas. An objection to the
                 general relevance of that law is also presented.",
  acknowledgement = ack-nhfb,
  classmath =    "91B82 (Statistical methods in economics) 91B74 (Models
                 of real-world systems)",
  fjournal =     "Economics Letters",
  keywords =     "rank-size law; Zipf's law",
}

@Article{Vogt:2000:BGS,
  author =       "W. Vogt",
  title =        "{Benford's Gesetz: Steuer- und Budgets{\"u}ndern auf
                 der Spur --- Zahlen l{\"u}gen nichts}. ({German})
                 [{Benford's Law}: tax and budget sinners lying on the
                 track --- Numbers do not lie]",
  journal =      "Schweizer Versicherung",
  volume =       "9",
  number =       "??",
  pages =        "27--29",
  month =        "????",
  year =         "2000",
  DOI =          "????",
  bibdate =      "Mon Feb 18 06:57:07 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.schweizerversicherung.ch/de/archiv_suche",
  language =     "German",
  remark =       "No ISSN assigned. Not found in journal archive on 18
                 February 2013.",
}

@Article{York:2000:ATB,
  author =       "D. York",
  title =        "Auditing Technique --- {Benford}'s law",
  journal =      j-ACCOUNTANCY,
  volume =       "126",
  number =       "1283",
  pages =        "126--??",
  month =        "????",
  year =         "2000",
  CODEN =        "ACTYAD",
  ISSN =         "0001-4664",
  ISSN-L =       "0001-4664",
  bibdate =      "Wed Nov 23 11:30:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountancy",
  journal-URL =  "https://www.cchdaily.co.uk/magazine",
  remark =       "No archives online before 2014",
}

@Article{Axtell:2001:ZDU,
  author =       "R. L. Axtell",
  title =        "{Zipf} Distribution of {U.S.} Firm Sizes",
  journal =      j-SCIENCE,
  volume =       "293",
  number =       "5536",
  pages =        "1818--1820",
  day =          "7",
  month =        sep,
  year =         "2001",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.1062081",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Wed Feb 27 06:38:34 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/293/5536/1818",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "Zipf's Law",
}

@Article{Dolgikh:2001:PCS,
  author =       "Dmitry G. Dolgikh and Andrei M. Sukhov",
  title =        "Parameters of cache systems based on a {Zipf}-like
                 distribution",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "37",
  number =       "6",
  pages =        "711--716",
  day =          "15",
  month =        dec,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1389-1286(01)00243-2",
  ISSN =         "1389-1286 (print), 1872-7069 (electronic)",
  ISSN-L =       "1389-1286",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "http://www.elsevier.com/locate/issn/13891286;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.elsevier.nl/gej-ng/10/15/22/67/36/31/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S1389128601002432",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks (Amsterdam, Netherlands: 1999)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/13891286",
  keywords =     "Zipf's Law",
}

@Article{Dubinsky:2001:MFF,
  author =       "Bruce G. Dubinsky",
  title =        "Math formula fights fraud",
  journal =      "Legal Times of {Washington}",
  volume =       "XXIV",
  number =       "9",
  pages =        "??--??",
  day =          "26",
  month =        feb,
  year =         "2001",
  ISSN =         "0732-7536",
  ISSN-L =       "0732-7536",
  bibdate =      "Sat Feb 16 17:35:39 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  xxjournal =    "Legal Times",
}

@Article{Gelbukh:2001:ZHL,
  author =       "Alexander Gelbukh and Grigori Sidorov",
  title =        "{Zipf} and {Heaps Laws}' Coefficients Depend on
                 Language",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2004",
  pages =        "332--??",
  year =         "2001",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Feb 2 13:03:22 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2004.htm;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2004/20040332.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2004/20040332.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@TechReport{Gent:2001:BL,
  author =       "Ian Gent and Toby Walsh",
  title =        "{Benford's Law}",
  type =         "Report",
  institution =  "School of Computer Science, University of St. Andrews,
                 and Department of Computer Science, University of
                 York",
  address =      "St. Andrews, Scotland and York, England",
  pages =        "7",
  day =          "2",
  month =        feb,
  year =         "2001",
  bibdate =      "Fri Nov 18 08:37:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.dcs.st-and.ac.uk/~apes/reports/apes-25-2001.pdf",
  abstract =     "Benford's Law predicts the frequency of the leading
                 digit in numbers met in a wide range of naturally
                 occurring phenomena. In data following Benford's Law,
                 numbers start with a small leading digit more often
                 those with a large leading digit. Here we demonstrate
                 that Benford's Law also describes a wide range of
                 computational phenomena. In particular, we show that a
                 number of different statistics associated with
                 computation like space and runtime often follow
                 Benford's Law. We also show that search cost on input
                 data that follows Benford's Law is often very different
                 to that on more uniform data. These results could be
                 used to improve algorithm performance (for example, for
                 load balancing or disk de-fragmentation), as well as to
                 help model algorithm performance. Benford's Law can
                 also be used to generate data for benchmarking
                 algorithms that may be more realistic than purely
                 random data.",
  acknowledgement = ack-nhfb,
  remark =       "PDF file no longer at the St. Andrews URL on 18
                 November 2011, but recovered from
                 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.3357.",
}

@Article{Harremoes:2001:MEF,
  author =       "Peter Harremo{\"e}s and Flemming Tops{\o}e",
  title =        "Maximum Entropy Fundamentals",
  journal =      j-ENTROPY,
  volume =       "3",
  number =       "3",
  pages =        "191--226",
  month =        sep,
  year =         "2001",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e3030191",
  ISSN =         "1099-4300",
  ISSN-L =       "1099-4300",
  bibdate =      "Thu Feb 28 10:55:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.mdpi.com/1099-4300/3/3/191",
  acknowledgement = ack-nhfb,
  fjournal =     "Entropy",
  keywords =     "continuity of entropy; entropy loss; exponential
                 family; game theoretical equilibrium; hyperbolic
                 distributions; information topology; maximum entropy;
                 minimum risk; Nash equilibrium code; partition
                 function; Zipf's law",
  remark =       "Open access journal.",
}

@Article{Hobza:2001:NBL,
  author =       "Tom{\'a}{\v{s}} Hobza and Igor Vajda",
  title =        "On the {Newcomb--Benford} law in models of statistical
                 data",
  journal =      "Revista Matem{\'a}tica Complutense",
  volume =       "14",
  number =       "2",
  pages =        "407--420",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "1139-1138, 1696-8220, 1988-2807",
  ISSN-L =       "1139-1138",
  MRclass =      "62E10",
  MRnumber =     "1871305 (2002j:62015)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Rev. Mat. Complut.",
  fjournal =     "Revista Matem{\'a}tica Complutense",
}

@Article{Huang:2001:PLE,
  author =       "Z. F. Huang and S. Solomon",
  title =        "Power, {L{\'e}vy}, exponential and {Gaussian}-like
                 regimes in autocatalytic financial systems",
  journal =      j-EUR-PHYS-J-B,
  volume =       "20",
  number =       "4",
  pages =        "601--607",
  month =        apr,
  year =         "2001",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1007/PL00011114",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Thu Feb 28 10:26:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/PL00011114",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
  keywords =     "power law; scale invariance; Zipf's law",
}

@MastersThesis{Jamain:2001:BL,
  author =       "Adrien Jamain",
  title =        "{Benford's Law}",
  type =         "{Master}'s thesis",
  school =       "Department of Mathematics, Imperial College of London
                 and ENSIMAG",
  address =      "London, UK",
  pages =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:06:41 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Not found in Imperial College Library or COPAC
                 catalogs on 16 February 2013. URL link is broken too.",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jamain_thesis01.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Jansen:2001:RNP,
  author =       "C. J. M. Jansen and M. M. W. Pollmann",
  title =        "On Round Numbers: Pragmatic Aspects of Numerical
                 Expressions",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "8",
  number =       "3",
  pages =        "187--201",
  month =        "????",
  year =         "2001",
  DOI =          "https://doi.org/10.1076/jqul.8.3.187.4095",
  ISSN =         "0929-6174 (print), 1744-5035 (electronic)",
  ISSN-L =       "0929-6174",
  bibdate =      "Sat Jan 07 09:51:05 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1076/jqul.8.3.187.4095",
  abstract =     "This paper describes and explains some regularities in
                 the frequency of numbers in text. An analysis of number
                 frequencies in text corpora in Dutch, English, German,
                 and French confirms the expectation that frequency is
                 highly dependent on two factors: magnitude and
                 roundness. Roundness (defined as number frequency in an
                 approximation context) proves to be related to three
                 arithmetical properties: `10-ness', `2-ness', and
                 `5-ness'. In predicting the frequency of numbers
                 irrespective of their context `$ 2 1 / 2 $-ness' should
                 be added to these factors, as is suggested in the work
                 of Sigurd (1988). The role of the four number
                 characteristics found in this study can be explained by
                 the preference of the language user for using base
                 numbers, and for doubling and halving quantities.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  onlinedate =   "09 Aug 2010",
}

@Article{Jolion:2001:IBL,
  author =       "Jean-Michel Jolion",
  title =        "Images and {Benford}'s law",
  journal =      j-J-MATH-IMAG-VIS,
  volume =       "14",
  number =       "1",
  pages =        "73--81",
  year =         "2001",
  CODEN =        "JMIVEK",
  DOI =          "https://doi.org/10.1023/A:1008363415314",
  ISSN =         "0924-9907 (print), 1573-7683 (electronic)",
  ISSN-L =       "0924-9907",
  MRclass =      "94A08 (68U10)",
  MRnumber =     "1818436 (2001m:94007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments and extensions in \cite[Chapter
                 19]{Miller:2015:BLT}.",
  URL =          "http://link.springer.com/article/10.1023/A%3A1008363415314",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Imaging and Vision: JMIV",
}

@Article{Knudsen:2001:ZLC,
  author =       "Thorbj{\o}rn Knudsen",
  title =        "{Zipf}'s law for cities and beyond: the case of
                 {Denmark}",
  journal =      j-AM-J-ECON-SOCIOL,
  volume =       "60",
  number =       "1",
  pages =        "123--146",
  month =        jan,
  year =         "2001",
  CODEN =        "AJESA3",
  DOI =          "https://doi.org/10.1111/1536-7150.00057",
  ISSN =         "0002-9246 (print), 1536-7150 (electronic)",
  ISSN-L =       "0002-9246",
  bibdate =      "Sat Feb 16 18:14:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/3487947",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Journal of Economics and Sociology",
}

@Article{Kretschmer:2001:RAI,
  author =       "Hildrun Kretschmer and Ronald Rousseau",
  title =        "Research: Author inflation leads to a breakdown of
                 {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "52",
  number =       "8",
  pages =        "610--614",
  month =        "????",
  year =         "2001",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.1118",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:41:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "27 Apr 2001",
}

@Article{Levene:2001:ZLW,
  author =       "Mark Levene and Jos{\'e} Borges and George Loizou",
  title =        "{Zipf}'s law for {Web} surfers",
  journal =      j-KNOWL-INFO-SYS,
  volume =       "3",
  number =       "1",
  pages =        "120--129",
  year =         "2001",
  CODEN =        "KISNCR",
  DOI =          "https://doi.org/10.1007/PL00011657",
  ISSN =         "0219-1377",
  bibdate =      "Sat Nov 12 11:00:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "0991.68622",
  abstract =     "One of the main activities of Web users, known as
                 `surfing', is to follow links. Lengthy navigation often
                 leads to disorientation when users lose track of the
                 context in which they are navigating and are unsure how
                 to proceed in terms of the goal of their original
                 query. Studying navigation patterns of Web users is
                 thus important, since it can lead us to a better
                 understanding of the problems users face when they are
                 surfing. We derive Zipf's rank frequency law (i.e., an
                 inverse power law) from an absorbing Markov chain model
                 of surfers' behavior assuming that less probable
                 navigation trails are, on average, longer than more
                 probable ones. In our model the probability of a trail
                 is interpreted as the relevance (or `value') of the
                 trail. We apply our model to two scenarios: in the
                 first the probability of a user terminating the
                 navigation session is independent of the number of
                 links he has followed so far, and in the second the
                 probability of a user terminating the navigation
                 session increases by a constant each time the user
                 follows a link. We analyze these scenarios using two
                 sets of experimental data sets showing that, although
                 the first scenario is only a rough approximation of
                 surfers' behavior, the data is consistent with the
                 second scenario and can thus provide an explanation of
                 surfers' behavior.",
  acknowledgement = ack-nhfb,
  classmath =    "68U99 (Computing methodologies) 68P15 (Database
                 theory) 68P20 (Information storage and retrieval)",
  fjournal =     "Knowledge and Information Systems",
  keywords =     "Markov chain; Web navigation; Zipf's law",
}

@Article{Losee:2001:TDB,
  author =       "Robert M. Losee",
  title =        "Term dependence: a basis for {Luhn} and {Zipf}
                 models",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "52",
  number =       "12",
  pages =        "1019--1025",
  year =         "2001",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.1155",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@Article{Malacarne:2001:QED,
  author =       "L. C. Malacarne and R. S. Mendes and E. K. Lenzi",
  title =        "$q$-exponential distribution in urban agglomeration",
  journal =      j-PHYS-REV-E,
  volume =       "65",
  number =       "??",
  pages =        "017106",
  day =          "21",
  month =        dec,
  year =         "2001",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.65.017106",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.65.017106",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf--Mandelbrot law",
}

@Article{Montemurro:2001:BZM,
  author =       "Marcelo A. Montemurro",
  title =        "Beyond the {Zipf--Mandelbrot} law in quantitative
                 linguistics",
  journal =      j-PHYSICA-A,
  volume =       "300",
  number =       "3--4",
  pages =        "567--578",
  day =          "15",
  month =        nov,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(01)00355-7",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437101003557",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@PhdThesis{Morters:2001:BGV,
  author =       "Peter M{\"o}rters",
  title =        "{Benford's Gesetz {\"u}ber die Verteilung der
                 Ziffern}. (German) [{Benford}'s law on the distribution
                 of digits]",
  type =         "{Habilitationsvorlesung}",
  school =       "????",
  address =      "Kaiserslauten, Germany, and Bath, UK",
  pages =        "4",
  month =        "????",
  year =         "2001",
  bibdate =      "Sat Feb 16 18:47:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://people.bath.ac.uk/maspm/benford.ps",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Nigrini:2001:DAU,
  author =       "Mark Nigrini",
  title =        "Digital Analysis Using {Benford's} Law: Tests and
                 Statistics for Auditors",
  journal =      j-EDPACS,
  volume =       "28",
  number =       "9",
  pages =        "1--2",
  month =        "????",
  year =         "2001",
  CODEN =        "EDPCDF",
  DOI =          "https://doi.org/10.1201/1079/43266.28.9.20010301/30389.4",
  ISSN =         "0736-6981 (print), 1936-1009 (electronic)",
  ISSN-L =       "0736-6981",
  bibdate =      "Sat Jan 07 09:08:09 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1201/1079/43266.28.9.20010301/30389.4",
  acknowledgement = ack-nhfb,
  fjournal =     "EDPACS",
  onlinedate =   "21 Dec 2006",
}

@Article{Pietronero:2001:EUD,
  author =       "L. Pietronero and E. Tosatti and V. Tosatti and A.
                 Vespignani",
  title =        "Explaining the uneven distribution of numbers in
                 nature: the laws of {Benford} and {Zipf}",
  journal =      j-PHYSICA-A,
  volume =       "293",
  number =       "1--2",
  pages =        "297--304",
  day =          "1",
  month =        apr,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(00)00633-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2001PhyA..293..297P;
                 http://www.sciencedirect.com/science/article/pii/S0378437100006336",
  abstract =     "The distribution of first digits in numbers series
                 obtained from very different origins shows a marked
                 asymmetry in favor of small digits that goes under the
                 name of Benford's law. We analyze in detail this
                 property for different data sets and give a general
                 explanation for the origin of the Benford's law in
                 terms of multiplicative processes. We show that this
                 law can be also generalized to series of numbers
                 generated from more complex systems like the catalogs
                 of seismic activity. Finally, we derive a relation
                 between the generalized Benford's law and the popular
                 Zipf's law which characterize the rank order statistics
                 and has been extensively applied to many problems
                 ranging from city population to linguistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Reed:2001:PZO,
  author =       "William J. Reed",
  title =        "The {Pareto}, {Zipf} and other power laws",
  journal =      j-ECONOM-LETT,
  volume =       "74",
  number =       "1",
  pages =        "15--19",
  day =          "20",
  month =        dec,
  year =         "2001",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/S0165-1765(01)00524-9",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176501005249",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@TechReport{Scott:2001:BLE,
  author =       "P. D. Scott and M. Fasli",
  title =        "{Benford's Law}: An Empirical Investigation and a
                 Novel Explanation",
  type =         "CSM Technical Report",
  number =       "349",
  institution =  "Department of Computer Science, University Essex",
  address =      "Colchester, UK",
  day =          "26",
  month =        oct,
  year =         "2001",
  bibdate =      "Tue Nov 22 21:05:22 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.essex.ac.uk/csee/research/publications/technicalreports/2001/CSM-349.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Sellke:2001:CVT,
  author =       "Thomas Sellke and M. J. Bayarri and James O. Berger",
  title =        "Calibration of $p$ Values for Testing Precise Null
                 Hypotheses",
  journal =      j-AMER-STAT,
  volume =       "55",
  number =       "1",
  pages =        "62--71",
  month =        feb,
  year =         "2001",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/000313001300339950",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Jan 27 18:16:34 MST 2012",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 http://www.jstor.org/journals/00031305.html;
                 http://www.jstor.org/stable/i326511;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/publications/tas/Sellke.htm;
                 http://www.jstor.org/stable/2685531;
                 http://www.tandfonline.com/doi/abs/10.1198/000313001300339950",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Snyder:2001:SAO,
  author =       "Mark A. Snyder and James H. Curry and Anne M.
                 Dougherty",
  title =        "Stochastic aspects of one-dimensional discrete
                 dynamical systems: {Benford}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "64",
  number =       "2",
  pages =        "026222:1--026222:5",
  month =        aug,
  year =         "2001",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.64.026222",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Mon Nov 14 17:44:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2001PhRvE..64b6222S;
                 http://pre.aps.org/abstract/PRE/v64/i2/e026222",
  abstract =     "Benford's law owes its discovery to the ``Grubby Pages
                 Hypothesis,'' a 19th century observation made by Simon
                 Newcomb that the beginning pages of logarithm books
                 were grubbier than the last few pages, implying that
                 scientists referenced the values toward the front of
                 the books more frequently. If a data set satisfies
                 Benford's law, then its significant digits will have a
                 logarithmic distribution, which favors smaller
                 significant digits. In this article we demonstrate two
                 ways of creating discrete one-dimensional dynamical
                 systems that satisfy Benford's law. We also develop a
                 numerical simulation methodology that we use to study
                 dynamical systems when analytical results are not
                 readily available.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  pagecount =    "5",
}

@InCollection{Solomon:2001:SPZ,
  author =       "Sorin Solomon and Peter Richmond",
  booktitle =    "Economics with heterogeneous interacting agents
                 ({Marseille}, 2000)",
  title =        "Stability of {Pareto--Zipf} law in non-stationary
                 economies",
  volume =       "503",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "141--159",
  year =         "2001",
  MRclass =      "91B28 (91B62)",
  MRnumber =     "1838925",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Econom. and Math. Systems",
  acknowledgement = ack-nhfb,
}

@Article{Zanette:2001:VTC,
  author =       "Dami{\'a}n H. Zanette and Susanna C. Manrubia",
  title =        "Vertical transmission of culture and the distribution
                 of family names",
  journal =      j-PHYSICA-A,
  volume =       "295",
  number =       "1--2",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2001",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(01)00046-2",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:03:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437101000462",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Abe:2002:STE,
  author =       "Sumiyoshi Abe",
  title =        "Stability of {Tsallis} entropy and instabilities of
                 {R{\'e}nyi} and normalized {Tsallis} entropies: a basis
                 for $q$-exponential distributions",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "??",
  pages =        "046134",
  day =          "24",
  month =        oct,
  year =         "2002",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.66.046134",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.66.046134",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Anonymous:2002:ZLM,
  author =       "Anonymous",
  title =        "{Zipf}'s law and maximum sustainable growth",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "??--??",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.jedc.2013.02.004",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165188913000341",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Zipf's Law",
  onlinedate =   "19 February 2013",
}

@InProceedings{Bhattacharya:2002:KBT,
  author =       "S. Bhattacharya",
  editor =       "????",
  booktitle =    "9th World Congress of Accounting Historians, Deakin
                 University, Melbourne, Australia July 30--August 3,
                 2002",
  title =        "From {Kautilya} to {Benford} --- Trends in Forensic
                 and Investigative Accounting",
  publisher =    "Accounting Association of Australia and New Zealand",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:22:29 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://ach.sagepub.com/",
  remark =       "I cannot find the published proceedings in online
                 catalogs or bookstores, or in the Deakin University
                 library catalogs. Where only selected papers published
                 from the conference in the journal Accounting
                 History??",
  review-doi =   "https://doi.org/10.1177/103237320200700207",
  review-url =   "http://dro.deakin.edu.au/view/DU:30012663;
                 http://www.highbeam.com/doc/1G1-97484707.html",
}

@Article{Bolton:2002:SFD,
  author =       "Richard J. Bolton and David J. Hand",
  title =        "Statistical Fraud Detection: A Review",
  journal =      j-STAT-SCI,
  volume =       "17",
  number =       "3",
  pages =        "235--255",
  month =        aug,
  year =         "2002",
  CODEN =        "STSCEP",
  ISSN =         "0883-4237 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  bibdate =      "Fri May 30 12:48:50 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statsci.bib",
  URL =          "http://projecteuclid.org/euclid.ss/1042727940",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
}

@Article{Brown:2002:ICF,
  author =       "Philip Brown and Angeline Chua and Jason Mitchell",
  title =        "The influence of cultural factors on price clustering:
                 Evidence from {Asia Pacific} stock markets",
  journal =      "Pacific-Basin Finance Journal",
  volume =       "10",
  number =       "3",
  pages =        "307--332",
  year =         "2002",
  DOI =          "https://doi.org/10.1016/S0927-538X(02)00049-5",
  ISSN =         "0927-538X (print), 1879-0585 (electronic)",
  ISSN-L =       "0927-538X",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "13th Annual PACAP/FMA Finance Conference",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927538X02000495",
  abstract =     "Price clustering is the tendency of prices to be
                 observed more frequently at some numbers than others.
                 It increases with haziness, or imprecision, about
                 underlying value. Most research on price clustering has
                 been conducted in Western financial markets, where
                 there is manifest preference for trading at round
                 numbers. We focus on number preferences under Chinese
                 culture. Many Chinese believe some numbers are unlucky
                 and to be avoided. For instance, the number 4 is
                 inauspicious because the Cantonese pronunciation of 4
                 is similar to the phrase to die. We first document
                 clustering of daily closing prices on six Asia Pacific
                 stock markets, three with predominantly Chinese
                 populations. Next, we fit binomial logit models within
                 these markets to estimate the association between
                 structural and economic factors, and culture, on price
                 clustering. We find some support for the influence of
                 Chinese culture and superstition on year-round number
                 preferences of traders, but it is located solely in the
                 Hong Kong market. Furthermore, in the Hong Kong market
                 Chinese culture and superstition help explain the
                 increased avoidance of the number 4 during the
                 auspicious Chinese New Year, Dragon Boat and Mid-Autumn
                 festivals.",
  acknowledgement = ack-nhfb,
  keywords =     "Attraction; Benford's Law; Haziness; Negotiation;
                 Price clustering",
}

@TechReport{Diekmann:2002:DFM,
  author =       "Andreas Diekmann",
  title =        "{Diagnose von Fehlerquellen und methodische
                 Qualit{\"a}t in der sozialwissenschaftlichen
                 Forschung}. ({German}) [{Diagnosis} of errors and
                 methodological quality in social science research]",
  type =         "Report",
  number =       "ITA-02-04",
  institution =  "Institut f{\"u}r Technikfolgen-Absch{\"a}tzung",
  address =      "Vienna, Austria",
  pages =        "????",
  year =         "2002",
  bibdate =      "Thu Nov 17 19:11:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Egghe:2002:DRC,
  author =       "L. Egghe and I. K. Ravichandra Rao",
  title =        "Duality revisited: {Construction} of fractional
                 frequency distributions based on two dual {Lotka}
                 laws",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "53",
  number =       "10",
  pages =        "789--801",
  month =        "????",
  year =         "2002",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10103",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:41:59 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "11 Jun 2002",
}

@Article{FerreriCancho:2002:ZLR,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "{Zipf}'s law and random texts",
  journal =      j-ADV-COMPLEX-SYST,
  volume =       "5",
  number =       "1",
  pages =        "1--6",
  year =         "2002",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S0219525902000468",
  ISSN =         "0219-5259",
  bibdate =      "Sat Nov 12 11:00:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1090.91595",
  abstract =     "Random-text models have been proposed as an
                 explanation for the power law relationship between word
                 frequency and rank, the so-called Zipf's law. They are
                 generally regarded as null hypotheses rather than
                 models in the strict sense. In this context, recent
                 theories of language emergence and evolution assume
                 this law as a priori information with no need of
                 explanation. Here, random texts and real texts are
                 compared through (a) the so-called lexical spectrum and
                 (b) the distribution of words having the same length.
                 It is shown that real texts fill the lexical spectrum
                 much more efficiently and regardless of the word
                 length, suggesting that the meaningfulness of Zipf's
                 law is high.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics)",
  fjournal =     "Advances in Complex Systems",
  journal-URL =  "http://www.worldscinet.com/acs/acs.shtml",
  keywords =     "Human language; monkey languages; random texts;
                 scaling; Zipf's law",
}

@Article{Gottwald:2002:NBL,
  author =       "Georg A. Gottwald and Matthew Nicol",
  title =        "On the nature of {Benford's Law}",
  journal =      j-PHYSICA-A,
  volume =       "303",
  number =       "3--4",
  pages =        "387--396",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(01)00497-6",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "60C05 (28D05 60E05 82B05)",
  MRnumber =     "1917635 (2003d:60015)",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://adsabs.harvard.edu/abs/2002PhyA..303..387G;
                 http://www.sciencedirect.com/science/article/pii/S0378437101004976",
  abstract =     "We study multiplicative and affine sequences of real
                 numbers defined by $ N(j + 1) = \zeta (j) N(j) + \eta
                 (j) $, where \{\zeta(j)\} and \{\eta(j)\} are sequences
                 of positive real numbers (in the multiplicative case $
                 \eta (j) = 0 $ for all $j$). We investigate the
                 conditions under which the leading digits $k$ of
                 \{N(j)\} have the following probability distribution,
                 known as Benford's Law, $ P(k) = \log_{10}((k + 1) /
                 k)$. We present two main results. First, we show that
                 contrary to the usual assumption in the literature,
                 \{\zeta(j)\} does not necessarily need to come from a
                 chaotic or independent random process for Benford's Law
                 to hold. The multiplicative driving force may be a
                 deterministic quasiperiodic or even periodic forcing.
                 Second, we give conditions under which the distribution
                 of the first digits of an affine process displays
                 Benford's Law. Our proofs use techniques from ergodic
                 theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Law of Anomalous Numbers;
                 Multiplicative process; Scaling laws; Zipf's Law",
}

@Article{Hasan:2002:ADA,
  author =       "Bassam Hasan",
  title =        "Assessing data authenticity with {Benford}'s law",
  journal =      "Information Systems Control Journal",
  volume =       "6",
  pages =        "??--??",
  year =         "2002",
  CODEN =        "ISYJFS",
  ISSN =         "1526-7407",
  bibdate =      "Sat Feb 16 17:45:21 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.isaca.org/Journal/Past-Issues/2002/Volume-6/Pages/Assessing-Data-Authenticity-With-Benfords-Law.aspx",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.isaca.org/",
  remark =       "Journal publication ceased at volume 6 in 2008,
                 according to one library catalog, but volumes up to
                 2013 are available at journal Web site.",
}

@InProceedings{Hill:2002:RAB,
  author =       "T. P. Hill",
  editor =       "????",
  booktitle =    "Conference, Leiden University",
  title =        "Recent applications of {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:55:46 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hoyle01042002,
  author =       "David C. Hoyle and Magnus Rattray and Ray Jupp and
                 Andrew Brass",
  title =        "Making sense of microarray data distributions",
  journal =      j-BIOINFORMATICS,
  volume =       "18",
  number =       "4",
  pages =        "576--584",
  year =         "2002",
  DOI =          "https://doi.org/10.1093/bioinformatics/18.4.576",
  ISSN =         "1367-4803 (print), 1367-4811 (electronic)",
  ISSN-L =       "1367-4803",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bioinformatics.oxfordjournals.org/content/18/4/576.abstract",
  abstract =     "Motivation: Typical analysis of microarray data has
                 focused on spot by spot comparisons within a single
                 organism. Less analysis has been done on the comparison
                 of the entire distribution of spot intensities between
                 experiments and between organisms.Results: Here we show
                 that mRNA transcription data from a wide range of
                 organisms and measured with a range of experimental
                 platforms show close agreement with Benford's law
                 (Benford, Proc. Am. Phil. Soc., 78, 551 572, 1938) and
                 Zipf's law (Zipf, The Psycho-biology of Language: an
                 Introduction to Dynamic Philology, 1936 and Human
                 Behaviour and the Principle of Least Effort, 1949). The
                 distribution of the bulk of microarray spot intensities
                 is well approximated by a log-normal with the tail of
                 the distribution being closer to power law. The
                 variance, 2, of log spot intensity shows a positive
                 correlation with genome size (in terms of number of
                 genes) and is therefore relatively fixed within some
                 range for a given organism. The measured value of 2 can
                 be significantly smaller than the expected value if the
                 mRNA is extracted from a sample of mixed cell types.
                 Our research demonstrates that useful biological
                 findings may result from analyzing microarray data at
                 the level of entire intensity distributions. Contact:
                 david.c.hoyle@man.ac.uk",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  journal-URL =  "http://bioinformatics.oxfordjournals.org/",
  keywords =     "Zipf's Law",
}

@Article{Hoyle:2002:MSM,
  author =       "David C. Hoyle and Magnus Rattray and Ray Jupp and
                 Andrew Brass",
  title =        "Making sense of microarray data distributions",
  journal =      j-BIOINFORMATICS,
  volume =       "18",
  number =       "4",
  pages =        "576--584",
  month =        apr,
  year =         "2002",
  ISSN =         "1367-4803 (print), 1367-4811 (electronic)",
  ISSN-L =       "1367-4803",
  bibdate =      "Fri Nov 25 11:16:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  journal-URL =  "http://bioinformatics.oxfordjournals.org/",
  keywords =     "Benford's Law; mRNA transcription data",
}

@Article{Huber:2002:NMG,
  author =       "John C. Huber",
  title =        "A new model that generates {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "53",
  number =       "3",
  pages =        "209--219",
  month =        "????",
  year =         "2002",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10025",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "28 Dec 2001",
}

@Article{Jones:2002:LDR,
  author =       "B. K. Jones",
  title =        "Logarithmic distributions in reliability analysis",
  journal =      j-MICROELECT-RELIABILITY,
  volume =       "42",
  number =       "4--5",
  pages =        "779--786",
  month =        apr # "\slash " # may,
  year =         "2002",
  CODEN =        "MCRLAS",
  DOI =          "https://doi.org/10.1016/S0026-2714(02)00031-8",
  ISSN =         "0026-2714 (print), 1872-941X (electronic)",
  ISSN-L =       "0026-2714",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0026271402000318",
  abstract =     "Real-life systems are complex, with many independent
                 parameters which can affect the system. Their behaviour
                 can therefore be very variable. This is especially true
                 of the more involved processes which occur in
                 reliability and degradation processes. However, there
                 are some characteristics which are observed which can
                 be understood simply because they are characteristic of
                 complex systems. These include distributions that are
                 very often logarithmic rather than uniform, log normal
                 failure distributions and $ 1 g / f $ noise. A wide
                 variety of diverse examples is given to illustrate the
                 common occurrence of such observations together with
                 the underlying unifying themes. There are several basic
                 reasons for the origin of logarithmic distributions.
                 One is that they arise from multiplicative processes.
                 Another is that although basic science is often
                 introduced as linear, with non-linear effects added as
                 a correction, complex systems are often inherently
                 non-linear. This produces multiplicative effects, such
                 as harmonic generation and fractal behaviour.",
  acknowledgement = ack-nhfb,
  fjournal =     "Microelectronics and Reliability",
  keywords =     "Benford's Law; Pareto distribution; Zipf's Law",
}

@Article{Kawamura:2002:UZL,
  author =       "Kenji Kawamura and Naomichi Hatano",
  title =        "Universality of {Zipf}'s law",
  journal =      j-J-PHYS-SOC-JAP,
  volume =       "71",
  number =       "5",
  pages =        "1211--1213",
  year =         "2002",
  CODEN =        "JUPSAU",
  DOI =          "https://doi.org/10.1143/JPSJ.71.1211",
  ISSN =         "0031-9015 (print), 1347-4073 (electronic)",
  ISSN-L =       "0031-9015",
  bibdate =      "Sat Nov 12 11:00:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jpsj.ipap.jp/",
  ZMnumber =     "1063.60114",
  abstract =     "The aim of the present paper is to propose and
                 simulate a simple and generic model that reproduces
                 Zipf's law. In the proposed model, the time evolution
                 is considered to be a random walk in the logarithmic
                 scale reflecting the company asset distribution and/or
                 the evolution of city populations (e.g. Zipf's law for
                 income distribution asserts that the size and number of
                 companies are in inverse proportional relationship).
                 The paper explains theoretically and shows by numerical
                 simulation that the introduced model of Zipf's law has
                 a very robust behaviour when applied to various natural
                 and social phenomena. The authors do not investigate
                 the famous case of Zipf's law application to the
                 frequency of English words, but they speculate that
                 this case might be also explained within the same time
                 development of the proposed model.",
  acknowledgement = ack-nhfb,
  classmath =    "60J60 (Diffusion processes) 60J70 (Appl. of diffusion
                 theory) 76R50 (Diffusion) 82C24 (Interface problems
                 (dynamic and non-equilibrium))",
  fjournal =     "Journal of the Physical Society of Japan",
  keywords =     "city population evolution; company asset distribution;
                 diffusion; generic model of Zipf's law; natural and
                 social phenomena; random walk in logarithmic scale",
  ZMreviewer =   "Neculai Curteanu (Ia\c si)",
}

@TechReport{Kreiner:2002:FDL,
  author =       "W. A. Kreiner",
  title =        "First digit law",
  type =         "Preprint",
  institution =  "Abteilung Chemische Physik, Arbeitsgruppe
                 Laseranwendungen, Universit{\"a}t Ulm",
  address =      "Ulm, Germany",
  pages =        "7",
  day =          "3",
  month =        may,
  year =         "2002",
  bibdate =      "Sat Feb 16 18:18:49 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://vts.uni-ulm.de/docs/2002/1441/vts_1441.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; First Digit Law; Newcomb; Statistisches
                 Fraktal",
  language =     "German",
}

@Article{Li:2002:ZLI,
  author =       "Wentian Li and Yaning Yang",
  title =        "{Zipf's Law} in Importance of Genes for Cancer
                 Classification Using Microarray Data",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "539--551",
  day =          "21",
  month =        dec,
  year =         "2002",
  CODEN =        "JTBIAP",
  DOI =          "https://doi.org/10.1006/jtbi.2002.3145",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  MRclass =      "92C40 (92D10)",
  MRnumber =     "2044066",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022519302931450",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@Book{Livio:2002:GRS,
  author =       "Mario Livio",
  title =        "The Golden Ratio: the Story of Phi, the World's Most
                 Astonishing Number",
  publisher =    "Broadway Books",
  address =      "New York, NY, USA",
  pages =        "viii + 294",
  year =         "2002",
  ISBN =         "0-7679-0815-5",
  ISBN-13 =      "978-0-7679-0815-3",
  LCCN =         "QA466 .L58 2002",
  bibdate =      "Tue Jul 08 12:29:44 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Benford's Law is treated on pages 231--237.",
  price =        "US\$24.95, CAN\$37.95",
  abstract =     "Throughout history, thinkers from mathematicians to
                 theologians have pondered the mysterious relationship
                 between numbers and the nature of reality. In this
                 fascinating book, the author tells the tale of a number
                 at the heart of that mystery: phi, or
                 1.6180339887\ldots{}. This curious mathematical
                 relationship, widely known as ``The Golden Ratio,'' was
                 discovered by Euclid more than two thousand years ago
                 because of its crucial role in the construction of the
                 pentagram, to which magical properties had been
                 attributed. Since then it has shown a propensity to
                 appear in the most astonishing variety of places, from
                 mollusk shells, sunflower florets, and rose petals to
                 the shape of the galaxy. Psychological studies have
                 investigated whether the Golden Ratio is the most
                 aesthetically pleasing proportion extant, and it has
                 been asserted that the creators of the Pyramids and the
                 Parthenon employed it. It is believed to feature in
                 works of art from Leonardo da Vinci's Mona Lisa to
                 Salvador Dali's The Sacrament of the Last Supper, and
                 poets and composers have used it in their works. It has
                 even been found to be connected to the behavior of the
                 stock market! This book is a captivating journey
                 through art and architecture, botany and biology,
                 physics and mathematics. It tells the human story of
                 numerous phi-fixated individuals, including the
                 followers of Pythagoras who believed that this
                 proportion revealed the hand of God; astronomer
                 Johannes Kepler, who saw phi as the greatest treasure
                 of geometry; such Renaissance thinkers as mathematician
                 Leonardo Fibonacci of Pisa; and such masters of the
                 modern world as Goethe, Cezanne, Bartok, and physicist
                 Roger Penrose. Wherever his quest for the meaning of
                 phi takes him, the author reveals the world as a place
                 where order, beauty, and eternal mystery will always
                 coexist.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Prelude to a number \\
                 The pitch and the pentagram \\
                 Under a star-Y-pointing pyramid? \\
                 The second treasure \\
                 Son of good nature \\
                 The divine proportion \\
                 Painters and poets have equal license \\
                 From the tiles to the heavens \\
                 Is God a mathematician?",
}

@InProceedings{Manaris:2002:PTR,
  author =       "B. Manaris and T. Purewal and C. McCormick",
  editor =       "{IEEE}",
  booktitle =    "Proceedings: IEEE SoutheastCon 2002: April 5--7, 2002,
                 Embassy Suites Hotel, Columbia, South Carolina, USA",
  title =        "Progress Towards Recognizing and Classifying Beautiful
                 Music with Computers: {MIDI}-Encoded Music and the
                 {Zipf-Mandelbrot Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  bookpages =    "xviii + 482",
  pages =        "52--57",
  year =         "2002",
  DOI =          "https://doi.org/10.1109/.2002.995557",
  ISBN =         "0-7803-7252-2",
  ISBN-13 =      "978-0-7803-7252-8",
  LCCN =         "TK7801 .I56 2002",
  bibdate =      "Mon Feb 18 10:40:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=7814",
  acknowledgement = ack-nhfb,
}

@Article{Mochty:2002:AMI,
  author =       "L. Mochty",
  title =        "{Die Aufdeckung von Manipulationen im Rechnungswesen
                 --- Was leistet das Benford's Law?}. ({German}) [{The}
                 disclosure of accounting manipulations --- what does
                 {Benford's Law} mean?]",
  journal =      "Die Wirtschaftspr{\"u}fung",
  volume =       "14",
  number =       "??",
  pages =        "725--736",
  month =        "????",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "0043-6313",
  ISSN-L =       "0043-6313",
  bibdate =      "Thu Nov 17 19:20:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Mosimann:2002:TDE,
  author =       "James Mosimann and John Dahlberg and Nancy Davidian
                 and John Krueger",
  title =        "Terminal Digits and the Examination of Questioned
                 Data",
  journal =      j-ACCOUNT-RES,
  volume =       "9",
  number =       "2",
  pages =        "75--92",
  month =        "????",
  year =         "2002",
  CODEN =        "ARQAEZ",
  DOI =          "https://doi.org/10.1080/08989620212969",
  ISSN =         "0898-9621 (print), 1545-5815 (electronic)",
  ISSN-L =       "0898-9621",
  bibdate =      "Sat Sep 10 15:08:21 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/08989620212969",
  acknowledgement = ack-nhfb,
  fjournal =     "Accountability in Research",
  journal-URL =  "http://www.tandfonline.com/toc/gacr20",
  keywords =     "Benford's Law",
}

@Book{Newman:2002:ME,
  author =       "M. E. J. (Mark E. J.) Newman and Richard G. Palmer",
  title =        "Modeling extinction",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  pages =        "xii + 102",
  year =         "2002",
  ISBN =         "0-19-515946-2 (paperback), 0-19-515945-4 (hardcover)",
  ISBN-13 =      "978-0-19-515946-2 (paperback), 978-0-19-515945-5
                 (hardcover)",
  LCCN =         "QH78 .N48 2002",
  bibdate =      "Thu Feb 28 10:36:25 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 library.ox.ac.uk:210/ADVANCE",
  series =       "Santa Fe Institute studies in the sciences of
                 complexity",
  acknowledgement = ack-nhfb,
  keywords =     "power law; Zipf's law",
  subject =      "Extinction (Biology); Statistical methods;
                 Mathematical models",
}

@Misc{Popescu:2002:LNZ,
  author =       "Ioan-Iovitz Popescu",
  title =        "On the {Lavelette}'s nonlinear {Zipf}'s law",
  howpublished = "Web preprint.",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat Feb 16 19:02:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://alpha2.infim.ro/~ltpd/Zipf's_Law.html",
  acknowledgement = ack-nhfb,
}

@Article{Reed:2002:GFG,
  author =       "William J. Reed and Barry D. Hughes",
  title =        "From gene families and genera to incomes and
                 {Internet} file sizes: Why power laws are so common in
                 nature",
  journal =      j-PHYS-REV-E,
  volume =       "66",
  number =       "6",
  pages =        "067103",
  month =        dec,
  year =         "2002",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.66.067103",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Wed Feb 27 06:58:05 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.66.067103",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Pareto's Law; rank-size property; Zipf's Law",
  pagecount =    "4",
}

@Article{Sandon:2002:DPC,
  author =       "F. Sandon",
  title =        "Do Populations Conform to the Law of Anomalous
                 Numbers?",
  journal =      "Population",
  volume =       "57",
  number =       "4",
  pages =        "755--761",
  month =        "????",
  year =         "2002",
  bibdate =      "Sat Sep 10 16:15:28 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.persee.fr/doc/pop_1634-2941_2002_num_57_4_18419",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.persee.fr/collection/pop",
  keywords =     "Benford's Law",
}

@Article{Sandron:2002:DPC,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Do populations conform to the {Law of Anomalous
                 Numbers}?",
  journal =      "Population",
  volume =       "57",
  number =       "4--5",
  pages =        "755--761",
  month =        "????",
  year =         "2002",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "1169-1018",
  ISSN-L =       "1169-1018",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translation from French by S. R. Hayford.",
  URL =          "http://www.cairn.info/article_p.php?ID_ARTICLE=POPE_204_0753",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.jstor.org/journals/11691018.html",
}

@Article{Sandron:2002:PSE,
  author =       "Fr{\'e}d{\'e}ric Sandron",
  title =        "Les populations suivent-elles la loi des nombres
                 anomaux? ({French}). [{Do} populations conform to the
                 {Law of Anomalous Numbers}?]",
  journal =      "Population ({French} edition)",
  volume =       "57",
  number =       "4--5",
  pages =        "761--768",
  month =        "????",
  year =         "2002",
  CODEN =        "POPUAQ",
  DOI =          "????",
  ISSN =         "0032-4663 (print), 1957-7966 (electronic)",
  ISSN-L =       "0032-4663",
  bibdate =      "Sat Feb 16 19:08:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2002_num_57_4_16873",
  acknowledgement = ack-nhfb,
  language =     "French",
}

@TechReport{Seaman:2002:BLB,
  author =       "R. S. Seaman",
  title =        "{Benford}'s law and and background field errors in
                 data assimilation",
  type =         "Preprint",
  institution =  "Bureau of Meteorology Research Centre",
  address =      "Melbourne, Australia",
  month =        "????",
  year =         "2002",
  bibdate =      "Sun Feb 17 14:01:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://amm.bom.gov.au/amoj/docs/2002/seaman.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Seaman:2002:RBL,
  author =       "R. S. Seaman",
  title =        "The relevance of {Benford's Law} to background field
                 errors in data assimilation",
  journal =      "Australian Meteorological Magazine",
  volume =       "51",
  number =       "1",
  pages =        "25--33",
  month =        "????",
  year =         "2002",
  CODEN =        "AMMGAS",
  ISSN =         "0004-9743",
  ISSN-L =       "0004-9743",
  bibdate =      "Mon Nov 14 16:08:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.bom.gov.au/amm/docs/2002/seaman.pdf;
                 http://www.bom.gov.au/amm/docs/2002/seaman_hres.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Aust. Met. Mag.",
  ajournal-2 =   "Aust. Meteorol. Mag.",
  fjournal =     "Australian Meteorological Magazine",
  journal-URL =  "http://www.bom.gov.au/amm/",
}

@Article{Taylor:2002:STD,
  author =       "Rosemary N. Taylor and Damian J. McEntegart and
                 Eleanor C. Stillman",
  title =        "Statistical techniques to detect fraud and other data
                 irregularities in clinical questionnaire data",
  journal =      "Drug Information Journal",
  volume =       "36",
  number =       "1",
  pages =        "115--125",
  month =        jan,
  year =         "2002",
  DOI =          "https://doi.org/10.1177/009286150203600115",
  ISSN =         "0092-8615",
  ISSN-L =       "0092-8615",
  bibdate =      "Mon Feb 18 06:42:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.diahome.org/DIAHome/resources/content.aspx?type=eopdf&file=%2Fproductfiles%2F8357%2Fdiaj_11524.pdf????",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{VanCaneghem:2002:EMI,
  author =       "T. {Van Caneghem}",
  title =        "Earnings Management Induced by Cognitive Reference
                 Points",
  journal =      "The British Accounting Review",
  volume =       "34",
  number =       "2",
  pages =        "167--178",
  year =         "2002",
  DOI =          "https://doi.org/10.1006/bare.2002.0190",
  ISSN =         "0890-8389 (print), 1095-8347 (electronic)",
  ISSN-L =       "0890-8389",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0890838902901903",
  abstract =     "Previous studies (Carslaw, 1988; Thomas, 1989;
                 Niskanen \& Keloharju, 2000) have shown that companies'
                 managers tend to round-up the first digits of reported
                 earnings (i.e. for companies reporting profits).
                 According to Carslaw (1988), this type of behaviour is
                 inspired by the existence of the so-called `\$1.99'
                 phenomenon where a price of \$1.99 is perceived as
                 being abnormally lower than one of \$2.00. In the
                 current study, we try to determine whether managers of
                 UK-listed companies also engage in this type of
                 `earnings rounding-up behaviour'. Analogous to the
                 earlier studies, our study compares observed and
                 expected frequencies for the second-from-the-left digit
                 in reported earnings. Our results suggest that managers
                 of UK-listed companies tend to round-up reported
                 pre-tax income, in a way that increases the first digit
                 by one, when they are faced with a nine in the
                 second-from-the-left position for this particular
                 earnings measure. The major contribution of the current
                 study is that it introduces discretionary accruals in
                 this line of research. Discretionary accruals were
                 estimated using both the Jones model (1991) and the
                 modified Jones model as proposed by Dechow et al.
                 (1995). Our results clearly suggest that discretionary
                 accruals are used in order to round-up reported
                 earnings figures. Moreover, discretionary accruals
                 enabled us to increase the power of the tests used in
                 previous studies.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Wallace:2002:AQD,
  author =       "W. A. Wallace",
  title =        "Assessing the quality of data used for benchmarking
                 and decision making",
  journal =      "Journal of Government Financial Management",
  volume =       "51",
  number =       "3",
  pages =        "16--22",
  month =        "????",
  year =         "2002",
  DOI =          "",
  ISSN =         "1533-1385",
  ISSN-L =       "1533-1385",
  bibdate =      "Thu Oct 13 09:17:04 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://www.agacgfm.org/Resources/Journal-of-Government-Financial-Management/Archives.aspx",
  keywords =     "Benford's Law",
  remark =       "Online archive access, even for journal metadata,
                 requires member account!",
}

@Article{Yeh:2002:SMZ,
  author =       "Hsiaw-Chan Yeh",
  title =        "Six multivariate {Zipf} distributions and their
                 related properties",
  journal =      j-STAT-PROB-LETT,
  volume =       "56",
  number =       "2",
  pages =        "131--141",
  day =          "15",
  month =        jan,
  year =         "2002",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/S0167-7152(01)00149-3",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "62H10",
  MRnumber =     "1881166 (2002m:62084)",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715201001493",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Zipf's Law",
}

@Article{Abdel-All:2003:GPP,
  author =       "N. H. Abdel-All and M. A. W. Mahmoud and H. N.
                 Abd-Ellah",
  title =        "Geometrical properties of {Pareto} distribution",
  journal =      j-APPL-MATH-COMP,
  volume =       "145",
  number =       "2--3",
  pages =        "321--339",
  day =          "25",
  month =        dec,
  year =         "2003",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Jan 9 08:41:12 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Alvarez-Ramirez:2003:ZMS,
  author =       "Jose Alvarez-Ramirez and Monica Meraz and Gustavo
                 Gallegos",
  title =        "{Zipf--Mandelbrot} scaling law for world track
                 records",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "545--560",
  day =          "15",
  month =        oct,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(03)00579-X",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037843710300579X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Book{Anastasi:2003:NFI,
  author =       "Joe Anastasi",
  title =        "The new forensics: investigating corporate fraud and
                 the theft of intellectual property",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 270",
  year =         "2003",
  ISBN =         "0-471-26994-8 (hardcover)",
  ISBN-13 =      "978-0-471-26994-6 (hardcover)",
  LCCN =         "HV8079.W47 A5 2003",
  bibdate =      "Tue Nov 22 11:42:36 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/wiley044/2003001697.html;
                 http://www.loc.gov/catdir/description/wiley037/2003001697.html;
                 http://www.loc.gov/catdir/toc/wiley031/2003001697.html",
  acknowledgement = ack-nhfb,
  remark =       "Brief mention of Benford's Law on pp. 184--185.",
  subject =      "white collar crime investigation; data processing;
                 case studies; fraud investigation; forensic accounting;
                 computer security",
}

@Article{Ausloos:2003:SIZ,
  author =       "M. Ausloos and Ph. Bronlet",
  title =        "Strategy for investments from {Zipf} law(s)",
  journal =      j-PHYSICA-A,
  volume =       "324",
  number =       "1--2",
  pages =        "30--37",
  day =          "1",
  month =        jun,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(02)01845-9",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B82",
  MRnumber =     "2030919",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "International Econophysics Conference IEC2002 (Bali)",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437102018459",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Book{Baldi:2003:MIW,
  author =       "Pierre Baldi and Paolo Frasconi and Padhraic Smyth",
  title =        "Modeling the {Internet} and the {Web}: probabilistic
                 methods and algorithms",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xix + 285",
  year =         "2003",
  ISBN =         "0-470-86492-3 (e-book), 0-470-84906-1",
  ISBN-13 =      "978-0-470-86492-0 (e-book), 978-0-470-84906-4",
  LCCN =         "TK5105.875.I57 B35 2003eb",
  bibdate =      "Fri Jun 3 10:03:23 MDT 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/pagerank.bib",
  acknowledgement = ack-nhfb,
  subject =      "Internet; Mathematical models; Telecommunication;
                 Traffic; World Wide Web; Cyberspace; Probabilities;
                 Computers; Web; General; Networking; Intranets and
                 Extranets",
  tableofcontents = "Mathematical Background \\
                 Probability and Learning from a Bayesian Perspective
                 \\
                 Parameter Estimation from Data \\
                 Basic principles \\
                 A simple die example \\
                 Mixture Models and the Expectation Maximization
                 Algorithm \\
                 Graphical Models \\
                 Bayesian networks \\
                 Belief propagation \\
                 Learning directed graphical models from data \\
                 Classification \\
                 Clustering \\
                 Power-Law Distributions \\
                 Scale-free properties (80/20 rule) \\
                 Applications to Languages: Zipf's and Heaps' Laws \\
                 Origin of power-law distributions and Fermi's model \\
                 Basic WWW Technologies \\
                 Web Documents \\
                 SGML and HTML \\
                 General structure of an HTML document \\
                 Links \\
                 Resource Identifiers: URI, URL, and URN \\
                 Protocols \\
                 Reference models and TCP/IP \\
                 The domain name system \\
                 The Hypertext Transfer Protocol \\
                 Programming examples \\
                 Log Files \\
                 Search Engines \\
                 Coverage \\
                 Basic crawling \\
                 Web Graphs \\
                 Internet and Web Graphs \\
                 Power-law size \\
                 Power-law connectivity \\
                 Small-world networks \\
                 Power law of PageRank \\
                 The bow-tie structure \\
                 Generative Models for the Web Graph and Other Networks
                 \\
                 Web page growth \\
                 Lattice perturbation models: between order and disorder
                 \\
                 Preferential attachment models, or the rich get richer
                 \\
                 Copy models \\
                 PageRank models \\
                 Applications \\
                 Distributed search algorithms \\
                 Subgraph patterns and communities \\
                 Robustness and vulnerability \\
                 Notes and Additional Technical References \\
                 Text Analysis \\
                 Indexing \\
                 Compression techniques \\
                 Lexical Processing \\
                 Tokenization",
}

@TechReport{Berger:2003:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like nonautonomous dynamical
                 systems",
  type =         "Preprint",
  institution =  "Vienna University of Technology",
  address =      "Vienna, Austria",
  year =         "2003",
  bibdate =      "Sat Feb 16 17:18:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Canessa:2003:TAFa,
  author =       "Enrique Canessa",
  title =        "Theory of Analogous Force on Number Sets",
  journal =      "ArXiv e-prints",
  year =         "2003",
  bibdate =      "Mon Nov 21 06:56:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/cond-mat/0307703",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $ p_x $ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $ p_x $ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $ f_x $ on number sets
                 proportional to $ (\frac {\partial p_x}{\partial x})_T
                 $ at an analogous system temperature $T$. In
                 particular, this yields to an understanding of the
                 uneven distribution of integers of random sets in terms
                 of analogous scale invariance and a screened inverse
                 square force acting on the significant digits. The
                 theory also allows to establish recursion relations to
                 predict sequences of Fibonacci numbers and to give an
                 answer to the interesting theoretical question of the
                 appearance of the Benford's law in Fibonacci numbers. A
                 possible relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  remark =       "To appear in Phys. A.",
}

@Article{Canessa:2003:TAFb,
  author =       "Enrique Canessa",
  title =        "Theory of analogous force on number sets",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "1--2",
  pages =        "44--52",
  month =        oct,
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(03)00526-0",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103005260",
  abstract =     "A general statistical thermodynamic theory that
                 considers given sequences of $x$-integers to play the
                 role of particles of known type in an isolated elastic
                 system is proposed. By also considering some explicit
                 discrete probability distributions $ p_x $ for natural
                 numbers, we claim that they lead to a better
                 understanding of probabilistic laws associated with
                 number theory. Sequences of numbers are treated as the
                 size measure of finite sets. By considering $ p_x $ to
                 describe complex phenomena, the theory leads to derive
                 a distinct analogous force $ f_x $ on number sets
                 proportional to $ (\partial p_x / \partial x)T $ at an
                 analogous system temperature $T$. In particular, this
                 leads to an understanding of the uneven distribution of
                 integers of random sets in terms of analogous scale
                 invariance and a screened inverse square force acting
                 on the significant digits. The theory also allows to
                 establish recursion relations to predict sequences of
                 Fibonacci numbers and to give an answer to the
                 interesting theoretical question of the appearance of
                 the Benford's law in Fibonacci numbers. A possible
                 relevance to prime numbers is also analyzed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Fibonacci numbers; Number theory; prime
                 numbers; Probability theory; Statistical physics and
                 thermodynamics",
}

@Article{Das:2003:RRE,
  author =       "Somnath Das and Huai Zhang",
  title =        "Rounding-up in reported {EPS}, behavioral thresholds,
                 and earnings management",
  journal =      "Journal of Accounting and Economics",
  volume =       "35",
  number =       "1",
  pages =        "31--50",
  year =         "2003",
  DOI =          "https://doi.org/10.1016/S0165-4101(02)00096-4",
  ISSN =         "0165-4101 (print), 1879-1980 (electronic)",
  ISSN-L =       "0165-4101",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165410102000964",
  abstract =     "Reported earnings per share (EPS) are frequently
                 rounded to the nearest cent. This paper provides
                 evidence that firms manipulate earnings so that they
                 can round-up and report one more cent of EPS.
                 Specifically, we examine the digit immediately right of
                 the decimal in the calculated {EPS} number expressed in
                 cents. Evidence is presented that firms are more likely
                 to round-up when managers ex ante expect rounding-up to
                 meet analysts forecasts, report positive profits, or
                 sustain recent performance. Further investigation
                 provides evidence that working capital accruals are
                 used to round-up EPS.",
  acknowledgement = ack-nhfb,
  keywords =     "Behavioral threshold; Benford's Law; Earnings
                 management; Earnings per share (EPS); Rounding",
}

@Article{Engel:2003:BLE,
  author =       "Hans-Andreas Engel and Christoph Leuenberger",
  title =        "{Benford}'s law for exponential random variables",
  journal =      j-STAT-PROB-LETT,
  volume =       "63",
  number =       "4",
  pages =        "361--365",
  day =          "15",
  month =        jul,
  year =         "2003",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/S0167-7152(03)00101-9",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60E99 (60C05)",
  MRnumber =     "1996184 (2004d:60050)",
  MRreviewer =   "Ulrich M. Hirth",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715203001019",
  abstract =     "Benford's law assigns the probability $ \log_{10}(1 +
                 1 / d) $ for finding a number starting with specific
                 significant digit $d$. We show that exponentially
                 distributed numbers obey this law approximatively,
                 i.e., within bounds of $ 0.03$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Exponential distribution; Significant
                 digit law",
}

@Article{FerreriCancho:2003:LEO,
  author =       "Ramon {Ferrer i Cancho} and Ricard V. Sol{\'e}",
  title =        "Least effort and the origins of scaling in human
                 language",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "100",
  number =       "3",
  pages =        "788--791",
  day =          "4",
  month =        feb,
  year =         "2003",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.0335980100",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Tue Nov 15 09:44:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/search",
  keywords =     "Zipf's Law",
  onlinedate =   "January 22, 2003",
}

@Book{Fleiss:2003:SMR,
  author =       "Joseph L. Fleiss and Bruce A. Levin and Myunghee Cho
                 Paik",
  title =        "Statistical Methods for Rates and Proportions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Third",
  pages =        "xxvii + 760",
  year =         "2003",
  ISBN =         "0-471-52629-0 (hardcover)",
  ISBN-13 =      "978-0-471-52629-2 (hardcover)",
  LCCN =         "QA279 .F58 2003",
  bibdate =      "Fri Mar 22 08:46:57 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in probability and statistics",
  URL =          "http://www.loc.gov/catdir/bios/wiley042/2002191005.html;
                 http://www.loc.gov/catdir/description/wiley034/2002191005.html;
                 http://www.loc.gov/catdir/toc/wiley031/2002191005.html",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Analysis of variance; Sampling (Statistics);
                 Biometry",
  tableofcontents = "Preface \\
                 Preface to the Second Edition \\
                 Preface to the First Edition \\
                 1. An Introduction to Applied Probability \\
                 2. Statistical Inference for a Single Proportion \\
                 3. Assessing Significance in a Fourfold Table \\
                 4. Determining Sample Sizes Needed to Detect a
                 Difference Between Two Proportions \\
                 5. How to Randomize \\
                 \\
                 6. Comparative Studies: Cross-Sectional, Naturalistic,
                 or Multinomial Sampling \\
                 \\
                 7. Comparative Studies: Prospective and Retrospective
                 Sampling \\
                 8. Randomized Controlled Trials \\
                 9. The Comparison of Proportions from Several
                 Independent Samples \\
                 10. Combining Evidence from Fourfold Tables \\
                 11. Logistic Regression \\
                 12. Poisson Regression \\
                 13. Analysis of Data from Matched Samples \\
                 14. Regression Models for Matched Samples \\
                 15. Analysis of Correlated Binary Data \\
                 16. Missing Data \\
                 17. Misclassification Errors: Effects, Control, and
                 Adjustment \\
                 18. The Measurement of Interrater Agreement \\
                 19. The Standardization of Rates \\
                 Appendix A. Numerical Tables \\
                 Appendix B. The Basic Theory of Maximum Likelihood",
}

@Article{Furusawa:2003:ZLG,
  author =       "Chikara Furusawa and Kunihiko Kaneko",
  title =        "{Zipf's Law} in Gene Expression",
  journal =      j-PHYS-REV-LET,
  volume =       "90",
  number =       "??",
  pages =        "088102",
  day =          "26",
  month =        feb,
  year =         "2003",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.90.088102",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.90.088102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Gabaix:2003:TPL,
  author =       "Xavier Gabaix and Parameswaran Gopikrishnan and
                 Vasiliki Plerou and H. Eugene Stanley",
  title =        "A theory of power-law distributions in financial
                 market fluctuations",
  journal =      j-NATURE,
  volume =       "423",
  number =       "6937",
  pages =        "267--270",
  day =          "15",
  month =        may,
  year =         "2003",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/nature01624",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Wed Feb 27 06:45:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v423/n6937/full/nature01624.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Zipf's Law",
}

@InProceedings{Grekos:2003:RSC,
  author =       "G. Grekos and R. Giuliano-Antonini",
  editor =       "????",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIII, Graz, July
                 6--12, 2003}",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:43:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hassan:2003:EDA,
  author =       "Bassam Hassan",
  title =        "Examining data accuracy and authenticity with leading
                 digit frequency analysis",
  journal =      "Industrial Management + Data Systems",
  volume =       "103",
  number =       "2",
  pages =        "121--125",
  month =        "????",
  year =         "2003",
  CODEN =        "MDSD8F",
  ISSN =         "0263-5577 (print), 1758-5783 (electronic)",
  ISSN-L =       "0263-5577",
  bibdate =      "Fri Nov 25 11:07:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Havil:2003:GEE,
  author =       "Julian Havil",
  title =        "{Gamma}: Exploring {Euler}'s Constant",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xxiii + 266",
  year =         "2003",
  ISBN =         "0-691-09983-9",
  ISBN-13 =      "978-0-691-09983-5",
  LCCN =         "QA41 .H23 2003",
  bibdate =      "Thu Sep 25 16:52:46 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  price =        "US\$29.95",
  URL =          "http://www.loc.gov/catdir/description/prin031/2002192453.html",
  abstract =     "Among the myriad of constants that appear in
                 mathematics, $ \pi $, $e$, and $i$ are the most
                 familiar. Following closely behind is $ \gamma $ or
                 gamma, a constant that arises in many mathematical
                 areas yet maintains a profound sense of mystery. In a
                 tantalizing blend of history and mathematics, Julian
                 Havil takes the reader on a journey through logarithms
                 and the harmonic series, the two defining elements of
                 gamma, toward the first account of gamma's place in
                 mathematics. Introduced by the Swiss mathematician
                 Leonhard Euler (1707--1783), who figures prominently in
                 this book, gamma is defined as the limit of the sum of
                 $ 1 + 1 / 2 + 1 / 3 + \cdots + 1 / n - \ln n$, the
                 numerical value being $ 0.5772156 \ldots {}$. But
                 unlike its more celebrated colleagues $ \pi $ and $e$,
                 the exact nature of gamma remains a mystery --- we
                 don't even know if it can be expressed as a fraction.
                 Among the numerous topics that arise during this
                 historical odyssey into fundamental mathematical ideas
                 are the Prime Number Theorem and the most important
                 open problem in mathematics today, the Riemann
                 Hypothesis (though no proof of either is offered!).
                 Sure to be popular with not only students and
                 instructors but all math aficionados, Gamma takes us
                 through countries, centuries, lives, and works,
                 unfolding along the way the stories of some remarkable
                 mathematics from some remarkable mathematicians.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword / xv \\
                 Acknowledgements / xvii \\
                 Introduction / xix \\
                 Chapter One: The Logarithmic Cradle / 1 \\
                 1.1 A Mathematical Nightmare- and an Awakening / 1 \\
                 1.2 The Baron's Wonderful Canon / 4 \\
                 1.3 A Touch of Kepler / 11 \\
                 1.4 A Touch of Euler / 13 \\
                 1.5 Napier's Other Ideas / 16 \\
                 Chapter Two: The Harmonic Series / 21 \\
                 2.1 The Principle / 21 \\
                 2.2 Generating Function for $H_n$ / 21 \\
                 2.3 Three Surprising Results / 22 \\
                 Chapter Three: Sub-Harmonic Series / 27 \\
                 3.1 A Gentle Start / 27 \\
                 3.2 Harmonic Series of Primes / 28 \\
                 3.3 The Kempner Series / 31 \\
                 3.4 Madelung's Constants / 33 \\
                 Chapter Four: Zeta Functions / 37 \\
                 4.1 Where $n$ Is a Positive Integer / 37 \\
                 4.2 Where $x$ Is a Real Number / 42 \\
                 4.3 Two Results to End With / 44 \\
                 Chapter Five: Gamma's Birthplace / 47 \\
                 5.1 Advent / 47 \\
                 5.2 Birth / 49 \\
                 Chapter Six: The Gamma Function / 53 \\
                 6.1 Exotic Definitions / 53 \\
                 6.2 Yet Reasonable Definitions / 56 \\
                 6.3 Gamma Meets Gamma / 57 \\
                 6.4 Complement and Beauty / 58 \\
                 Chapter Seven: Euler's Wonderful Identity / 61 \\
                 7.1 The All-Important Formula / 61 \\
                 7.2 And a Hint of Its Usefulness / 62 \\
                 Chapter Eight: A Promise Fulfilled / 65 \\
                 Chapter Nine: What Is Gamma Exactly? / 69 \\
                 9.1 Gamma Exists / 69 \\
                 9.2 Gamma Is What Number? 739.3 A Surprisingly Good
                 Improvement / 75 \\
                 9.4 The Germ of a Great Idea / 78 \\
                 Chapter Ten: Gamma as a Decimal / 81 \\
                 10.1 Bernoulli Numbers / 81 \\
                 10.2 Euler--Maclaurin Summation / 85 \\
                 10.3 Two Examples / 86 \\
                 10.4 The Implications for Gamma / 88 \\
                 Chapter Eleven: Gamma as a Fraction / 91 \\
                 11.1 A Mystery / 91 \\
                 11.2 A Challenge / 91 \\
                 11.3 An Answer / 93 \\
                 11.4 Three Results / 95 \\
                 11.5 Irrationals / 95 \\
                 11.6 Pell's Equation Solved / 97 \\
                 11.7 Filling the Gaps / 98 \\
                 11.8 The Harmonic Alternative / 98 \\
                 Chapter Twelve: Where Is Gamma? / 101 \\
                 12.1 The Alternating Harmonic Series Revisited / 101
                 \\
                 12.2 In Analysis / 105 \\
                 12.3 In Number Theory / 112 \\
                 12.4 In Conjecture / 116 \\
                 12.5 In Generalization / 116 \\
                 Chapter Thirteen: It's a Harmonic World / 119 \\
                 13.1 Ways of Means / 119 \\
                 13.2 Geometric Harmony / 121 \\
                 13.3 Musical Harmony / 123 \\
                 13.4 Setting Records / 125 \\
                 13.5 Testing to Destruction / 126 \\
                 13.6 Crossing the Desert / 127 \\
                 13.7 Shuffiing Cards / 127 \\
                 13.8 Quicksort / 128 \\
                 13.9 Collecting a Complete Set / 130 \\
                 13.10 A Putnam Prize Question / 131 \\
                 13.11 Maximum Possible Overhang / 132 \\
                 13.12 Worm on a Band / 133 \\
                 13.13 Optimal Choice / 134 \\
                 Chapter Fourteen: It's a Logarithmic World / 139 \\
                 14.1 A Measure of Uncertainty / 139 \\
                 14.2 Benford's Law / 145 \\
                 14.3 Continued-Fraction Behaviour / 155 \\
                 Chapter Fifteen: Problems with Primes / 163 \\
                 15.1 Some Hard Questions about Primes / 163 \\
                 15.2 A Modest Start / 164 \\
                 15.3 A Sort of Answer / 167 \\
                 15.4 Picture the Problem / 169 \\
                 15.5 The Sieve of Eratosthenes / 171 \\
                 15.6 Heuristics / 172 \\
                 15.7 A Letter / 174 \\
                 15.8 The Harmonic Approximation / 179 \\
                 15.9 Different-and Yet the Same / 180 \\
                 15.10 There are Really Two Questions, Not Three / 182
                 \\
                 15.11 Enter Chebychev with Some Good Ideas / 183 \\
                 15.12 Enter Riemann, Followed by Proof(s) / 186 \\
                 Chapter Sixteen: The Riemann Initiative / 189 \\
                 16.1 Counting Primes the Riemann Way / 189 \\
                 16.2 A New Mathematical Tool / 191 \\
                 16.3 Analytic Continuation / 191 \\
                 16.4 Riemann's Extension of the Zeta Function / 193 \\
                 16.5 Zeta's Functional Equation / 193 \\
                 16.6 The Zeros of Zeta / 193 \\
                 16.7 The Evaluation of $\Pi(x)$ and $\pi(x)$ / 196 \\
                 16.8 Misleading Evidence / 197 \\
                 16.9 The Von Mangoldt Explicit Formula --- and How It
                 Is Used to Prove the Prime Number Theorem / 200 \\
                 16.10 The Riemann Hypothesis / 202 \\
                 16.11 Why Is the Riemann Hypothesis Important? / 204
                 \\
                 16.12 Real Alternatives / 206 \\
                 16.13 A Back Route to Immortality-Partly Closed / 207
                 \\
                 16.14 Incentives, Old and New / 210 \\
                 16.15 Progress / 213 \\
                 Appendix A: The Greek Alphabet / 217 \\
                 Appendix B: Big Oh Notation / 219 \\
                 Appendix C: Taylor Expansions / 221 \\
                 C.1 Degree 1 / 221 \\
                 C.2 Degree 2 / 221 \\
                 C.3 Examples / 223 \\
                 C.4 Convergence / 223 \\
                 Appendix D: Complex Function Theory / 225 \\
                 D.1 Complex Differentiation / 225 \\
                 D.2 Weierstrass Function / 230 \\
                 D.3 Complex Logarithms / 231 \\
                 D.4 Complex Integration / 232 \\
                 D.5 A Useful Inequality / 235 \\
                 D.6 The Indefinite Integral / 235 \\
                 D.7 The Seminal Result / 237 \\
                 D.8 An Astonishing Consequence / 238 \\
                 D.9 Taylor Expansions-and an Important Consequence /
                 239 \\
                 D.10 Laurent Expansions --- and Another Important
                 Consequence / 242 \\
                 D.11 The Calculus of Residues / 245 \\
                 D.12 Analytic Continuation / 247 \\
                 Appendix E: Application to the Zeta Function / 249 \\
                 E.1 Zeta Analytically Continued / 249 \\
                 E.2 Zeta's Functional Relationship / 253",
}

@Article{Hurlimann:2003:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "A generalized {Benford} law and its application",
  journal =      j-ADV-APPL-STAT,
  volume =       "3",
  number =       "3",
  pages =        "217--228",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0972-3617",
  ISSN-L =       "0972-3617",
  MRclass =      "11K31 (11B73)",
  MRnumber =     "2034405 (2004k:11125)",
  MRreviewer =   "Vydas {\v{C}}ekanavi{\v{c}}ius",
  bibdate =      "Wed Aug 16 07:36:50 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
}

@Article{Ioannides:2003:ZLC,
  author =       "Yannis M. Ioannides and Henry G. Overman",
  title =        "{Zipf}'s law for cities: an empirical examination",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "33",
  number =       "2",
  pages =        "127--137",
  day =          "1",
  month =        mar,
  year =         "2003",
  CODEN =        "RSUEDM",
  DOI =          "https://doi.org/10.1016/S0166-0462(02)00006-6",
  ISSN =         "0166-0462 (print), 1879-2308 (electronic)",
  ISSN-L =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0166046202000066",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Article{Kreiner:2003:NBL,
  author =       "W. A. Kreiner",
  title =        "On the {Newcomb--Benford} law",
  journal =      j-Z-NATURFORSCH,
  volume =       "58a",
  number =       "11",
  pages =        "618--622",
  month =        "????",
  year =         "2003",
  CODEN =        "ZNTFA2",
  ISSN =         "0372-9516",
  ISSN-L =       "0372-9516",
  bibdate =      "Sat Feb 16 18:19:41 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.znaturforsch.com/aa/v58a/s58a0618.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "{Zeitschrift f{\"u}r Naturforschung}",
  journal-URL =  "http://www.degruyter.com/view/j/zna",
}

@InCollection{Kumar:2003:BLA,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  editor =       "Cheng-Few Lee",
  booktitle =    "Advances in Financial Planning and Forecasting",
  title =        "{Benford}'s law and its application in financial fraud
                 detection",
  volume =       "11",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  bookpages =    "ix + 177",
  pages =        "57--70",
  year =         "2003",
  ISBN =         "0-7623-1016-2",
  ISBN-13 =      "978-0-7623-1016-6",
  ISSN =         "1046-5847",
  LCCN =         "????",
  bibdate =      "Wed Nov 23 16:45:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lagarias:2003:PAB,
  author =       "Jeffrey C. Lagarias",
  title =        "The $ 3 x + 1 $ problem: An annotated bibliography
                 (1963--1999) (sorted by author)",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  month =        sep,
  year =         "2003",
  bibdate =      "Sat Sep 10 12:58:10 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0309224",
  abstract =     "The $ 3 x + 1 $ problem concerns iteration of the map
                 on the integers given by $ T(n) = (3 n + 1) / 2 $ if
                 $n$ is odd; $ T(n) = n / 2$ if $n$ is even. The $ 3 x +
                 1$ Conjecture asserts that for every positive integer $
                 n > 1$ the forward orbit of $n$ under iteration by $T$
                 includes the integer 1. This paper is an annotated
                 bibliography of work done on the $ 3 x + 1$ problem and
                 related problems from 1963 through 1999. At present the
                 $ 3 x + 1$ Conjecture remains unsolved.",
  acknowledgement = ack-nhfb,
  pagecount =    "74",
  remark =       "At least 13 updates have been made up to
                 11-Jan-2011.",
}

@Article{Lanza:2003:FSP,
  author =       "Richard B. Lanza",
  title =        "Fear Not the Software: Proactively Detecting
                 Occupational Fraud Using Computer Audit Reports",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        sep # "\slash " # feb,
  year =         "2003",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:14:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967868",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@InProceedings{Manaris:2003:EMZ,
  author =       "Bill Manaris and Dallas Vaughan and Christopher Wagner
                 and Juan Romero and Robert B. Davis",
  title =        "Evolutionary Music and the {Zipf--Mandelbrot Law}:
                 Developing Fitness Functions for Pleasant Music",
  crossref =     "Raidl:2003:AEC",
  pages =        "522--534",
  year =         "2003",
  bibdate =      "Mon Feb 18 10:49:54 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{McAllister:2003:ARE,
  author =       "James W. McAllister",
  title =        "Algorithmic randomness in empirical data",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "34",
  number =       "3",
  pages =        "633--646",
  month =        sep,
  year =         "2003",
  CODEN =        "SHPSB5",
  DOI =          "https://doi.org/10.1016/S0039-3681(03)00047-5",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See replies
                 \cite{Twardy:2005:EDS,McAllister:2005:ACE}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0039368103000475",
  abstract =     "According to a traditional view, scientific laws and
                 theories constitute algorithmic compressions of
                 empirical data sets collected from observations and
                 measurements. This article defends the thesis that, to
                 the contrary, empirical data sets are algorithmically
                 incompressible. The reason is that individual data
                 points are determined partly by perturbations, or
                 causal factors that cannot be reduced to any pattern.
                 If empirical data sets are incompressible, then they
                 exhibit maximal algorithmic complexity, maximal entropy
                 and zero redundancy. They are therefore maximally
                 efficient carriers of information about the world.
                 Since, on algorithmic information theory, a string is
                 algorithmically random just if it is incompressible,
                 the thesis entails that empirical data sets consist of
                 algorithmically random strings of digits. Rather than
                 constituting compressions of empirical data, scientific
                 laws and theories pick out patterns that data sets
                 exhibit with a certain noise.",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part
                 {A}",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
  keywords =     "Algorithmic randomness; Benford's Law; Compression;
                 Empirical data; Information; Law; Pattern",
}

@Article{Mitzenmacher:2003:BHG,
  author =       "Michael Mitzenmacher",
  title =        "A Brief History of Generative Models for Power Law and
                 Lognormal Distributions",
  journal =      j-INTERNET-MATH,
  volume =       "1",
  number =       "2",
  pages =        "226--251",
  month =        dec,
  year =         "2003",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/15427951.2004.10129088",
  ISSN =         "1542-7951 (print), 1944-9488 (electronic)",
  ISSN-L =       "1542-7951",
  bibdate =      "Thu Nov 24 13:38:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.im/1089229510;
                 http://www.eecs.harvard.edu/~michaelm/CS223/powerlaw.pdf;
                 http://www.tandfonline.com/toc/uinm20/1/2",
  acknowledgement = ack-nhfb,
  ajournal =     "Internet Math.",
  fjournal =     "Internet Mathematics",
  journal-URL =  "http://projecteuclid.org/info/euclid.im",
  keywords =     "Fibonacci sequence; lognormal distribution; monkeys
                 typing randomly; Pareto distribution; power-law
                 distribution; Yule distribution; Zipf's Law",
  remark =       "This is a survey article with a six-page bibliography
                 of earlier work, and a clear description of the
                 differences between lognormal and power-law
                 distributions, which otherwise look similar on log-log
                 plots. Lognormal distributions have finite means and
                 moments, while power-law distributions may have
                 infinite means and/or moments, depending on the
                 exponent. The preprint at author's Web site (last URL)
                 contains additional material on the acrimonious debate
                 between Beno{\^\i}t Mandelbrot and Herbert A. Simon
                 (see \cite{Mandelbrot:1959:NCS,Simon:1955:CSD}, and
                 other references in Mitzenmacher's paper) on the
                 derivation and modeling of Zipf's Law distributions.",
}

@PhdThesis{Muller:2003:AZP,
  author =       "Mathias M{\"u}ller",
  title =        "{Anwendungsm{\"o}glichkeiten der Ziffernanalyse in der
                 Pr{\"u}fungspraxis mit Schwerpunkt auf Benford's Law}.
                 ({German}) [Applications of the digit analysis in the
                 audit practice with a focus on {Benford's Law}]",
  type =         "{Diplomarbeit}",
  school =       "Wirtschaftsuniversit{\"a}t Wien",
  address =      "Wien, Austria",
  pages =        "v + 75",
  month =        "????",
  year =         "2003",
  bibdate =      "Sat Feb 16 18:44:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://permalink.obvsg.at/wuw/AC03895842",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Naldi:2003:CIZ,
  author =       "M. Naldi",
  title =        "Concentration indices and {Zipf}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "78",
  number =       "3",
  pages =        "329--334",
  month =        mar,
  year =         "2003",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/S0165-1765(02)00251-3",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "91B82",
  MRnumber =     "1959355",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176502002513",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Newby:2003:OSS,
  author =       "Gregory B. Newby and Jane Greenberg and Paul Jones",
  title =        "Open source software development and {Lotka's Law}:
                 {Bibliometric} patterns in programming",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "54",
  number =       "2",
  pages =        "169--178",
  day =          "15",
  month =        jan,
  year =         "2003",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.10177",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:09 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  note =         "See comments \cite{Burrell:2004:LEF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "10 Dec 2002",
}

@Article{Nguyen:2003:DPL,
  author =       "H. T. Nguyen and V. Kreinovich and L. Longpre",
  title =        "Dirty pages of logarithm tables, lifetime of the
                 universe, and subjective (fuzzy) probabilities on
                 finite and infinite intervals",
  journal =      j-IEEE-TRANS-FUZZY-SYSTEMS,
  volume =       "1",
  pages =        "67--73",
  year =         "2003",
  CODEN =        "IEFSEV",
  DOI =          "https://doi.org/10.1109/FUZZ.2003.1209339",
  ISSN =         "1063-6706 (print), 1941-0034 (electronic)",
  ISSN-L =       "1063-6706",
  bibdate =      "Sat Feb 16 18:51:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The 12th IEE International Conference on Fuzzy
                 Systems. FUZZ'03",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Fuzzy Systems",
  xxnote =       "Is this the listed journal, or a conference paper??",
}

@Article{Peter:2003:ADE,
  author =       "Manfred Peter",
  title =        "The asymptotic distribution of elements in automatic
                 sequences",
  journal =      j-THEOR-COMP-SCI,
  volume =       "301",
  number =       "1 3",
  pages =        "285--312",
  year =         "2003",
  CODEN =        "TCSCDI",
  DOI =          "https://doi.org/10.1016/S0304-3975(02)00587-X",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S030439750200587X",
  abstract =     "In an automatic sequence an element need not have an
                 asymptotic density. In this paper a necessary and
                 sufficient criterion is proved for the existence of the
                 asymptotic density of a given element. If it does not
                 exist the asymptotic distribution of the element can be
                 described in terms of a function H whose graph is
                 self-similar. An algorithm is given to decide whether H
                 is piecewise continuously differentiable, and in this
                 case it can be computed effectively. Finally, it is
                 shown that the H -density of an element in an automatic
                 sequence always exists and equals its logarithmic
                 density.",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
  keywords =     "Asymptotics; Automata; Benford's Law; Density;
                 H{\"o}lder mean; Oscillating sum; Self-similarity",
}

@Article{Quick:2003:BLD,
  author =       "Reiner Quick and Matthias Wolz",
  title =        "{Benford's Law in deutschen Rechnungslegungsdaten}.
                 ({German}) [{Benford's Law} in {German} accounting
                 data]",
  journal =      "Betriebswirtschaftliche Forschung und Praxis",
  volume =       "55",
  number =       "2",
  pages =        "208--224",
  month =        "????",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0340-5370",
  ISSN-L =       "0340-5370",
  bibdate =      "Sat Dec 10 12:01:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "Betriebswirtschaftliche Forschung und Praxis ==
                 Business Research and Practice.",
}

@Article{Reed:2003:PLI,
  author =       "William J. Reed",
  title =        "The {Pareto} law of incomes---an explanation and an
                 extension",
  journal =      j-PHYSICA-A,
  volume =       "319",
  number =       "1--4",
  pages =        "469--486",
  year =         "2003",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/S0378-4371(02)01507-8",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B70",
  MRnumber =     "1965596",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Rose:2003:TEF,
  author =       "Anna M. Rose and Jacob M. Rose",
  title =        "Turn {Excel} into a financial sleuth: an easy-to-use
                 digital analysis tool can red-flag irregularities",
  journal =      j-J-ACCOUNTANCY,
  volume =       "196",
  number =       "2",
  pages =        "58--??",
  month =        aug,
  year =         "2003",
  CODEN =        "JACYAD",
  ISSN =         "0021-8448 (print), 1945-0729 (electronic)",
  ISSN-L =       "0021-8448",
  bibdate =      "Sat Feb 16 19:07:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.journalofaccountancy.com/Issues/2003/Aug/TurnExcelIntoAFinancialSleuth",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Accountancy",
  journal-URL =  "http://www.journalofaccountancy.com/",
}

@Article{Sinai:2003:SP,
  author =       "Ya. G. Sinai",
  title =        "Statistical $ (3 x + 1) $ problem",
  journal =      j-COMM-PURE-APPL-MATH,
  volume =       "56",
  number =       "7",
  pages =        "1016--1028",
  month =        jul,
  year =         "2003",
  CODEN =        "CPAMAT, CPMAMV",
  DOI =          "https://doi.org/10.1002/cpa.10084",
  ISSN =         "0010-3640 (print), 1097-0312 (electronic)",
  ISSN-L =       "0010-3640",
  bibdate =      "Mon Nov 21 07:52:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Dedicated to the memory of J{\"u}rgen K. Moser.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications on Pure and Applied Mathematics (New
                 York)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0312",
}

@InProceedings{Swanson:2003:DPF,
  author =       "David Swanson and Moon Jung Cho and John Eltinge",
  editor =       "????",
  booktitle =    "Proceedings of the Survey Research Section",
  title =        "Detecting possibly fraudulent or error-prone survey
                 data using {Benford's Law}",
  publisher =    "American Statistical Association",
  address =      "Washington, DC, USA",
  pages =        "4172--4177",
  year =         "2003",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Wed Nov 16 10:21:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.amstat.org/sections/srms/proceedings/y2003/Files/JSM2003-000205.pdf.",
  acknowledgement = ack-nhfb,
}

@Article{Wales:2003:IWI,
  author =       "Elspeth Wales",
  title =        "Is it Worth Investing in Software to Combat Fraud?",
  journal =      "Computer Fraud \& Security",
  volume =       "2003",
  number =       "5",
  pages =        "6--8",
  year =         "2003",
  DOI =          "https://doi.org/10.1016/S1361-3723(03)05009-7",
  ISSN =         "1361-3723 (print), 1873-7056 (electronic)",
  ISSN-L =       "1361-3723",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1361372303050097",
  abstract =     "Despite the tendency for businesses to keep fraud to
                 themselves, the consensus is that the problem is
                 becoming worse. On the plus side though software
                 solutions that can detect potential fraudulent activity
                 are evolving in their scope and ability to
                 automatically track transactions in real-time.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InCollection{Warren:2003:DLD,
  author =       "Henry S. Warren",
  title =        "The distribution of leading digits",
  crossref =     "Warren:2003:HD",
  chapter =      "15.3",
  pages =        "264--267",
  year =         "2003",
  bibdate =      "Fri Mar 16 08:02:56 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2003:IPD,
  author =       "Shuo-Jye Wu and Chun-Tao Chang",
  title =        "Inference in the {Pareto} distribution based on
                 progressive {Type II} censoring with random removals",
  journal =      j-J-APPL-STAT,
  volume =       "30",
  number =       "2",
  pages =        "163--172",
  month =        "????",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Tue Dec 16 15:40:48 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Wu:2003:PDC,
  author =       "Wei Biao Wu and Chinya V. Ravishankar",
  title =        "The performance of difference coding for sets and
                 relational tables",
  journal =      j-J-ACM,
  volume =       "50",
  number =       "5",
  pages =        "665--693",
  month =        sep,
  year =         "2003",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/876638.876641",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Mon Sep 8 17:55:23 MDT 2003",
  bibsource =    "http://portal.acm.org/; http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "We characterize the performance of difference coding
                 for compressing sets and database relations through an
                 analysis of the problem of estimating the number of
                 bits needed for storing the spacings between values in
                 sets of integers. We provide analytical expressions for
                 estimating the effectiveness of difference coding when
                 the elements of the sets or the attribute fields in
                 database tuples are drawn from the uniform and Zipf
                 distributions. We also examine the case where a
                 uniformly distributed domain is combined with a Zipf
                 distribution, and with an arbitrary distribution. We
                 present limit theorems for most cases, and
                 probabilistic convergence results in other cases. We
                 also examine the effects of attribute domain reordering
                 on the compression ratio. Our simulations show
                 excellent agreement with theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Computing Machinery",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Aoyama:2004:KDP,
  author =       "Hideaki Aoyama and Yoshi Fujiwara and Wataru Souma",
  title =        "Kinematics and dynamics of {Pareto--Zipf}'s law and
                 {Gibrat}'s law",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "117--121",
  day =          "1",
  month =        dec,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2004.06.099",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104009185",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@TechReport{Berger:2004:DDU,
  author =       "A. Berger",
  title =        "Dynamics and digits: on the ubiquity of {Benford's
                 Law}",
  type =         "Preprint",
  institution =  "Institute of Mechanics, Vienna University of
                 Technology",
  address =      "Vienna, Austria",
  pages =        "3",
  day =          "19",
  month =        nov,
  year =         "2004",
  bibdate =      "Sat Feb 16 17:20:58 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.leidenuniv.nl/~verduyn/EQUADIFF03/MS14/berger_eqdiff03.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Burrell:2004:LEF,
  author =       "Quentin L. Burrell",
  title =        "Letters to the {Editor}: Fitting {Lotka's Law}: {Some}
                 cautionary observations on a recent paper by {Newby} et
                 al. (2003)",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "55",
  number =       "13",
  pages =        "1209--1210",
  month =        nov,
  year =         "2004",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20086",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:16 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  note =         "See \cite{Newby:2003:OSS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "17 Aug 2004",
}

@Article{Challet:2004:BPD,
  author =       "Damien Challet and Andrea Lombardoni",
  title =        "Bug propagation and debugging in asymmetric software
                 structures",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "4",
  pages =        "046109",
  month =        oct,
  year =         "2004",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.70.046109",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Thu Feb 28 08:15:07 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.70.046109;
                 http://pre.aps.org/abstract/PRE/v70/i4/e046109",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "4",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Linux; Unix; Zipf's Law",
  pagecount =    "5",
}

@Article{Chen:2004:MFM,
  author =       "Yanguang Chen and Yixing Zhou",
  title =        "Multi-fractal measures of city-size distributions
                 based on the three-parameter {Zipf} model",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "22",
  number =       "4",
  pages =        "793--805",
  day =          "1",
  month =        nov,
  year =         "2004",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2004.02.059",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0960077904001031",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Cong:2004:WTP,
  author =       "Lin Cong and Zhipeng Li",
  title =        "On {Wilson}'s theorem and {Polignac} conjecture",
  journal =      "ArXiv e-prints",
  day =          "2",
  month =        aug,
  year =         "2004",
  bibdate =      "Mon Feb 18 07:03:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math.NT/0408018",
  abstract =     "We introduce Wilson's theorem and Clement's result and
                 present a necessary and sufficient condition for $p$
                 and $ p + 2 k $ to be primes where $k$ is a positive
                 integer. By using Simiov's Theorem, we derive an
                 improved version of Clement's result and
                 characterizations of Polignac twin primes which
                 parallel previous characterizations.",
  acknowledgement = ack-nhfb,
}

@TechReport{Diekmann:2004:DEE,
  author =       "Andreas Diekmann",
  title =        "{Datenf{\"a}lschung. Ergebnisse aus Experimenten mit
                 der Benford Verteilung}. ({German}) [{Data}
                 falsification. {Results} from experiments with the
                 {Benford} distribution]",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  year =         "2004",
  bibdate =      "Fri Nov 18 12:09:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Diekmann:2004:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  type =         "Report",
  institution =  "ETH Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "26",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Dec 10 11:12:29 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rfe.cs.oswego.edu/eps/othr/papers/0507/0507001.pdf",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by ``Benford's law''. Recently, a test
                 against this distribution was used to identify
                 fraudulent accounting data. This test is based on the
                 supposition that real data follow the Benford
                 distribution while fabricated data do not. Is it
                 possible to apply Benford tests to detect fabricated or
                 falsified scientific data as well as fraudulent
                 financial data? We approached this question in two
                 ways. First, we examined the use of the Benford
                 distribution as a standard by checking digit
                 frequencies in published statistical estimates. Second,
                 we conducted experiments in which subjects were asked
                 to fabricate statistical estimates (regression
                 coefficients). These experimental data were scrutinized
                 for possible deviations from the Benford distribution.
                 There were two main findings. First, the digits of the
                 published regression coefficients were approximately
                 Benford distributed. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. At least in the case of regression
                 coefficients, there were indications that checks for
                 digit-preference anomalies should focus less on the
                 first and more on the second and higher-digits",
  acknowledgement = ack-nhfb,
}

@Article{Durtschi:2004:EUB,
  author =       "C. Durtschi and W. Hillison and C. Pacini",
  title =        "The Effective Use of {Benford's Law} to Assist in
                 Detecting Fraud in Accounting Data",
  journal =      j-J-FORENSIC-ACCOUNT,
  volume =       "5",
  number =       "1",
  pages =        "17--34",
  month =        "????",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1524-5586",
  bibdate =      "Sun Nov 13 11:35:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Forensic Accounting",
}

@Article{Fontanari:2004:SNM,
  author =       "J. F. Fontanari and L. I. Perlovsky",
  title =        "Solvable null model for the distribution of word
                 frequencies",
  journal =      j-PHYS-REV-E,
  volume =       "70",
  number =       "??",
  pages =        "042901",
  day =          "25",
  month =        oct,
  year =         "2004",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.70.042901",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.70.042901",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:DPZ,
  author =       "Yoshi Fujiwara and Corrado {Di Guilmi} and Hideaki
                 Aoyama and Mauro Gallegati and Wataru Souma",
  title =        "Do {Pareto--Zipf} and {Gibrat} laws hold true? {An}
                 analysis with {European} firms",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "1--2",
  pages =        "197--216",
  day =          "1",
  month =        apr,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2003.12.015",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103011294",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:GPZ,
  author =       "Yoshi Fujiwara and Hideaki Aoyama and Corrado {Di
                 Guilmi} and Wataru Souma and Mauro Gallegati",
  title =        "{Gibrat} and {Pareto--Zipf} revisited with {European}
                 firms",
  journal =      j-PHYSICA-A,
  volume =       "344",
  number =       "1--2",
  pages =        "112--116",
  day =          "1",
  month =        dec,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2004.06.098",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104009173",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Fujiwara:2004:ZLF,
  author =       "Yoshi Fujiwara",
  title =        "{Zipf} law in firms bankruptcy",
  journal =      j-PHYSICA-A,
  volume =       "337",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        jun,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2004.01.037",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B38",
  MRnumber =     "2092316",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437104001165",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Garcia-Berthou:2004:IBT,
  author =       "Emili Garc{\'i}a-Berthou and Carles Alcaraz",
  title =        "Incongruence between test statistics and {$P$} values
                 in medical papers",
  journal =      "BMC Medical Research Methodology",
  volume =       "4",
  number =       "1",
  pages =        "1--5",
  year =         "2004",
  DOI =          "https://doi.org/10.1186/1471-2288-4-13",
  ISSN =         "1471-2288",
  ISSN-L =       "1471-2288",
  bibdate =      "Sat Sep 10 11:16:07 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Given an observed test statistic and its degrees of
                 freedom, one may compute the observed P value with most
                 statistical packages. It is unknown to what extent test
                 statistics and P values are congruent in published
                 medical papers.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://bmcmedresmethodol.biomedcentral.com/",
  keywords =     "Benford's Law; digit frequencies",
}

@Article{Geyer:2004:DFD,
  author =       "Christina Lynn Geyer and Patricia Pepple Williamson",
  title =        "Detecting fraud in data sets using {Benford's Law}",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "B33",
  number =       "1",
  pages =        "229--246",
  month =        "????",
  year =         "2004",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1081/SAC-120028442",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  MRclass =      "62-07",
  MRnumber =     "2044866",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Comm. Statist. Simulation Comput.",
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Hurlimann:2004:IPB,
  author =       "Werner H{\"u}rlimann",
  title =        "Integer powers and {Benford}'s law",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "11",
  number =       "1",
  pages =        "39--46",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "1311-8080 (print), 1314-3395 (electronic)",
  ISSN-L =       "1314-3395",
  MRclass =      "62E15 (11B83 11K31 62E20)",
  MRnumber =     "2033394 (2005c:62030)",
  MRreviewer =   "I. N. Volodin",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
  journal-URL =  "http://ijpam.eu/",
}

@Article{Ismail:2004:SES,
  author =       "Sanaa Isma{\"\i}l",
  title =        "A Simple Estimator for the Shape Parameter of the
                 {Pareto} Distribution with Economics and Medical
                 Applications",
  journal =      j-J-APPL-STAT,
  volume =       "31",
  number =       "1",
  pages =        "3--13",
  month =        jan,
  year =         "2004",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Sat Dec 4 12:10:37 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Janvresse:2004:UDB,
  author =       "{\'E}lise Janvresse and Thierry de la Rue",
  title =        "From uniform distributions to {Benford}'s law",
  journal =      j-J-APPL-PROBAB,
  volume =       "41",
  number =       "4",
  pages =        "1203--1210",
  year =         "2004",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.1239/jap/1101840566",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  MRclass =      "60J20 (60J10)",
  MRnumber =     "2122815 (2006b:60161)",
  MRreviewer =   "Michael Drmota",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/getRecord?id=euclid.jap/1101840566;
                 http://www.jstor.org/stable/4141393;
                 https://www.univ-rouen.fr/LMRS/Persopage/Delarue/Publis/PDF/uniform_distribution_to_Benford_law.pdf",
  abstract =     "We provide a new, probabilistic explanation for the
                 appearance of Benford's law in everyday-life numbers,
                 by showing that it arises naturally when we consider
                 mixtures of uniform distributions. Then we connect our
                 result to a result of Flehinger, for which we provide a
                 shorter proof, and the speed of convergence.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "http://www.jstor.org/journals/00219002.html;
                 http://projecteuclid.org/euclid.jap/",
}

@Book{Judson:2004:GBF,
  author =       "Horace Freeland Judson",
  title =        "The Great Betrayal: Fraud in Science",
  publisher =    "Harcourt",
  address =      "Orlando, FL, USA",
  pages =        "xiv + 463",
  year =         "2004",
  ISBN =         "0-15-100877-9",
  ISBN-13 =      "978-0-15-100877-3",
  LCCN =         "Q175.37 .J84 2004",
  bibdate =      "Sat Sep 10 12:29:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/bios/har051/2004005906.html;
                 http://www.loc.gov/catdir/description/har051/2004005906.html;
                 http://www.loc.gov/catdir/samples/har051/2004005906.html;
                 http://www.loc.gov/catdir/toc/ecip0416/2004005906.html",
  acknowledgement = ack-nhfb,
  remark =       "No mention of Benford's Law or first digit phenomenon,
                 but nevertheless relevant for applications of Benford's
                 Law to detection of fraud in data.",
  subject =      "Fraud in science",
  tableofcontents = "Preface / xi \\
                 Prologue / 1 \\
                 1: A Culture of Fraud / 9 \\
                 2: What's It Like? A Typology of Scientific Fraud / 43
                 \\
                 3: Patterns of Complicity: Recent Cases / 98 \\
                 4: Hard to Measure, Hard to Define: The Incidence of
                 Scientific Fraud and the Struggle Over Its Definition /
                 155 \\
                 5: The Baltimore Affair / 191 \\
                 6: The Problems of Peer Review / 244 \\
                 7: Authorship, Ownership: The Problems of Credit,
                 Plagiarism, and Property / 287 \\
                 8: The Rise of Open Publication on the Internet / 325
                 \\
                 9: Laboratory to Law: The Problems of Institutions When
                 Misconduct is Charged / 369 \\
                 Epilogue / 404 \\
                 Notes / 419 \\
                 Index / 447",
}

@TechReport{Kollath-Romano:2004:DSD,
  author =       "P. Kollath-Romano",
  title =        "On the distribution of significant digits in numbers",
  type =         "Preprint",
  institution =  "Rensselaer Polytechnic Institute",
  address =      "Troy, NY, USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:15:19 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Kotz:2004:FDP,
  author =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  editor =       "Samuel Kotz and N. Balakrishnan and Campbell B. Read
                 and Brani Vidakovic",
  booktitle =    "Encyclopedia of Statistical Sciences",
  title =        "First-Digit Problem",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Second",
  pages =        "??--??",
  year =         "2004",
  DOI =          "https://doi.org/10.1002/0471667196.ess0783.pub2",
  ISBN =         "0-471-66719-6 (e-book)",
  ISBN-13 =      "978-0-471-66719-3 (e-book)",
  bibdate =      "Sun Feb 24 10:49:25 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kristiansen:2004:BTZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf} relation used in dynamics of
                 magnetic microparticles",
  journal =      j-ECONOM-LETT,
  volume =       "30",
  number =       "1",
  pages =        "2387--2388",
  day =          "1",
  month =        may,
  year =         "2004",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/j.jmmm.2003.12.1288",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304885303019127",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Kristiansen:2004:EOZ,
  author =       "Kai de Lange Kristiansen and Geir Helgesen and Arne T.
                 Skjeltorp",
  title =        "Experimental observation of {Zipf--Mandelbrot}
                 relation",
  journal =      j-PHYSICA-A,
  volume =       "335",
  number =       "3--4",
  pages =        "413--420",
  day =          "15",
  month =        apr,
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2003.12.024",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "82D10 (76T99 82-05)",
  MRnumber =     "2044153",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437103011804",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Kulikova:2004:OSS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "One-sided stable distributions and {Benford}'s law",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "49",
  number =       "1",
  pages =        "178--184",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1137/S0040585X97980944",
  ISSN =         "0040-361X",
  ISSN-L =       "0040-361X",
  MRclass =      "60E07 (60F05)",
  MRnumber =     "2141338 (2005m:60028)",
  MRreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Lanza:2004:CBS,
  author =       "Richard B. Lanza",
  title =        "Comparing Best Software for Fraud Examinations: Fraud
                 Data Interrogation Tools",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        nov # "\slash " # dec,
  year =         "2004",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:17:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967837",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Lehner:2004:DVG,
  author =       "B. Lehner and P. Doll",
  title =        "Development and validation of a global database of
                 lakes",
  journal =      j-J-HYDROL,
  volume =       "296",
  number =       "1--4",
  pages =        "1--22",
  day =          "20",
  month =        aug,
  year =         "2004",
  CODEN =        "JHYDA7",
  DOI =          "https://doi.org/10.1016/j.jhydrol.2004.03.028",
  ISSN =         "0022-1694 (print), 1879-2707 (electronic)",
  ISSN-L =       "0022-1694",
  bibdate =      "Fri Mar 22 08:54:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022169404001404",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  fjournal =     "Journal of Hydrology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00221694",
  keywords =     "Benford's Law",
}

@Article{Li:2004:DBL,
  author =       "Zhi-peng Li and Lin Cong and Hua-jia Wang",
  title =        "Discussion on {Benford's Law} and its Application",
  journal =      "ArXiv e-prints",
  pages =        "1--13",
  year =         "2004",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 16:17:04 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2004math......8057L;
                 http://arxiv.org/abs/math/0408057",
  abstract =     "The probability that a number in many naturally
                 occurring tables of numerical data has first
                 significant digit $d$ is predicted by Benford's Law $
                 {\rm Prob} (d) = \log_{10} (1 + {\displaystyle {1 \over
                 d}}), d = 1, 2, \ldots, 9 $. Illustrations of Benford's
                 Law from both theoretical and real-life sources on both
                 science and social science areas are shown in detail
                 with some novel ideas and generalizations developed
                 solely by the authors of this paper. Three tests,
                 Chi-Square test, total variation distance, and maximum
                 deviations are adopted to examine the fitness of the
                 datasets to Benford's distribution. Finally,
                 applications of Benford's Law are summarized and
                 explored to reveal the power of this mathematical
                 principle.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "math/0408057",
}

@Article{Lindsay:2004:DFD,
  author =       "D. H. Lindsay and P. S. Foote and A. Campbell and D.
                 R. Reilly",
  title =        "Detecting fraud in the data using automatic
                 intervention detection",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2004",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sat Feb 16 18:32:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Book{Miller:2004:JFM,
  author =       "Irwin Miller and Marylees Miller",
  title =        "{John E. Freund}'s mathematical statistics with
                 applications",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  edition =      "Seventh",
  pages =        "x + 614",
  year =         "2004",
  ISBN =         "0-13-142706-7",
  ISBN-13 =      "978-0-13-142706-8",
  LCCN =         "QA276 .M4726 2004",
  bibdate =      "Thu Oct 13 07:01:49 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1928--",
  remark =       "Revised edition of \cite{Miller:1999:JFM}.",
  subject =      "Mathematical statistics",
}

@TechReport{Miller:2004:STB,
  author =       "Steven J. Miller",
  title =        "Some thoughts on {Benford}'s law",
  type =         "Preprint",
  institution =  "Williams College",
  address =      "Williamstown, MA 01267 USA",
  year =         "2004",
  bibdate =      "Sat Feb 16 18:43:46 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.williams.edu/go/math/sjmiller/public_html/BrownClasses/1/BenfordTreatise.pdf",
  acknowledgement = ack-nhfb,
  remark =       "URL not found on 17 February 2013; perhaps in ReCALL
                 2004 proceedings",
}

@Article{Molchanov:2004:BEL,
  author =       "Stanislav Molchanov and Xian Wang",
  title =        "On the {Benford}'s empirical law",
  journal =      "Random Oper. Stochastic Equations",
  volume =       "12",
  number =       "3",
  pages =        "201--210",
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1163/1569397042222495",
  ISSN =         "0926-6364 (print), 1569-397X (electronic)",
  ISSN-L =       "0926-6364",
  MRclass =      "11K16 (11B39 60B15)",
  MRnumber =     "2084074 (2005h:11162)",
  MRreviewer =   "A. N. Philippou",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Random Operators and Stochastic Equations",
}

@Article{Nabeshima:2004:ZLP,
  author =       "Terutaka Nabeshima and Yukio-Pegio Gunji",
  title =        "{Zipf}'s law in phonograms and {Weibull} distribution
                 in ideograms: comparison of {English} with {Japanese}",
  journal =      j-BIOSYSTEMS,
  volume =       "73",
  number =       "2",
  pages =        "131--139",
  day =          "20",
  month =        feb,
  year =         "2004",
  CODEN =        "BSYMBO",
  DOI =          "https://doi.org/10.1016/j.biosystems.2003.11.002",
  ISSN =         "0303-2647 (print), 1872-8324 (electronic)",
  ISSN-L =       "0303-2647",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0303264703002260",
  acknowledgement = ack-nhfb,
  fjournal =     "Biosystems (A6E)",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03032647",
  keywords =     "Zipf's Law",
}

@Article{Nguyen:2004:DPL,
  author =       "Hung T. Nguyen and Vladik Kreinovich and Luc
                 Longpr{\'e}",
  title =        "Dirty Pages of Logarithm Tables, Lifetime of the
                 Universe, and (Subjective) Probabilities on Finite and
                 Infinite Intervals",
  journal =      j-RELIABLE-COMPUTING,
  volume =       "10",
  number =       "2",
  pages =        "83--106",
  month =        apr,
  year =         "2004",
  CODEN =        "RCOMF8",
  DOI =          "https://doi.org/10.1023/B:REOM.0000015848.19449.12",
  ISSN =         "1385-3139 (print), 1573-1340 (electronic)",
  ISSN-L =       "1385-3139",
  bibdate =      "Mon Feb 6 07:42:05 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=1385-3139&volume=10&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/rc.bib",
  URL =          "http://link.springer.com/article/10.1023/B%3AREOM.0000015848.19449.12/;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=1385-3139&volume=10&issue=2&spage=83-106",
  acknowledgement = ack-nhfb # "\slash " # ack-rbk # "\slash " # ack-vk,
  fjournal =     "Reliable Computing = Nadezhnye vychisleniia",
  journal-URL =  "http://link.springer.com/journal/11155",
}

@InProceedings{Pericchi:2004:LNB,
  author =       "Luis R{\'a}ul Pericchi and David Torres",
  editor =       "????",
  booktitle =    "{Third Universidad Simon Bolivar Seminar on
                 Statistical Analyses of the Venezuelan Recall
                 Referendum}",
  title =        "La {Ley de Newcomb--Benford} y sus aplicaciones al
                 Referendum Revocatorio en {Venezuela}. ({Spanish}) [The
                 {Newcomb--Benford Law} and its applications to the
                 recall referendum in {Venezuela}]",
  publisher =    "????",
  address =      "????",
  pages =        "1--7",
  day =          "1",
  month =        oct,
  year =         "2004",
  bibdate =      "Fri Feb 15 18:25:14 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reporte T{\'e}cnico no-definitivo 2a. Presented on
                 September 23, 2004.",
  URL =          "http://esdata.info/pdf/pericchi-torres.pdf;
                 https://sites.google.com/a/upr.edu/probability-and-statistics/home/techical-reports",
  acknowledgement = ack-nhfb,
  language =     "Spanish",
}

@TechReport{Posch:2004:BBH,
  author =       "Peter N. Posch",
  title =        "{Benford} or not-{Benford}? {How} to test for the
                 first digit law",
  type =         "Working paper.",
  institution =  "Department of Finance, University of Ulm",
  address =      "Ulm, Germany",
  year =         "2004",
  bibdate =      "Sat Feb 16 19:05:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@TechReport{Posch:2004:SSD,
  author =       "Peter N. Posch",
  title =        "A survey on sequences and distribution functions
                 satisfying {Benford}'s law",
  type =         "Working paper.",
  institution =  "Department of Finance, University of Ulm",
  address =      "Ulm, Germany",
  day =          "25",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Feb 16 19:05:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.posch.org/paper/posch_benforddist.pdf",
  acknowledgement = ack-nhfb,
}

@TechReport{Posch:2004:ZFB,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse in der F{\"a}lschungsaufsp{\"u}rung.
                 Benford's Gesetz und Steuererkl{\"a}rungen in Theorie
                 und Praxis}. ({German}) [Digit analysis in fake
                 tracing. {Benford's Law} and tax returns in theory and
                 practice]",
  type =         "Arbeitspapier",
  institution =  "Abteilung Finanzwirtschaft, University Ulm",
  address =      "Ulm, Germany",
  month =        oct,
  year =         "2004",
  bibdate =      "Sat Feb 16 19:03:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Pustet:2004:ZHH,
  author =       "Regina Pustet",
  title =        "{Zipf} and his heirs",
  journal =      j-LANG-SCI,
  volume =       "26",
  number =       "1",
  pages =        "1--25",
  day =          "1",
  month =        jan,
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S0388-0001(03)00018-4",
  ISSN =         "0388-0001 (print), 1873-5746 (electronic)",
  ISSN-L =       "0388-0001",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0388000103000184",
  abstract =     "During the first half of this century, George Kingsley
                 Zipf devised a comprehensive model of language mainly
                 on the empirical basis of frequency counts in
                 discourse. Although Zipf is remembered particularly for
                 establishing the general formula the higher the
                 discourse frequency of a linguistic item, the shorter
                 it will be, his model is complex enough to merit
                 re-evaluation especially in the light of more recent
                 findings of discourse-based models of language and
                 grammaticalization theory.",
  acknowledgement = ack-nhfb,
  fjournal =     "Language Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03880001",
  keywords =     "Benford's Law; Diachronic development of language;
                 Discourse analysis; George Kingsley Zipf; Usage-based
                 models of language; Word frequency; Zipf's Law",
}

@Article{Quarantelli:2004:ISA,
  author =       "Mario Quarantelli and Karim Berkouk and Anna Prinster
                 and Brigitte Landeau and Claus Svarer and Laszlo Balkay
                 and Bruno Alfano and Arturo Brunetti and Jean-Claude
                 Baron and Marco Salvatore",
  title =        "Integrated Software for the Analysis of Brain
                 {PET\slash SPECT} Studies with Partial-Volume Effect
                 Correction",
  journal =      j-NUCL-MED,
  volume =       "45",
  number =       "2",
  pages =        "192--201",
  day =          "1",
  month =        feb,
  year =         "2004",
  CODEN =        "JNMEAQ",
  ISSN =         "0161-5505 (print), 1535-5667 (electronic)",
  ISSN-L =       "0161-5505",
  bibdate =      "Sat Sep 10 15:45:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jnm.snmjournals.org/content/45/2/192.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Nuclear Medicine",
  journal-URL =  "http://jnm.snmjournals.org/content/by/year",
  keywords =     "Benford's Law",
}

@Article{Rawlings:2004:EBP,
  author =       "Philip K. Rawlings and David Reguera and Howard
                 Reiss",
  title =        "Entropic basis of the {Pareto} law",
  journal =      j-PHYSICA-A,
  volume =       "343",
  number =       "1--4",
  pages =        "643--652",
  year =         "2004",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2004.06.152",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B26 (91B82)",
  MRnumber =     "2094418 (2005e:91065)",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Rodriguez:2004:FSD,
  author =       "Ricardo J. Rodriguez",
  title =        "First Significant Digit Patterns From Mixtures of
                 Uniform Distributions",
  journal =      j-AMER-STAT,
  volume =       "58",
  number =       "1",
  pages =        "64--71",
  month =        feb,
  year =         "2004",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/0003130042782",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Fri Feb 20 06:14:28 MST 2004",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://oberon.ingentaselect.com/cgi-bin/linker?ini=asa&reqidx=/cw/asa/00031305/v58n1/s13/p64",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  keywords =     "Benford's Law",
}

@TechReport{Saville:2004:SWN,
  author =       "Adrian D. Saville",
  title =        "Sorry, wrong number. {How} accounting data are wrong
                 and how the numbers can be fixed",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2004",
  bibdate =      "Sat Feb 16 19:11:00 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Sigurd:2004:WLS,
  author =       "Bengt Sigurd and Mats Eeg-Olofsson and Joost {Van
                 Weijer}",
  title =        "Word length, sentence length and frequency --- {Zipf}
                 revisited",
  journal =      j-STUD-LINGUISTICA,
  volume =       "58",
  number =       "1",
  pages =        "37--52",
  year =         "2004",
  DOI =          "https://doi.org/10.1111/j.0039-3193.2004.00109.x",
  ISSN =         "0039-3193 (print), 1467-9582 (electronic)",
  ISSN-L =       "0039-3193",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Studia Linguistica",
}

@Article{Skousen:2004:AUP,
  author =       "Christopher J. Skousen and Liming Guan and T. Sterling
                 Wetzel",
  title =        "Anomalies and Unusual Patterns in Reported Earnings:
                 {Japanese} Managers Round Earnings",
  journal =      j-J-INT-FINANC-MANAG-ACCOUNT,
  volume =       "15",
  number =       "3",
  pages =        "212--234",
  month =        oct,
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1467-646X.2004.00108.x",
  ISSN =         "0954-1314 (print), 1467-646X (electronic)",
  ISSN-L =       "0954-1314",
  bibdate =      "Fri Nov 25 11:11:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of International Financial Management and
                 Accounting",
}

@Book{Tijms:2004:UPC,
  author =       "Henk C. Tijms",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "x + 380",
  year =         "2004",
  ISBN =         "0-521-83329-9 (hardcover), 0-521-54036-4 (paperback)",
  ISBN-13 =      "978-0-521-83329-5 (hardcover), 978-0-521-54036-0
                 (paperback)",
  LCCN =         "QA273 .T48 2004",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Probabilities; Mathematical analysis; Chance;
                 Wahrscheinlichkeit; (Math.); Gesamtdarstellung",
}

@Article{Vanichpun:2004:OCU,
  author =       "Sarut Vanichpun and Armand M. Makowski",
  title =        "The output of a cache under the independent reference
                 model: where did the locality of reference go?",
  journal =      j-SIGMETRICS,
  volume =       "32",
  number =       "1",
  pages =        "295--306",
  month =        jun,
  year =         "2004",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1012888.1005722",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Fri Jun 27 09:21:18 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "We consider a cache operating under a demand-driven
                 replacement policy when document requests are modeled
                 according to the Independent Reference Model (IRM). We
                 characterize the popularity pmf of the stream of misses
                 from the cache, the so-called output of the cache, for
                 a large class of demand-driven cache replacement
                 policies. We measure strength of locality of reference
                 in a stream of requests through the skewness of its
                 popularity distribution. Using the notion of
                 majorization to capture this degree of skewness, we
                 show that for the policy $ A_0 $ and the random policy,
                 the output always has less locality of reference than
                 the input. However, we show by counterexamples that
                 this is not always the case under the LRU and CLIMB
                 policies when the input is selected according to a
                 Zipf-like pmf. In that case, conjectures are offered
                 (and supported by simulations) as to when LRU or CLIMB
                 caching indeed reduces locality of reference.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "locality of reference; majorization; output of a
                 cache; popularity",
}

@InProceedings{Acebo:2005:BLN,
  author =       "E. Acebo and M. Sbert",
  editor =       "L. Neumann and M. Sbert and B. Gooch and W.
                 Purgathofer",
  booktitle =    "Conference: Computational Aesthetics 2005:
                 Eurographics Workshop on Computational Aesthetics in
                 Graphics, Visualization and Imaging 2005, Girona,
                 Spain, May 18--20, 2005",
  title =        "{Benford's Law} for Natural and Synthetic Images",
  publisher =    "????",
  address =      "????",
  pages =        "169--176",
  year =         "2005",
  DOI =          "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
  bibdate =      "Sat Sep 10 11:34:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Alexanderson:2005:BRG,
  author =       "Gerald L. Alexanderson",
  title =        "Book Review: {{\booktitle{Gamma: Exploring Euler's
                 Constant}}, by Julian Havil. Princeton, Princeton
                 University Press 2003. xxiii + 266 pages. US \$29.95.
                 ISBN 0-691-09983-9}",
  journal =      j-MATH-INTEL,
  volume =       "27",
  number =       "1",
  pages =        "86--88",
  month =        dec,
  year =         "2005",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/BF02984820",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/BF02984820",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
  keywords =     "Benford's Law",
}

@Article{Anonymous:2005:UZL,
  author =       "Anonymous",
  title =        "The use of {Zipf}'s law in animal communication
                 analysis",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "??--??",
  day =          "20",
  month =        jan,
  year =         "2005",
  CODEN =        "ANBEA8",
  DOI =          "https://doi.org/10.1016/j.anbehav.2004.08.004",
  ISSN =         "0003-3472 (print), 1095-8282 (electronic)",
  ISSN-L =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0003347204003471",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Article{Antonini:2005:RSC,
  author =       "Rita Giuliano Antonini and Georges Grekos",
  title =        "Regular sets and conditional density: an extension of
                 {Benford}'s law",
  journal =      j-COLLOQ-MATH,
  volume =       "103",
  number =       "2",
  pages =        "173--192",
  year =         "2005",
  CODEN =        "CQMAAQ",
  DOI =          "https://doi.org/10.4064/cm103-2-3",
  ISSN =         "0010-1354 (print), 1730-6302 (electronic)",
  ISSN-L =       "0010-1354",
  MRclass =      "11B05 (11K99)",
  MRnumber =     "2197847 (2006j:11012)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1092.11009",
  acknowledgement = ack-nhfb,
  fjournal =     "Colloquium Mathematicum",
  keywords =     "asymptotic density; Benford's law; conditional
                 density; first digit problem; logarithmic density;
                 regular set; regular varying function",
  ZMclass =      "11B05 (Topology etc. of sets of numbers); 11K99
                 (Probabilistic theory)",
}

@Article{Berger:2005:BLP,
  author =       "Arno Berger",
  title =        "{Benford}'s law in power-like dynamical systems",
  journal =      j-STOCH-DYNAM,
  volume =       "5",
  number =       "4",
  pages =        "587--607",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1142/S0219493705001602",
  ISSN =         "0219-4937",
  ISSN-L =       "0219-4937",
  MRclass =      "37B55 (11K06 37A50 37E05)",
  MRnumber =     "2185507 (2008i:37029)",
  MRreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Stoch. Dyn.",
  fjournal =     "Stochastics and Dynamics",
}

@InCollection{Berger:2005:DDU,
  author =       "A. Berger",
  booktitle =    "{EQUADIFF} 2003",
  title =        "Dynamics and digits: on the ubiquity of {Benford}'s
                 law",
  publisher =    "World Sci. Publ., Hackensack, NJ",
  pages =        "693--695",
  year =         "2005",
  DOI =          "https://doi.org/10.1142/9789812702067_0115",
  MRclass =      "37A45 (11K55)",
  MRnumber =     "2185113",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2005:MDD,
  author =       "Arno Berger",
  title =        "Multi-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-DISCRETE-CONTIN-DYN-SYST,
  volume =       "13",
  number =       "1",
  pages =        "219--237",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.3934/dcds.2005.13.219",
  ISSN =         "1078-0947 (print), 1553-5231 (electronic)",
  ISSN-L =       "1078-0947",
  MRclass =      "37A45 (11K36 28D05 37A50 60F05)",
  MRnumber =     "2128801 (2005m:37016)",
  MRreviewer =   "Reinhard Winkler",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Discrete and Continuous Dynamical Systems. Series A",
}

@Article{Berger:2005:ODD,
  author =       "Arno Berger and Leonid A. Bunimovich and Theodore P.
                 Hill",
  title =        "One-dimensional dynamical systems and {Benford}'s
                 law",
  journal =      j-TRANS-AM-MATH-SOC,
  volume =       "357",
  number =       "1",
  pages =        "197--219",
  year =         "2005",
  CODEN =        "TAMTAM",
  DOI =          "https://doi.org/10.1090/S0002-9947-04-03455-5",
  ISSN =         "0002-9947 (print), 1088-6850 (electronic)",
  ISSN-L =       "0002-9947",
  MRclass =      "37A45 (11K06 37A50 37E05 60F05 82B05)",
  MRnumber =     "2098092 (2005m:37017)",
  MRreviewer =   "Peter Raith",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Transactions of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/tran/",
}

@Article{Bhattacharya:2005:CPA,
  author =       "Sukanto Bhattacharya and Kuldeep Kumar and Florentin
                 Smarandache",
  title =        "Conditional probability of actually detecting a
                 financial fraud --- a neutrosophic extension to
                 {Benford}'s law",
  journal =      "International Journal of Applied Mathematics",
  volume =       "17",
  number =       "1",
  pages =        "7--14",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "1311-1728",
  MRclass =      "62G10 (91B28)",
  MRnumber =     "2170667",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0504520",
  abstract =     "This study actually draws from and builds on an
                 earlier paper (Kumar and Bhattacharya, 2002). Here we
                 have basically added a neutrosophic dimension to the
                 problem of determining the conditional probability that
                 a financial fraud has been actually committed, given
                 that no Type I error occurred while rejecting the null
                 hypothesis H0: The observed first-digit frequencies
                 approximate a Benford distribution; and accepting the
                 alternative hypothesis H1: The observed first-digit
                 frequencies do not approximate a Benford distribution.
                 We have also suggested a conceptual model to implement
                 such a neutrosophic fraud detection system.",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Appl. Math.",
  fjournal =     "International Journal of Applied Mathematics",
}

@Article{Bhattacharyya:2005:COP,
  author =       "P. Bhattacharyya and A. Chatterjee and B. K.
                 Chakrabarti",
  title =        "A common origin of the power law distributions in
                 models of market and earthquake",
  journal =      "ArXiv e-prints",
  year =         "2005",
  bibdate =      "Sat Feb 16 17:25:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/physics/0510038",
  acknowledgement = ack-nhfb,
}

@Article{Brown:2005:BLS,
  author =       "Richard J. C. Brown",
  title =        "{Benford}'s law and the screening of analytical data:
                 the case of pollutant concentrations in ambient air",
  journal =      j-ANALYST,
  volume =       "130",
  number =       "9",
  pages =        "1280--1285",
  month =        "????",
  year =         "2005",
  CODEN =        "ANALAO",
  DOI =          "https://doi.org/10.1039/B504462F",
  ISSN =         "0003-2654 (print), 1364-5528 (electronic)",
  ISSN-L =       "0003-2654",
  bibdate =      "Sat Feb 16 17:27:51 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pubmed/16096674",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
  journal-URL =  "http://pubs.rsc.org/en/journals/journalissues/an",
}

@Article{Campi:2005:ZLM,
  author =       "X. Campi and H. Krivine",
  title =        "{Zipf}'s law in multifragmentation",
  journal =      j-PHYS-REV-C,
  volume =       "72",
  number =       "??",
  pages =        "057602",
  day =          "30",
  month =        nov,
  year =         "2005",
  CODEN =        "PRVCAN",
  DOI =          "https://doi.org/10.1103/PhysRevC.72.057602",
  ISSN =         "0556-2813 (print), 1089-490X, 1538-4497",
  ISSN-L =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevC.72.057602",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  journal-URL =  "http://prc.aps.org/browse",
  keywords =     "Zipf's Law",
}

@TechReport{Ciofalo:2005:EBF,
  author =       "Michele Ciofalo",
  title =        "Entropy, {Benford}'s first digit law, and the
                 distribution of everything",
  type =         "Report",
  institution =  "Dipartimento di Ingegneria Nucleare, Universit{\`a}
                 degli Studi di Palermo",
  address =      "Palermo, Italy",
  pages =        "34",
  year =         "2005",
  bibdate =      "Sun Feb 17 08:23:55 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.din.unipa.it/Struttura/Personale/Profili/ciofalo_allegati/Paper_Benford.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Cleary:2005:ADA,
  author =       "Richard Cleary and Jay C. Thibodeau",
  title =        "Applying Digital Analysis Using {Benford's Law} to
                 Detect Fraud: The Dangers of Type {I} Errors",
  journal =      j-AUDITING,
  volume =       "24",
  number =       "1",
  pages =        "77--81",
  month =        may,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2308/aud.2005.24.1.77",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Tue Nov 15 09:17:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaapubs.org/loi/ajpt;
                 http://link.aip.org/link/AJPTXX/v24/i1/p77/s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@Article{Cohen:2005:PCL,
  author =       "Edith Cohen and Carsten Lund",
  title =        "Packet classification in large {ISPs}: design and
                 evaluation of decision tree classifiers",
  journal =      j-SIGMETRICS,
  volume =       "33",
  number =       "1",
  pages =        "73--84",
  month =        jun,
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1064212.1064222",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Fri Jun 27 09:21:27 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Packet classification, although extensively studied,
                 is an evolving problem. Growing and changing needs
                 necessitate the use of larger filters with more complex
                 rules. The increased complexity and size pose
                 implementation challenges on current hardware solutions
                 and drive the development of software classifiers, in
                 particular, decision-tree based classifiers. Important
                 performance measures for these classifiers are time and
                 memory due to required high throughput and use of
                 limited fast memory. We analyze Tier 1 ISP data that
                 includes filters and corresponding traffic from over a
                 hundred edge routers and thousands of interfaces. We
                 provide a comprehensive view on packet classification
                 in an operational network and glean insights that help
                 us design more effective classification algorithms. We
                 propose and evaluate decision tree classifiers with
                 {\em common branches}. These classifiers have linear
                 worst-case memory bounds and require much less memory
                 than standard decision tree classifiers, but
                 nonetheless, we show that on our data have similar
                 average and worst-case time performance. We argue that
                 common-branches exploit structure that is present in
                 real-life data sets. We observe a strong Zipf-like
                 pattern in the usage of rules in a classifier, where a
                 very small number of rules resolves the bulk of traffic
                 and most rules are essentially never used. Inspired by
                 this observation, we propose {\em traffic-aware\/}
                 classifiers that obtain superior average-case and
                 bounded worst-case performance. Good average-case can
                 boost performance of software classifiers that can be
                 used in small to medium sized routers and are also
                 important for traffic analysis and traffic
                 engineering.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "access control lists; decision trees; packet
                 filtering; routing",
}

@Article{Dahui:2005:TRZ,
  author =       "Wang Dahui and Li Menghui and Di Zengru",
  title =        "True reason for {Zipf}'s law in language",
  journal =      j-PHYSICA-A,
  volume =       "358",
  number =       "2--4",
  pages =        "545--550",
  day =          "15",
  month =        dec,
  year =         "2005",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2005.04.021",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437105004085",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@InProceedings{DelAcebo:2005:BLN,
  author =       "Esteve {Del Acebo} and Mateu Sbert",
  title =        "{Benford's Law} for Natural and Synthetic Images",
  crossref =     "Neumann:2005:CAE",
  pages =        "169--176",
  year =         "2005",
  DOI =          "https://doi.org/10.2312/COMPAESTH/COMPAESTH05/169-176",
  bibdate =      "Tue Nov 15 08:46:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.eg.org/EG/DL/WS/COMPAESTH/COMPAESTH05/169-176.pdf",
  acknowledgement = ack-nhfb,
}

@Book{Durrett:2005:PTE,
  author =       "Richard Durrett",
  title =        "Probability: theory and examples",
  publisher =    "Thomson Brooks\slash Cole",
  address =      "Belmont, CA, USA",
  edition =      "Third",
  pages =        "xi + 497",
  year =         "2005",
  ISBN =         "0-534-42441-4",
  ISBN-13 =      "978-0-534-42441-1",
  LCCN =         "QA273 .D865 2005",
  bibdate =      "Mon Nov 21 10:00:11 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Duxbury advanced series",
  acknowledgement = ack-nhfb,
  remark =       "Benford's Law is treated on pp. 337ff. Hill \cite[page
                 893]{Hill:1995:BII} reports that the 1991 edition has a
                 proof that the $k$-th digit of powers of integers
                 follows Benford's Law.",
  subject =      "Probabilities",
}

@Book{Egghe:2005:PLI,
  author =       "Leo Egghe",
  title =        "Power laws in the information production process:
                 {Lotkaian} informetrics",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xvii + 427",
  year =         "2005",
  ISBN =         "0-12-088753-3, 0-08-048011-X (e-book)",
  ISBN-13 =      "978-0-12-088753-8, 978-0-08-048011-4 (e-book)",
  LCCN =         "Z669.8 .E44 2005",
  bibdate =      "Mon Feb 25 10:42:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See pages 204--205 for Benford's Law discussion.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject-dates = "Lotka, Alfred James, (1880--1949)",
  tableofcontents = "Basic theory of Lotkaian informetrics \\
                 Three-dimensional Lotkaian informetrics \\
                 Lotkaian concentration theory \\
                 Lotkaian fractal complexity theory \\
                 Lotkaian informetrics of systems in which items can
                 have multiple sources \\
                 Further applications in Lotkaian informetrics \\
                 Lotkaian informetrics: an introduction",
}

@Article{Egghe:2005:PPL,
  author =       "L. Egghe",
  title =        "The power of power laws and an interpretation of
                 {Lotkaian} informetric systems as self-similar
                 fractals",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "56",
  number =       "7",
  pages =        "669--675",
  month =        may,
  year =         "2005",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20158",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "16 Mar 2005",
}

@Article{Egghe:2005:RBC,
  author =       "L Egghe",
  title =        "Relations between the continuous and the discrete
                 {Lotka} power function",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "56",
  number =       "7",
  pages =        "664--668",
  month =        may,
  year =         "2005",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20157",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "11 Mar 2005",
}

@Article{Egghe:2005:ZLC,
  author =       "L. Egghe",
  title =        "{Zipfian} and {Lotkaian} continuous concentration
                 theory",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "56",
  number =       "9",
  pages =        "935--945",
  month =        jul,
  year =         "2005",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20186",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:28 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "21 Apr 2005",
}

@Article{elSehity:2005:PDA,
  author =       "Tarek el Sehity and Erik Hoelzl and Erich Kirchler",
  title =        "Price developments after a nominal shock: {Benford's
                 Law} and psychological pricing after the euro
                 introduction",
  journal =      j-INT-J-RES-MARK,
  volume =       "22",
  number =       "4",
  pages =        "471--480",
  month =        dec,
  year =         "2005",
  CODEN =        "IJRME6",
  DOI =          "https://doi.org/10.1016/j.ijresmar.2005.09.002",
  ISSN =         "0167-8116 (print), 1873-8001 (electronic)",
  ISSN-L =       "0167-8116",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167811605000522",
  abstract =     "Retail managers use psychological pricing to make the
                 prices of goods appear to be just below a round number.
                 The euro introduction in 2002, with its various
                 exchange rates, distorted existing nominal price
                 patterns while at the same time retaining real prices.
                 We studied consumer prices before and after the
                 introduction of the euro by using Benford's Law as a
                 benchmark for price adjustments. Results indicate the
                 usefulness of this benchmark for detecting
                 irregularities in prices, and a clear trend towards
                 psychological pricing after the nominal shock of the
                 euro introduction. In addition, the tendency towards
                 psychological prices results in different inflation
                 rates in dependence of the price pattern.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Research in Marketing",
  keywords =     "Benford's Law; Digital analysis; Price endings; Retail
                 pricing",
}

@Article{Fairthorne:2005:PDE,
  author =       "Robert A. Fairthorne",
  title =        "Progress in Documentation: Empirical Hyperbolic
                 Distributions ({Bradford--Zipf--Mandelbrot}) for
                 Bibliometric Description and Prediction",
  journal =      j-J-DOC,
  volume =       "61",
  number =       "2",
  pages =        "171--193",
  month =        "????",
  year =         "2005",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/00220410510585179",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 06:27:27 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Reprint of \cite{Fairthorne:1969:PDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  remark =       "According to \cite{Potter:1981:LLR}, this paper is the
                 first to link the distributions of Bradford, Zipf,
                 Mandelbrot, and Lotka.",
}

@Article{FerreriCancho:2005:CZL,
  author =       "Ramon {Ferrer i Cancho} and Oliver Riordan and
                 B{\'e}la Bollob{\'a}s",
  title =        "The consequences of {Zipf}'s law for syntax and
                 symbolic reference",
  journal =      j-PROC-R-SOC-LOND-SER-B-BIO-SCI,
  volume =       "272",
  number =       "1562",
  pages =        "561--565",
  day =          "7",
  month =        mar,
  year =         "2005",
  CODEN =        "PRLBA4",
  DOI =          "https://doi.org/10.1098/rspb.2004.2957",
  ISSN =         "0962-8452 (print), 1471-2954 (electronic)",
  ISSN-L =       "0962-8452",
  bibdate =      "Tue Nov 15 11:27:26 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rspb.royalsocietypublishing.org/content/272/1562/561.full",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society of London. Series B.
                 Biological sciences",
}

@TechReport{Giles:2005:BLN,
  author =       "David E. Giles",
  title =        "{Benford's Law} and Naturally Occurring Prices in
                 Certain {ebaY} Auctions",
  type =         "Econometrics Working Paper",
  number =       "EWP0505",
  institution =  "Department of Economics, University of Victoria",
  address =      "Victoria, BC, Canada",
  month =        may,
  year =         "2005",
  ISSN =         "1485-6441",
  bibdate =      "Thu Feb 15 16:24:39 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://web.uvic.ca/econ/ewp0505.pdf",
  abstract =     "We show that certain the winning bids for certain ebaY
                 auctions obey Benford's Law. One implication of this is
                 that it is unlikely that these bids are subject to
                 collusion among bidders, or ``shilling'' on the part of
                 sellers. Parenthetically, we also show that numbers
                 from the naturally occurring Fibonacci and Lucas
                 sequences also obey Benford's Law.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
}

@Article{Harremoes:2005:ZLHa,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  journal =      j-PHYSICA-A,
  volume =       "328",
  number =       "3--4",
  pages =        "315--318",
  day =          "1",
  month =        aug,
  year =         "2005",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.endm.2005.07.075",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1571065305051450",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@InCollection{Harremoes:2005:ZLHb,
  author =       "Peter Harremo{\"e}s and Flemming Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics.",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "21",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "315--318",
  year =         "2005",
  DOI =          "https://doi.org/10.1016/j.endm.2005.07.075",
  bibdate =      "Sat Nov 12 11:07:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Electronic Notes in Discrete Mathematics",
  ZMnumber =     "1158.91482",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@Article{Hill:2005:RDS,
  author =       "Theodore P. Hill and Klaus Sch{\"u}rger",
  title =        "Regularity of digits and significant digits of random
                 variables",
  journal =      j-STOCH-PROC-APPL,
  volume =       "115",
  number =       "10",
  pages =        "1723--1743",
  month =        oct,
  year =         "2005",
  CODEN =        "STOPB7",
  DOI =          "https://doi.org/10.1016/j.spa.2005.05.003",
  ISSN =         "0304-4149 (print), 1879-209X (electronic)",
  ISSN-L =       "0304-4149",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304414905000657",
  abstract =     "A random variable X is digit-regular (respectively,
                 significant-digit-regular) if the probability that
                 every block of $k$ given consecutive digits
                 (significant digits) appears in the b-adic expansion of
                 $X$ approaches $ b - k$ as the block moves to the
                 right, for all integers $ b > 1$ and $ k \geq 1$.
                 Necessary and sufficient conditions are established, in
                 terms of convergence of Fourier coefficients, and in
                 terms of convergence in distribution modulo 1, for a
                 random variable to be digit-regular
                 (significant-digit-regular), and basic relationships
                 between digit-regularity and various classical classes
                 of probability measures and normal numbers are given.
                 These results provide a theoretical basis for analyses
                 of roundoff errors in numerical algorithms which use
                 floating-point arithmetic, and for detection of fraud
                 in numerical data via using goodness-of-fit of the
                 least significant digits to uniform, complementing
                 recent tests for leading significant digits based on
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03044149",
  keywords =     "Benford's Law; Digit-regular random variable;
                 Floating-point numbers; Law of least significant
                 digits; Nonleading digits; Normal numbers; Significant
                 digits; Significant-digit-regular random variable;
                 Trailing digits",
}

@InProceedings{Hjorland:2005:BLS,
  author =       "Birger Hj{\o}rland and Jeppe Nicolaisen",
  editor =       "Fabio Crestani and Ian Ruthven",
  booktitle =    "Context: nature, impact, and role: {5th International
                 Conference on Conceptions of Library and Information
                 Sciences, CoLIS 2005, Glasgow, UK, June 4--8, 2005;
                 proceedings}",
  title =        "{Bradford}'s law of scattering: ambiguities in the
                 concept of ``subject''",
  volume =       "3507",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xiii + 250",
  pages =        "96--106",
  year =         "2005",
  ISBN =         "3-540-26178-8",
  ISBN-13 =      "978-3-540-26178-0",
  LCCN =         "Z672.5 .I5616 2005",
  bibdate =      "Fri Nov 25 11:52:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Article{Ioannidis:2005:WMP,
  author =       "John P. A. Ioannidis",
  title =        "Why Most Published Research Findings Are False",
  journal =      j-PLOS-MED,
  volume =       "2",
  number =       "8",
  pages =        "696--701",
  month =        aug,
  year =         "2005",
  CODEN =        "PMLEAC",
  DOI =          "https://doi.org/10.1371/journal.pmed.0020124",
  ISSN =         "1549-1277 (print), 1549-1676 (electronic)",
  ISSN-L =       "1549-1277",
  bibdate =      "Fri Nov 18 12:42:05 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0020124",
  abstract =     "There is increasing concern that most current
                 published research findings are false. The probability
                 that a research claim is true may depend on study power
                 and bias, the number of other studies on the same
                 question, and, importantly, the ratio of true to no
                 relationships among the relationships probed in each
                 scientific field. In this framework, a research finding
                 is less likely to be true when the studies conducted in
                 a field are smaller; when effect sizes are smaller;
                 when there is a greater number and lesser preselection
                 of tested relationships; where there is greater
                 flexibility in designs, definitions, outcomes, and
                 analytical modes; when there is greater financial and
                 other interest and prejudice; and when more teams are
                 involved in a scientific field in chase of statistical
                 significance. Simulations show that for most study
                 designs and settings, it is more likely for a research
                 claim to be false than true. Moreover, for many current
                 scientific fields, claimed research findings may often
                 be simply accurate measures of the prevailing bias. In
                 this essay, I discuss the implications of these
                 problems for the conduct and interpretation of
                 research.",
  acknowledgement = ack-nhfb,
  articleno =    "e124",
  fjournal =     "PLoS Medicine",
  journal-URL =  "http://medicine.plosjournals.org/",
  remark =       "This article does not discuss Benford's Law, but is
                 related to the use of that law in the detection of
                 fraud in research data. Ioannidis discusses the abuse
                 of statistics for limited experimental data, a topic
                 that receives book-length treatment in
                 \cite{Ziliak:2008:CSS}.",
}

@Article{Jolissaint:2005:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. ({French}) [{Benford}'s
                 Law, recurrence relations, and equidistributed
                 sequences]",
  journal =      j-ELEM-MATH,
  volume =       "60",
  number =       "1",
  pages =        "10--18",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4171/EM/2",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "11K36 (37A45 60E99)",
  MRnumber =     "2188341 (2006j:11109)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Kechedzhi:2005:RDW,
  author =       "K. E. Kechedzhi and O. V. Usatenko and V. A.
                 Yampol{\cprime}skii",
  title =        "Rank distributions of words in correlated symbolic
                 systems and the {Zipf} law",
  journal =      j-PHYS-REV-E,
  volume =       "72",
  number =       "4",
  pages =        "046138",
  day =          "28",
  month =        oct,
  year =         "2005",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.72.046138",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  MRclass =      "82C31",
  MRnumber =     "2183723 (2006f:82069)",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.72.046138",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@Article{Kontorovich:2005:BLV,
  author =       "Alex V. Kontorovich and Steven J. Miller",
  title =        "{Benford}'s law, values of {$L$}-functions and the {$
                 3 x + 1 $} problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  year =         "2005",
  CODEN =        "AARIA9",
  DOI =          "https://doi.org/10.4064/aa120-3-4",
  ISSN =         "0065-1036 (print), 1730-6264 (electronic)",
  ISSN-L =       "0065-1036",
  MRclass =      "11K06 (11B37 11M06 37A45)",
  MRnumber =     "2188844 (2007c:11085)",
  MRreviewer =   "J. C. Lagarias",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005AcAri.120..269K;
                 http://arxiv.org/abs/math/0412003",
  abstract =     "We show the leading digits of a variety of systems
                 satisfying certain conditions follow Benford's Law. For
                 each system proving this involves two main ingredients.
                 One is a structure theorem of the limiting
                 distribution, specific to the system. The other is a
                 general technique of applying Poisson Summation to the
                 limiting distribution. We show the distribution of
                 values of $L$-functions near the central line and (in
                 some sense) the iterates of the $ 3 x + 1 $ Problem are
                 Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@Article{Kulikova:2005:CAS,
  author =       "A. A. Kulikova and Yu. V. Prokhorov",
  title =        "Completely Asymmetric Stable Laws and {Benford's
                 Law}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "49",
  number =       "1",
  pages =        "163--169",
  month =        mar,
  year =         "2005",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/S0040585X97980944",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Thu Jul 7 19:15:48 MDT 2005",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/49/1;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/98094",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
  journal-URL =  "http://epubs.siam.org/tvp",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Kulikova:2005:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H. F. D.} ({$H$}-function distribution) and the
                 {Benford} law. {I}",
  journal =      "Teor. Veroyatn. Primen.",
  volume =       "50",
  number =       "2",
  pages =        "366--371",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1137/S0040585X97981706",
  ISSN =         "0040-361X",
  ISSN-L =       "0040-361X",
  MRclass =      "60E07 (60F05)",
  MRnumber =     "2221718 (2007b:60029)",
  MRreviewer =   "S{\'a}ndor Cs{\"o}rg{\H{o}}",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoriya
                 Veroyatnoste{\u\i} i ee Primeneniya",
}

@Article{Lagarias:2005:BLF,
  author =       "J. C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $ 3 x + 1 $ function",
  journal =      "ArXiv Mathematics e-prints",
  month =        sep,
  year =         "2005",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2005math......9175L;
                 http://arxiv.org/abs/math/0509175",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0509175",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability",
}

@Article{Li:2005:ZLP,
  author =       "Yujian Li and Chuangbai Xiao",
  title =        "{Zipf}'s law probably existing in protein sequences",
  journal =      "J. Beijing Univ. Technol.",
  volume =       "31",
  number =       "4",
  pages =        "366--368",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Nov 12 11:10:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1084.92019",
  abstract =     "In order to analyze whether Zipf's law in linguistics
                 exists in protein sequences, this paper uses $ 1.735 \,
                 7 \times 10^4 $ protein sequences labeled with
                 secondary structures which are selected from the DSSP
                 database. The segments of successive amino acid
                 residues with a same code of secondary structure are
                 defined as words. The results show that the
                 distribution of words emerging frequency follows Zipf's
                 law with the exponent $ 0.981 $.",
  acknowledgement = ack-nhfb,
  classmath =    "92C40 (Biochemistry, etc.); 62P10 (Appl. of statistics
                 to biology): 92D20 (Protein sequences, DNA sequences)",
  language =     "Chinese. English summary",
  xxremark =     "Which journal is this? Beijing gong ye da xue xue bao
                 = Journal of Beijing Polytechnic University (ISSN
                 0254-0037), or Beijing ke ji da xue xue bao = Journal
                 of University of Science and Technology, Beijing (ISSN
                 1001-053X), or something different?",
}

@Article{Lu:2005:CZL,
  author =       "Tim Lu and Christine M. Costello and Peter J. P.
                 Croucher and Robert H{\"a}sler and G{\"u}nther Deuschl
                 and Stefan Schreiber",
  title =        "Can {Zipf}'s law be adapted to normalize
                 microarrays?",
  journal =      j-BMC-BIOINFORMATICS,
  volume =       "6",
  number =       "??",
  pages =        "37--49",
  month =        "????",
  year =         "2005",
  CODEN =        "BBMIC4",
  DOI =          "https://doi.org/10.1186/1471-2105-6-37",
  ISSN =         "1471-2105",
  ISSN-L =       "1471-2105",
  bibdate =      "Sat Feb 16 18:38:50 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1186/1471-2105-6-37;
                 http://www.biomedcentral.com/1471-2105/6/37",
  acknowledgement = ack-nhfb,
  fjournal =     "BMC Bioinformatics",
  journal-URL =  "http://www.biomedcentral.com/bmcbioinformatics/",
}

@InProceedings{Lu:2005:DFH,
  author =       "Fletcher Lu and J. Efrim Boritz",
  title =        "Detecting Fraud in Health Insurance Data: Learning to
                 Model Incomplete {Benford's Law} Distributions",
  crossref =     "Gama:2005:MLE",
  pages =        "633--640",
  year =         "2005",
  DOI =          "https://doi.org/10.1007/11564096_63",
  bibdate =      "Tue Nov 15 08:55:45 2011",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/ecml/ecml2005.html#LuB05;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer.com/chapter/10.1007/11564096_63",
  acknowledgement = ack-nhfb,
}

@Article{Ma:2005:CBL,
  author =       "Y. G. Ma and J. B. Natowitz and R. Wada and K. Hagel
                 and J. Wang and T. Keutgen and Z. Majka and M. Murray
                 and L. Qin and P. Smith and R. Alfaro and J. Cibor and
                 M. Cinausero and Y. El Masri and D. Fabris and E.
                 Fioretto and A. Keksis and M. Lunardon and A. Makeev
                 and N. Marie and E. Martin and A. Martinez-Davalos and
                 A. Menchaca-Rocha and G. Nebbia and G. Prete and V.
                 Rizzi and A. Ruangma and D. V. Shetty and G. Souliotis
                 and P. Staszel and M. Veselsky and G. Viesti and E. M.
                 Winchester and S. J. Yennello",
  title =        "Critical behavior in light nuclear systems:
                 Experimental aspects",
  journal =      j-PHYS-REV-C,
  volume =       "71",
  number =       "5",
  pages =        "054606",
  day =          "26",
  month =        may,
  year =         "2005",
  CODEN =        "PRVCAN",
  DOI =          "https://doi.org/10.1103/PhysRevC.71.054606",
  ISSN =         "0556-2813 (print), 1089-490X, 1538-4497",
  ISSN-L =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevC.71.054606",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  journal-URL =  "http://prc.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Manaris:2005:ZLM,
  author =       "Bill Manaris and Juan Romero and Penousal Machado and
                 Dwight Krehbiel and Timothy Hirzel and Walter Pharr and
                 Robert B. Davis",
  title =        "{Zipf}'s law, music classification, and aesthetics",
  journal =      j-COMP-MUSIC-J,
  volume =       "29",
  number =       "1",
  pages =        "55--69",
  month =        "Spring",
  year =         "2005",
  CODEN =        "CMUJDY",
  ISSN =         "0148-9267 (print), 1531-5169 (electronic)",
  ISSN-L =       "0148-9267",
  bibdate =      "Sat Feb 16 18:40:14 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://muse.jhu.edu/journals/cmj/summary/v029/29.1manaris.html;
                 http://muse.jhu.edu/journals/computer_music_journal/v029/29.1manaris.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Music Journal",
  keywords =     "Benford's Law; Zipf's Law; Zipf--Mandelbrot Law",
}

@Article{Martinson:2005:SBB,
  author =       "Brian C. Martinson and Melissa S. Anderson and Raymond
                 de Vries",
  title =        "Scientists Behaving Badly",
  journal =      j-NATURE,
  volume =       "435",
  number =       "7043",
  pages =        "737--738",
  day =          "9",
  month =        jun,
  year =         "2005",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1007/s00221-007-0889-0",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Sat Sep 10 13:14:54 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v435/n7043/pdf/435737a.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  keywords =     "Benford's Law",
  remark =       "No mention of Benford's Law or first digit phenomenon,
                 but nevertheless relevant for applications of Benford's
                 Law to detection of fraud in science.",
}

@Article{Maslov:2005:GTS,
  author =       "V. P. Maslov",
  title =        "On a general theorem of set theory that leads to the
                 {Gibbs}, {Bose--Einstein}, and {Pareto} distributions
                 and to the {Zipf--Mandelbrot} law for the stock
                 market",
  journal =      j-MAT-ZAMETKI,
  volume =       "78",
  number =       "6",
  pages =        "870--877",
  year =         "2005",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11006-005-0186-9",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "91B28 (90C29)",
  MRnumber =     "2249037 (2007b:91077)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
  journal-URL =  "http://link.springer.com/journal/11006",
}

@Article{Maslov:2005:RZLa,
  author =       "V. P. Maslov",
  title =        "Refining {Zipf}'s law for frequency dictionaries",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "405",
  number =       "5",
  pages =        "591--594",
  year =         "2005",
  CODEN =        "DANKAS",
  ISSN =         "0869-5652",
  ISSN-L =       "0869-5652",
  MRclass =      "94A15 (60C05)",
  MRnumber =     "2340762",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}

@Article{Maslov:2005:RZLb,
  author =       "V. P. Maslov",
  title =        "Refinement of {Zipf}'s law for frequency
                 dictionaries",
  journal =      j-DOKL-MATH,
  volume =       "72",
  number =       "3",
  pages =        "942--945",
  year =         "2005",
  CODEN =        "????",
  ISSN =         "1064-5624 (print), 1531-8362 (electronic)",
  ISSN-L =       "1064-5624",
  bibdate =      "Sat Nov 12 11:05:14 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1206.82009",
  acknowledgement = ack-nhfb,
  classmath =    "82B10 (Quantum equilibrium statistical mechanics
                 (general)) 68T50 (Natural language processing) 68Q45
                 (Formal languages)",
  fjournal =     "Doklady Mathematics",
  journal-URL =  "http://link.springer.com/journal/11472",
  keywords =     "Bose--Einstein statistics",
  language =     "English. Russian original",
}

@Article{Maslov:2005:ZML,
  author =       "V. P. Maslov",
  title =        "The {Zipf--Mandelbrot} law: quantization and an
                 application to the stock market",
  journal =      j-RUSS-J-MATH-PHYS,
  volume =       "12",
  number =       "4",
  pages =        "483--488",
  year =         "2005",
  CODEN =        "RJMPEL",
  ISSN =         "1061-9208 (print), 1555-6638 (electronic)",
  ISSN-L =       "1061-9208",
  MRclass =      "91B28 (82B99)",
  MRnumber =     "2201312 (2006i:91053)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Russian Journal of Mathematical Physics",
}

@Article{McAllister:2005:ACE,
  author =       "James W. McAllister",
  title =        "Algorithmic compression of empirical data: reply to
                 {Twardy}, {Gardner}, and {Dowe}",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "36",
  number =       "2",
  pages =        "403--410",
  month =        jun,
  year =         "2005",
  CODEN =        "SHPSB5",
  DOI =          "https://doi.org/10.1016/j.shpsa.2005.04.005",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:58 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See \cite{McAllister:2003:ARE,Twardy:2005:EDS}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0039368105000221",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
}

@Article{McCowan:2005:AUZ,
  author =       "B. McCowan and L. R. Doyle and J. M. Jenkins and S. F.
                 Hanser",
  title =        "The appropriate use of {Zipf}'s law in animal
                 communication studies",
  journal =      j-ANIM-BEHAV,
  volume =       "69",
  number =       "1",
  pages =        "F1--F7",
  day =          "20",
  month =        jan,
  year =         "2005",
  CODEN =        "ANBEA8",
  DOI =          "https://doi.org/10.1016/j.anbehav.2004.09.002",
  ISSN =         "0003-3472 (print), 1095-8282 (electronic)",
  ISSN-L =       "0003-3472",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S000334720400346X",
  acknowledgement = ack-nhfb,
  fjournal =     "Animal Behaviour",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00033472",
  keywords =     "Zipf's Law",
}

@Article{Miller:2005:BLV,
  author =       "Steven J. Miller and A. Kontorovich",
  title =        "{Benford}'s law, values of {$L$}-functions and the $ 3
                 x + 1 $ problem",
  journal =      j-ACTA-ARITHMETICA,
  volume =       "120",
  number =       "3",
  pages =        "269--297",
  month =        "????",
  year =         "2005",
  CODEN =        "AARIA9",
  DOI =          "https://doi.org/10.4064/aa120-3-4",
  ISSN =         "0065-1036 (print), 1730-6264 (electronic)",
  ISSN-L =       "0065-1036",
  MRclass =      "11K06, 60A10, 11B83, 11M06 (60F05, 11J86, 60J65,
                 46F12)",
  bibdate =      "Tue Feb 26 06:11:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Arithmetica",
}

@InProceedings{Nagasaka:2005:BLD,
  author =       "Kenji Nagasaka",
  editor =       "G. Barat and H. Daud{\'e} and M. Laurent and P.
                 Liardet and S. Louboutin and A. Thomas",
  booktitle =    "{Journ{\'e}es Arithm{\'e}tiques XXIV, Marseilles, July
                 4--8, 2005, Universit{\'e} de Provence and
                 Universit{\'e} de la M{\'e}diterran{\'e}e and CNRS
                 Marseilles, France}",
  title =        "{Benford}'s law with different basis",
  publisher =    "????",
  address =      "????",
  pages =        "1--2",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 18:49:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://atlas-conferences.com/c/a/r/e/47.htm",
  acknowledgement = ack-nhfb,
}

@Article{Newman:2005:PLP,
  author =       "M. E. J. Newman",
  title =        "Power laws, {Pareto} distributions and {Zipf}'s law",
  journal =      j-CONTEMP-PHYS,
  volume =       "46",
  number =       "5",
  pages =        "323--351",
  month =        sep,
  year =         "2005",
  CODEN =        "CTPHAF",
  DOI =          "https://doi.org/10.1080/00107510500052444",
  ISSN =         "0010-7514 (print), 1366-5812 (electronic)",
  ISSN-L =       "0010-7514",
  bibdate =      "Thu Feb 18 20:07:22 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/contempphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "When the probability of measuring a particular value
                 of some quantity varies inversely as a power of that
                 value, the quantity is said to follow a power law, also
                 known variously as Zipf's law or the Pareto
                 distribution. Power laws appear widely in physics,
                 biology, earth and planetary sciences, economics and
                 finance, computer science, demography and the social
                 sciences. For instance, the distributions of the sizes
                 of cities, earthquakes, forest fires, solar flares,
                 moon craters and people's personal fortunes all appear
                 to follow power laws. The origin of power-law behaviour
                 has been a topic of debate in the scientific community
                 for more than a century. Here we review some of the
                 empirical evidence for the existence of power-law forms
                 and the theories proposed to explain them.",
  acknowledgement = ack-nhfb,
  fjournal =     "Contemporary Physics",
  journal-URL =  "http://www.tandfonline.com/loi/tcph20",
  keywords =     "Benford's Law; critical phenomena; Legendre beta
                 function; Pareto distribution; percolation; phase
                 transitions; power-law distributions; random walks;
                 Riemann zeta function; scale-free distributions; Yule
                 process; Zipf's Law",
  remark =       "This article is an excellent survey of continuous and
                 discrete distributions that follow a power law, and
                 some that do not. It is well worth reading.",
  subject =      "astrophysics; atomic and nuclear physics; chemical
                 physics; computational physics; condensed matter
                 physics; environmental physics; experimental physics;
                 general physics; particle and high energy physics;
                 plasma physics; space science; theoretical physics",
}

@Article{Nigrini:2005:ACI,
  author =       "Mark Nigrini",
  title =        "An assessment of the change in the incidence of
                 earnings management around the {Enron--Andersen}
                 episode",
  journal =      "Review of Accounting and Finance",
  volume =       "4",
  number =       "1",
  pages =        "92--110",
  month =        "????",
  year =         "2005",
  DOI =          "https://doi.org/10.1108/eb043420",
  ISSN =         "1475-7702 (print), 1758-7700 (electronic)",
  ISSN-L =       "1475-7702",
  bibdate =      "Fri Mar 22 09:08:37 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.emeraldinsight.com/journals.htm?issn=1475-7702&volume=4&issue=1&articleid=1657234",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Nitsch:2005:ZZ,
  author =       "Volker Nitsch",
  title =        "{Zipf} zipped",
  journal =      j-J-URBAN-ECON,
  volume =       "57",
  number =       "1",
  pages =        "86--100",
  day =          "15",
  month =        jan,
  year =         "2005",
  CODEN =        "JUECDW",
  DOI =          "https://doi.org/10.1016/j.jue.2004.09.002",
  ISSN =         "0094-1190 (print), 1095-9068 (electronic)",
  ISSN-L =       "0094-1190",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0094119004000981",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00941190",
  keywords =     "Zipf's Law",
}

@Article{Perline:2005:SWF,
  author =       "Richard Perline",
  title =        "Strong, weak and false inverse power laws",
  journal =      j-STAT-SCI,
  volume =       "20",
  number =       "1",
  pages =        "68--88",
  month =        "????",
  year =         "2005",
  CODEN =        "STSCEP",
  ISSN =         "0883-4237 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  bibdate =      "Fri Nov 18 12:15:56 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
  keywords =     "Benford's Law",
}

@Book{Posch:2005:ZTP,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse in Theorie und Praxis: Testverfahren
                 zur F{\"a}lschungsaufsp{\"u}rung mit Benfords Gesetz}",
  publisher =    "Shaker",
  address =      "Aachen, Germany",
  pages =        "iv + 87 + v",
  year =         "2005",
  ISBN =         "3-8322-4492-1",
  ISBN-13 =      "978-3-8322-4492-7",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 18:01:33 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.gbv.de:20011/gvk",
  price =        "EUR 29.80 (DE)",
  series =       "Berichte aus der Statistik",
  URL =          "http://www.gbv.de/dms/hbz/toc/ht014717371.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Rousseau:2005:RFE,
  author =       "Ronald Rousseau",
  title =        "{Robert Fairthorne} and the empirical power laws",
  journal =      j-J-DOC,
  volume =       "61",
  number =       "2",
  pages =        "194--202",
  month =        "????",
  year =         "2005",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/00220410510585188",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 06:42:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
  remark =       "Review of
                 \cite{Fairthorne:1969:PDE,Fairthorne:2005:PDE}.",
}

@Article{Rowlands:2005:EAD,
  author =       "Ian Rowlands",
  title =        "{Emerald} authorship data, {Lotka}'s law and research
                 productivity",
  journal =      j-ASLIB-PROC,
  volume =       "57",
  number =       "1",
  pages =        "5--10",
  month =        "????",
  year =         "2005",
  CODEN =        "ASLPAO",
  DOI =          "https://doi.org/10.1108/00012530510579039",
  ISSN =         "0001-253X (print), 1758-3748 (electronic)",
  ISSN-L =       "0001-253X",
  bibdate =      "Fri Nov 25 07:25:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ASLIB Proceedings",
  keywords =     "brand loyalty; publishing; research results",
  remark =       "This paper applies Lotka's Law to the question of the
                 likelihood of an author remaining with a particular
                 publisher.",
}

@Article{Schaefer:2005:AIF,
  author =       "Christin Schaefer and J{\"o}rg-Peter Schr{\"a}pler and
                 Klaus-Robert M{\"u}ller and Gert G. Wagner",
  title =        "Automatic Identification of Faked and Fraudulent
                 Interviews in the {German SOEP}",
  journal =      "Journal of Applied Social Science Studies",
  volume =       "125",
  number =       "??",
  pages =        "183--193",
  month =        "",
  year =         "2005",
  DOI =          "",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.diw.de/documents/publikationen/73/diw_01.c.42515.de/dp441.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; SOEP (German Socio-Economic Panel
                 Study)",
  remark =       "Cannot find online archive of this journal: Web links
                 to it are dead.",
}

@Article{Shan:2005:GZD,
  author =       "Shi Shan",
  title =        "On the generalized {Zipf} distribution. {Part I}",
  journal =      j-INFO-PROC-MAN,
  volume =       "41",
  number =       "6",
  pages =        "1369--1386",
  day =          "1",
  month =        dec,
  year =         "2005",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/j.ipm.2005.03.003",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S030645730500018X",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Zipf's Law",
}

@Article{Soo:2005:ZLC,
  author =       "Kwok Tong Soo",
  title =        "{Zipf's Law} for cities: a cross-country
                 investigation",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "35",
  number =       "3",
  pages =        "239--263",
  day =          "1",
  month =        may,
  year =         "2005",
  CODEN =        "RSUEDM",
  DOI =          "https://doi.org/10.1016/j.regsciurbeco.2004.04.004",
  ISSN =         "0166-0462 (print), 1879-2308 (electronic)",
  ISSN-L =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016604620400033X",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Article{Stadje:2005:APD,
  author =       "Wolfgang Stadje",
  title =        "Asymptotic properties of digit sequences of random
                 numbers",
  journal =      j-MATH-NACHR,
  volume =       "278",
  number =       "10",
  pages =        "1209--1229",
  month =        "????",
  year =         "2005",
  CODEN =        "MTMNAQ",
  DOI =          "https://doi.org/10.1002/mana.200310303",
  ISSN =         "0025-584X",
  ISSN-L =       "0025-584X",
  bibdate =      "Mon Feb 18 06:36:36 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1073.11053",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematische Nachrichten",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1522-2616",
  keywords =     "ergodicity; limit theorem; Markov chain; moments;
                 occurrence probability; random digit sequence;
                 stationary digits; transition function",
  ZMclass =      "11K31 (Special sequences); 60G10 (Stationary
                 processes); 60J05 (Discrete-time Markov processes on
                 general state spaces); 60F99 (Limit theorems
                 (probability))",
}

@TechReport{Taylor:2005:TMT,
  author =       "Jonathan Taylor",
  title =        "Too many ties? {An} empirical analysis of the
                 {Venezuelan} recall referendum counts",
  type =         "Technical report",
  number =       "??",
  institution =  "Department of Statistics, Stanford University",
  address =      "Stanford, CA 94305, USA",
  year =         "2005",
  bibdate =      "Fri Feb 15 18:29:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://esdata.info/pdf/Taylor-Ties.pdf;
                 http://www.benfordonline.net/fullreference/577",
  acknowledgement = ack-nhfb,
  remark =       "Cited in \cite{Pericchi:2011:QAD}, with ``Statist.
                 Sci. To appear 2009''. However, the article is not yet
                 found there in February 2013. This report was issued as
                 a result of the Carter Center's investigation of
                 fairness of 2004 voting in Venezuela. Its conclusion,
                 that there was no demonstrable electoral fraud, has
                 been challenged; see \cite{Pericchi:2011:QAD}.",
}

@Article{Twardy:2005:EDS,
  author =       "Charles Twardy and Steve Gardner and David L. Dowe",
  title =        "Empirical data sets are algorithmically compressible:
                 reply to {McAllister}?",
  journal =      j-STUD-HIST-PHILOS-SCI,
  volume =       "36",
  number =       "2",
  pages =        "391--402",
  month =        jun,
  year =         "2005",
  CODEN =        "SHPSB5",
  DOI =          "https://doi.org/10.1016/j.shpsa.2005.04.004",
  ISSN =         "0039-3681 (print), 1879-2510 (electronic)",
  ISSN-L =       "0039-3681",
  bibdate =      "Mon Nov 7 12:11:58 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/shps-a.bib;
                 http://www.sciencedirect.com/science/journal/00393681",
  note =         "See \cite{McAllister:2003:ARE,McAllister:2005:ACE}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S003936810500021X",
  acknowledgement = ack-nhfb,
  fjournal =     "Studies in History and Philosophy of Science Part A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00393681",
}

@Article{vanLeijenhorst:2005:FDH,
  author =       "D. C. van Leijenhorst and Th. P. van der Weide",
  title =        "A formal derivation of {Heaps}' law",
  journal =      j-INFO-SCI,
  volume =       "170",
  number =       "2--4",
  pages =        "263--272",
  year =         "2005",
  CODEN =        "ISIJBC",
  DOI =          "https://doi.org/10.1016/j.ins.2004.03.006",
  ISSN =         "0020-0255 (print), 1872-6291 (electronic)",
  ISSN-L =       "0020-0255",
  MRclass =      "60C05",
  MRnumber =     "2120894 (2005h:60024)",
  bibdate =      "Sat Nov 12 10:28:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Word frequencies in text documents can be reasonably
                 described by the Mandelbrot distribution, which has
                 Zipf's law as a special case. Furthermore, the growth
                 of vocabulary size as a function of the text size (its
                 number of words) has been described in Heaps' law. It
                 has been shown that these two experimental laws are
                 related. In this paper we go a step further, and
                 provide a (formal) derivation of Heaps' law from the
                 Mandelbrot distribution. We also provide a
                 specification of the validity area for applying Heaps'
                 law.",
  acknowledgement = ack-nhfb,
  ajournal =     "Inform. Sci.",
  fjournal =     "Information Sciences. An International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200255",
}

@Book{Wells:2005:PNM,
  author =       "D. G. (David G.) Wells",
  title =        "Prime Numbers: the Most Mysterious Figures in Math",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xv + 272",
  year =         "2005",
  ISBN =         "0-471-46234-9 (hardcover), 0-471-71892-0 (ebook)",
  ISBN-13 =      "978-0-471-46234-7 (hardcover), 978-0-471-71892-5
                 (e-book)",
  LCCN =         "QA246 .W35 2005",
  bibdate =      "Wed Feb 21 14:25:53 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/u/ulam-stanislaw-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0616/2004019974-b.html;
                 http://www.loc.gov/catdir/enhancements/fy0616/2004019974-d.html;
                 http://www.loc.gov/catdir/toc/ecip0422/2004019974.html",
  abstract =     "A fascinating journey into the mind-bending world of
                 prime numbers Cicadas of the genus Magicicada appear
                 once every 7, 13, or 17 years. Is it just a coincidence
                 that these are all prime numbers? How do twin primes
                 differ from cousin primes, and what on earth (or in the
                 mind of a mathematician) could be sexy about prime
                 numbers? What did Albert Wilansky find so fascinating
                 about his brother-in-law's phone number? Mathematicians
                 have been asking questions about prime numbers for more
                 than twenty-five centuries, and every answer seems to
                 generate a new rash of questions. In Prime Numbers: The
                 Most Mysterious Figures in Math, you'll meet the
                 world's most gifted mathematicians, from Pythagoras and
                 Euclid to Fermat, Gauss, and Erd{\H{o}}s, and you'll
                 discover a host of unique insights and inventive
                 conjectures that have both enlarged our understanding
                 and deepened the mystique of prime numbers. This
                 comprehensive, A-to-Z guide covers everything you ever
                 wanted to know-and much more that you never
                 suspected-about prime numbers, including: the unproven
                 Riemann hypothesis and the power of the zeta function,
                 the ``Primes is in P'' algorithm, the sieve of
                 Eratosthenes of Cyrene, Fermat and Fibonacci numbers,
                 the Great Internet Mersenne Prime Search, and much,
                 much more.",
  acknowledgement = ack-nhfb,
  libnote =      "Not yet in my library.",
  tableofcontents = "Introduction \\
                 List of Entries \\
                 abc conjecture \\
                 abundant number \\
                 AKS algorithm for primality testing \\
                 aliquot sequences (sociable chains) \\
                 almost-primes \\
                 amicable numbers \\
                 amicable curiosities \\
                 Andrica's conjecture \\
                 arithmetic progressions, of primes \\
                 Aurifeuillian factorization \\
                 average prime \\
                 Bang's theorem \\
                 Bateman's conjecture \\
                 Beal's conjecture, and prize \\
                 Benford's law \\
                 Bernoulli numbers \\
                 Bernoulli number curiosities \\
                 Bertrand's postulate \\
                 Bonse's inequality \\
                 Brier numbers \\
                 Brocard's conjecture \\
                 Brun's constant \\
                 Buss's function \\
                 Carmichael numbers \\
                 Catalan's conjecture \\
                 Catalan's Mersenne conjecture \\
                 Champion numbers \\
                 Chinese remainder theorem \\
                 cicadas and prime periods \\
                 circle, prime \\
                 circular prime \\
                 Clay prizes, the \\
                 compositorial \\
                 concatenation of primes \\
                 conjectures \\
                 consecutive integer sequence \\
                 consecutive numbers \\
                 consecutive primes, sums of \\
                 Conway's prime-producing machine \\
                 cousin primes \\
                 Cullen primes \\
                 Cunningham project \\
                 Cunningham chains \\
                 decimals, recurring (periodic) \\
                 deficient number \\
                 deletable and truncatable primes \\
                 Demlo numbers \\
                 descriptive primes \\
                 Dickson's conjecture \\
                 digit properties \\
                 Diophantus (c.200: died 284) \\
                 Dirichlet's theorem and primes in arithmetic series \\
                 distributed computing \\
                 divisibility tests \\
                 divisors (factors) \\
                 economical numbers \\
                 Electronic Frontier Foundation \\
                 elliptic curve primality proving \\
                 emirp \\
                 Eratosthenes of Cyrene, the sieve of \\
                 Erd{\H{o}}s, Paul (1913--1996) \\
                 errors \\
                 Euclid \\
                 Unique factorisation \\
                 $\sqrt{2}$ is irrational \\
                 Euclid and the infinity of primes \\
                 Consecutive composite numbers \\
                 Primes of the form $4 n + 3$ \\
                 A recursive sequence \\
                 Euclid and the first perfect number \\
                 Euclidean algorithm \\
                 Euler, Leonhard (1707--1783) \\
                 Euler's convenient numbers \\
                 The Basel problem \\
                 Euler's constant \\
                 Euler and the reciprocals of the primes \\
                 Euler's phi [totient] function \\
                 Carmichael's totient function conjecture \\
                 Curiosities of $\phi(n)$ \\
                 Euler's quadratic \\
                 The Lucky Numbers of Euler \\
                 factorial \\
                 factors of factorials \\
                 factorial primes \\
                 factorial sums \\
                 factorials, double, triple, \ldots{} \\
                 factorization, methods of \\
                 factors of particular forms \\
                 Fermat's algorithm \\
                 Legendre's method \\
                 How difficult is it to factor large numbers? \\
                 quantum computation \\
                 Feit--Thompson conjecture \\
                 Fermat Pierre de (1607--1665) \\
                 Fermat's Little Theorem \\
                 Fermat quotient \\
                 Fermat and primes of the form $x^2 + y^2$ \\
                 Fermat's conjecture, Fermat numbers and Fermat primes
                 \\
                 Fermat factorisation, from $F_6$ to $F_{30}$ \\
                 Generalized Fermat numbers \\
                 Fermat's Last Theorem \\
                 The first case of Fermat's Last Theorem: \\
                 Wall--Sun--Sun primes \\
                 Fermat--Catalan equation and conjecture \\
                 Fibonacci numbers \\
                 divisibility properties \\
                 Fibonacci curiosities \\
                 {\'E}douard Lucas and the Fibonacci numbers \\
                 Fibonacci composite sequences \\
                 formulae for primes \\
                 Fortunate numbers and Fortune's conjecture \\
                 gaps between primes, and composite runs \\
                 Gauss Johann Carl Friedrich (1777--1855) \\
                 Gauss and the distribution of primes \\
                 Gaussian primes \\
                 Gauss's circle problem \\
                 Gilbreath conjecture \\
                 GIMPS = Great Internet Mersenne Primes Search \\
                 Giuga's conjecture \\
                 Giuga numbers \\
                 Goldbach's conjecture \\
                 good primes \\
                 graph, prime number \\
                 Grimm's problem \\
                 Hardy, G. H. (1877--1947) \\
                 Hardy--Littlewood conjectures \\
                 heuristic reasoning \\
                 Hilbert's 23 problems \\
                 home prime \\
                 hypothesis H \\
                 illegal prime \\
                 inconsummate number \\
                 induction jumping champion \\
                 $k$-tuples conjecture, prime \\
                 knots, prime and composite \\
                 Landau, Edmund (1877--1938) \\
                 left-truncatable prime \\
                 Legendre A. M. (1752--1833) \\
                 Legendre's theorem (1808) \\
                 Lehmer, Derrick Norman (1867--1938) \\
                 Lehmer, Derrick Henry (1905--1991) \\
                 Linnik's constant \\
                 Liouville, Joseph (1809--1882) \\
                 Littlewood's theorem \\
                 the prime numbers race \\
                 Look and Say sequence \\
                 Lucas, {\'E}douard (1842--1891) \\
                 the Lucas sequence \\
                 primality testing \\
                 Lucas's game of calculation \\
                 the Lucas--Lehmer test \\
                 lucky numbers \\
                 the number of Lucky numbers and primes \\
                 `random' primes' \\
                 magic squares \\
                 Matijasevic and Hilbert's 10th problem \\
                 Mersenne numbers and Mersenne primes \\
                 Mersenne numbers \\
                 hunting for Mersenne primes \\
                 the coming of electronic computers \\
                 Mersenne prime conjectures \\
                 the New Mersenne Conjecture \\
                 how many Mersenne primes? \\
                 Eberhart's conjecture \\
                 factors of Mersenne Numbers \\
                 Lucas--Lehmer test for Mersenne primes \\
                 Mertens' theorem \\
                 Mertens' constant \\
                 Mill's theorem \\
                 Wright's theorem \\
                 mixed bag \\
                 multiplication, fast \\
                 Niven Numbers \\
                 odd numbers as $p + 2 a^2$ \\
                 Opperman's conjecture \\
                 palindromic primes \\
                 pandigital primes \\
                 Pascal's Triangle and the binomial coefficients \\
                 Pascal's triangle and Sierpinski's gasket \\
                 Pascal triangle curiosities \\
                 patents on prime numbers \\
                 P{\'e}pin's test for Fermat numbers \\
                 perfect numbers \\
                 odd perfect numbers \\
                 perfect, multiply \\
                 permutable primes \\
                 $o$, primes in the decimal expansion of \\
                 Pocklington's theorem \\
                 Polignac's conjectures \\
                 Polignac or obstinate numbers \\
                 powerful numbers \\
                 consecutive powerful numbers \\
                 primality testing \\
                 probabilistic methods \\
                 prime number graph \\
                 prime number theorem and the prime counting function
                 \\
                 history \\
                 elementary proof \\
                 record calculations \\
                 estimating $p(n)$ \\
                 calculating $p(n)$ \\
                 a curiosity \\
                 prime pretender \\
                 primitive prime factor \\
                 primitive roots \\
                 Artin's conjecture \\
                 a curiosity \\
                 primorial \\
                 primorial primes \\
                 Proth's Theorem \\
                 pseudoperfect numbers \\
                 bases and pseudpoprimes \\
                 pseudoprimes, strong \\
                 public key encryption \\
                 pyramid, prime \\
                 Pythagorean triangles, prime \\
                 quadratic residues \\
                 residual curiosities \\
                 polynomial congruences \\
                 quadratic reciprocity, law of \\
                 Euler's criterion \\
                 Ramanujan, Srinivasa (1887--1920) \\
                 Highly Composite Numbers \\
                 randomness, of primes \\
                 Von Sternach and a prime random walk \\
                 record primes \\
                 some records \\
                 repunits, prime \\
                 Rhonda numbers \\
                 Riemann hypothesis \\
                 Farey sequence and Riemann's Hypothesis \\
                 Riemann's hypothesis and $\sigma(n)$, the sum of
                 divisor function \\
                 squarefree and blue and red numbers \\
                 the Mertens conjecture \\
                 Riemann Hypothesis curiosities \\
                 Riesel number \\
                 right-truncatable prime \\
                 RSA algorithm \\
                 Martin Gardner's challenge \\
                 RSA Factoring Challenge, The New \\
                 Ruth--Aaron numbers \\
                 Scherk's conjecture \\
                 semi-primes \\
                 sexy primes \\
                 Shank's Conjecture \\
                 Siamese primes \\
                 Sierpinski numbers \\
                 Sierpinski strings \\
                 Sierpinski's quadratic \\
                 Sierpinski's $\phi(n)$ conjecture \\
                 Sloane's On-Line Encyclopedia of Integer Sequences \\
                 Smith numbers \\
                 Smith Brothers \\
                 smooth numbers \\
                 Sophie Germain primes \\
                 safe primes \\
                 square-free numbers \\
                 Stern prime \\
                 strong law of small numbers \\
                 triangular numbers \\
                 trivia \\
                 twin primes \\
                 twin curiosities \\
                 Ulam spiral \\
                 unitary divisors \\
                 unitary perfect \\
                 untouchable numbers \\
                 weird numbers \\
                 Wieferich primes \\
                 Wilson's theorem \\
                 twin primes \\
                 Wilson's quotient \\
                 Wilson primes \\
                 Wolstenholme's numbers, and theorems \\
                 more factors of Wolstenholme numbers \\
                 Woodall primes \\
                 zeta mysteries: the quantum connection \\
                 Appendix A: The First 500 Primes \\
                 Appendix B: Arithmetic Functions \\
                 Glossary \\
                 Bibliography \\
                 Index",
}

@Article{Aban:2006:PET,
  author =       "Inmaculada B. Aban and Mark M. Meerschaert and Anna K.
                 Panorska",
  title =        "Parameter Estimation for the Truncated {Pareto}
                 Distribution",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "101",
  number =       "473",
  pages =        "270--277",
  month =        mar,
  year =         "2006",
  CODEN =        "JSTNAL",
  DOI =          "https://doi.org/10.1198/016214505000000411",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Thu Aug 26 11:26:31 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/jasa/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
}

@Article{Baskerville:2006:SEM,
  author =       "Kim Baskerville and Maya Paczuski",
  title =        "Subgraph ensembles and motif discovery using an
                 alternative heuristic for graph isomorphism",
  journal =      j-PHYS-REV-E,
  volume =       "74",
  number =       "??",
  pages =        "051903",
  day =          "3",
  month =        nov,
  year =         "2006",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.74.051903",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.74.051903",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Bohachevsky:2006:DBL,
  author =       "Ihor O. Bohachevsky and Mark E. Johnson and Myron L.
                 Stein",
  title =        "A derivation of {Benford}'s law",
  journal =      j-AM-J-MATH-MANAGE-SCI,
  volume =       "26",
  number =       "3--4",
  pages =        "355--370",
  year =         "2006",
  CODEN =        "AMMSDX",
  ISSN =         "0196-6324",
  ISSN-L =       "0196-6324",
  MRclass =      "60E99 (11K36)",
  MRnumber =     "2312400 (2008h:60062)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Journal of Mathematical and Management
                 Sciences",
}

@Article{Briscoe:2006:MLW,
  author =       "Bob Briscoe and Andrew Odlyzko and Benjamin Tilly",
  title =        "{Metcalfe's Law} is wrong --- communications networks
                 increase in value as they add members --- but by how
                 much?",
  journal =      j-IEEE-SPECTRUM,
  volume =       "43",
  number =       "7",
  pages =        "34--39",
  month =        jul,
  year =         "2006",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.2006.1653003",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Sat Jan 18 12:29:46 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeespectrum2000.bib",
  abstract =     "This paper argues that Metcalfe's law, which states
                 that the value of a communications network is
                 proportional to the square of the number of its users,
                 is incorrect. By seeming to assure that the value of a
                 network would increase quadratically - proportionately
                 to the square of the number of its participants - while
                 costs would, at most, grow linearly, Metcalfe's law
                 gave an air of credibility to the mad rush for growth
                 and the neglect of profitability. The paper discusses
                 the fundamental flaw of Metcalfe's law and describes
                 how Zipf's law can be used as basis to justify the $ n
                 \log (n) $ rule-of-thumb valuation of a general
                 communications network of size $n$.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  keywords =     "Communication networks; communications network;
                 Computer networks; Costs; Ethernet networks; Internet;
                 Internet telephony; Investments; IP networks; Metcalfe
                 Law; Profitability; profitability; rule-of-thumb
                 valuation; Web pages; Web sites; Zipf law",
}

@InProceedings{Dallacasa:2006:TBS,
  author =       "F. Dallacasa and Valerio Dallacasa",
  editor =       "????",
  booktitle =    "{5th International Conference: APLIMAT 2006, Slovak
                 University of Technology, Bratislava}",
  title =        "Temporal behaviour of stock data from {Benford}'s
                 law",
  publisher =    "????",
  address =      "????",
  pages =        "425--432",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 17:32:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  price =        "US\$",
  URL =          "http://archiv.aplimat.com/2006/Aplimat/Proceedings/Communications/Financial_Actuary_math/Dallasca-Dallasca.pdf",
  acknowledgement = ack-nhfb,
}

@Article{deMarchi:2006:AAS,
  author =       "Scott de Marchi and James Hamilton",
  title =        "Assessing the Accuracy of Self-Reported Data: an
                 Evaluation of the Toxics Release Inventory",
  journal =      j-J-RISK-UNCERT,
  volume =       "32",
  number =       "1",
  pages =        "57--76",
  month =        jan,
  year =         "2006",
  CODEN =        "JRUNEN",
  DOI =          "https://doi.org/10.1007/s10797-006-6666-3",
  ISSN =         "0895-5646 (print), 1573-0476 (electronic)",
  ISSN-L =       "0895-5646",
  bibdate =      "Fri Nov 25 11:25:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Risk and Uncertainty",
  journal-URL =  "http://link.springer.com/journal/11166",
}

@Article{Dorogovtsev:2006:FON,
  author =       "S. N. Dorogovtsev and J. F. F. Mendes and J. G.
                 Oliveira",
  title =        "Frequency of occurrence of numbers in the {World Wide
                 Web}",
  journal =      j-PHYSICA-A,
  volume =       "360",
  number =       "2",
  pages =        "548--556",
  month =        feb,
  year =         "2006",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2005.06.064",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://arxiv.org/abs/physics/0504185;
                 http://www.sciencedirect.com/science/article/pii/S0378437105006874",
  abstract =     "The distribution of numbers in human documents is
                 determined by a variety of diverse natural and human
                 factors, whose relative significance can be evaluated
                 by studying the numbers frequency of occurrence.
                 Although it has been studied since the 1880's, this
                 subject remains poorly understood. Here, we obtain the
                 detailed statistics of numbers in the World Wide Web,
                 finding that their distribution is a heavy-tailed
                 dependence which splits in a set of power-law ones. In
                 particular, we find that the frequency of numbers
                 associated to western calendar years shows an uneven
                 behavior: 2004 represents a singular critical point,
                 appearing with a strikingly high frequency; as we move
                 away from it, the decreasing frequency allows us to
                 compare the amounts of existing information on the past
                 and on the future. Moreover, while powers of ten occur
                 extremely often, allowing us to obtain statistics up to
                 the huge 10 127, non-round numbers occur in a much more
                 limited range, the variations of their frequencies
                 being dramatically different from standard statistical
                 fluctuations. These findings provide a view of the
                 array of numbers used by humans as a highly
                 non-equilibrium and inhomogeneous system, and shed a
                 new light on an issue that, once fully investigated,
                 could lead to a better understanding of many
                 sociological and psychological phenomena.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Critical point; Fluctuations; Power-law
                 distributions; Search engines; Statistics of natural
                 numbers; The World Wide Web",
}

@Article{Duranton:2006:SFZ,
  author =       "Gilles Duranton",
  title =        "Some foundations for {Zipf}'s law: Product
                 proliferation and local spillovers",
  journal =      j-REG-SCI-URBAN-ECON,
  volume =       "36",
  number =       "4",
  pages =        "542--563",
  day =          "1",
  month =        jul,
  year =         "2006",
  CODEN =        "RSUEDM",
  DOI =          "https://doi.org/10.1016/j.regsciurbeco.2006.03.008",
  ISSN =         "0166-0462 (print), 1879-2308 (electronic)",
  ISSN-L =       "0166-0462",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0166046206000354",
  acknowledgement = ack-nhfb,
  fjournal =     "Regional Science and Urban Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01660462",
  keywords =     "Zipf's Law",
}

@Article{Egghe:2006:DHL,
  author =       "L. Egghe",
  title =        "The dependence of the height of a {Lorenz} curve of a
                 {Zipf} function on the size of the system",
  journal =      j-MATH-COMP-MODELLING,
  volume =       "43",
  number =       "7--8",
  pages =        "870--879",
  day =          "15",
  month =        apr,
  year =         "2006",
  CODEN =        "MCMOEG",
  DOI =          "https://doi.org/10.1016/j.mcm.2005.09.033",
  ISSN =         "0895-7177 (print), 1872-9479 (electronic)",
  ISSN-L =       "0895-7177",
  MRclass =      "94A15 (91B82)",
  MRnumber =     "2218323 (2006k:94033)",
  MRreviewer =   "Ulrich Tamm",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S089571770500508X",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical and Computer Modelling",
  keywords =     "Zipf's Law",
}

@Article{Gaite:2006:CSZ,
  author =       "Jos{\'e} Gaite",
  title =        "Cut-out sets and the {Zipf} law for fractal voids",
  journal =      j-PHYSICA-D,
  volume =       "223",
  number =       "2",
  pages =        "248--255",
  day =          "15",
  month =        nov,
  year =         "2006",
  CODEN =        "PDNPDT",
  DOI =          "https://doi.org/10.1016/j.physd.2006.09.021",
  ISSN =         "0167-2789 (print), 1872-8022 (electronic)",
  ISSN-L =       "0167-2789",
  MRclass =      "28A80",
  MRnumber =     "2307212",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167278906003848",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica. D, Nonlinear phenomena",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01672789",
  keywords =     "Zipf's Law",
}

@Article{Gan:2006:ZLS,
  author =       "Li Gan and Dong Li and Shunfeng Song",
  title =        "Is the {Zipf} law spurious in explaining city-size
                 distributions?",
  journal =      j-ECONOM-LETT,
  volume =       "92",
  number =       "2",
  pages =        "256--262",
  day =          "1",
  month =        aug,
  year =         "2006",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/j.econlet.2006.03.004",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176506000772",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Handurukande:2006:PSB,
  author =       "S. B. Handurukande and A.-M. Kermarrec and F. {Le
                 Fessant} and L. Massouli{\'e} and S. Patarin",
  title =        "Peer sharing behaviour in the {eDonkey} network, and
                 implications for the design of server-less file sharing
                 systems",
  journal =      j-OPER-SYS-REV,
  volume =       "40",
  number =       "4",
  pages =        "359--371",
  month =        oct,
  year =         "2006",
  CODEN =        "OSRED8",
  DOI =          "https://doi.org/10.1145/1218063.1217970",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Fri Jun 20 17:14:10 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this paper we present an empirical study of a
                 workload gathered by crawling the eDonkey network --- a
                 dominant peer-to-peer file sharing system --- for over
                 50 days. We first confirm the presence of some known
                 features, in particular the prevalence of free-riding
                 and the Zipf-like distribution of file popularity. We
                 also analyze the evolution of document popularity. We
                 then provide an in-depth analysis of several clustering
                 properties of such workloads. We measure the
                 geographical clustering of peers offering a given file.
                 We find that most files are offered mostly by peers of
                 a single country, although popular files don't have
                 such a clear home country. We then analyze the overlap
                 between contents offered by different peers. We find
                 that peer contents are highly clustered according to
                 several metrics of interest. We propose to leverage
                 this property by allowing peers to search for content
                 without server support, by querying suitably identified
                 semantic neighbours. We find via trace-driven
                 simulations that this approach is generally effective,
                 and is even more effective for rare files. If we
                 further allow peers to query both their semantic
                 neighbours, and in turn their neighbours' neighbours,
                 we attain hit rates as high as over 55\% for neighbour
                 lists of size 20.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J597",
  keywords =     "file sharing; peer-to-peer; simulation; trace",
}

@InCollection{Harremoes:2006:ZLH,
  author =       "P. Harremo{\"e}s and F. Topsoe",
  editor =       "Rudolf Ahlswede and others",
  booktitle =    "General theory of information transfer and
                 combinatorics",
  title =        "{Zipf}'s law, hyperbolic distributions and entropy
                 loss",
  volume =       "4123",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "788--792",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11889342_50",
  bibdate =      "Sat Nov 12 11:15:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  ZMnumber =     "1158.91481",
  abstract =     "Zipf's law --- or Estoup-Zipf's law --- is an
                 empirical fact of computational linguistics which
                 relates rank and frequency of words in natural
                 languages. The law suggests modelling by distributions
                 of ``hyperbolic type''. We present a satisfactory
                 general definition and an information-theoretical
                 characterization of the resulting hyperbolic
                 distributions. When applied to linguistics this leads
                 to a property of stability and flexibility, explaining
                 that a language can develop towards higher and higher
                 expressive powers without changing its basic
                 structure.",
  acknowledgement = ack-nhfb,
  classmath =    "91F20 (Linguistics) 94A15 (General topics of
                 information theory) 94A17 (Measures of information)",
  keywords =     "entropy loss; hyperbolic distributions; Zipf's law",
}

@Article{Horn:2006:DSA,
  author =       "B. Horn and M. Kreuzer and E. Kochs and G. Schneider",
  title =        "Different States of Anesthesia Can Be Detected by
                 {Benford's Law}",
  journal =      "Journal of Neurosurgical Anesthesiology",
  volume =       "18",
  number =       "4",
  pages =        "328--329",
  month =        oct,
  year =         "2006",
  ISSN =         "0898-4921 (print), 1537-1921 (electronic)",
  ISSN-L =       "0898-4921",
  bibdate =      "Sat Sep 10 12:15:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Neurosurgical Anesthesiology",
  journal-URL =  "http://www.edmgr.com/JNA/;
                 http://journals.lww.com/jnsa/pages/default.aspx",
  keywords =     "Benford's Law",
}

@TechReport{Humenberger:2006:BGV,
  author =       "Hans Humenberger",
  title =        "{Das ,,Benford-Gesetz'' {\"u}ber die Verteilung der
                 ersten Ziffer von Zahn}. ({German}) [{Benford}'s Law on
                 the distribution of the first digit of numbers]",
  type =         "Report",
  institution =  "Institut f{\"u}r Mathematik und Angewandte Statistik,
                 Universit{\"a}t f{\"u}r Bodenkultur",
  address =      "Gregor Mendel-Stra{\ss}e 33, A-1180, Wien, Austria",
  month =        aug,
  year =         "2006",
  bibdate =      "Sun Feb 17 09:37:40 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.mathematik.uni-kassel.de/didaktik/HomePersonal/fischer/StochScan/1996-3_Hum.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@TechReport{Hurlimann:2006:BLB,
  author =       "Werner H{\"u}rlimann",
  title =        "{Benford's Law} from 1881 to 2006: a bibliography",
  type =         "Report",
  address =      "Feldstrasse 145, CH-8004 Z{\"u}rich, Switzerland",
  pages =        "15",
  day =          "5",
  month =        jul,
  year =         "2006",
  bibdate =      "Fri Mar 30 11:32:30 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/pdf/math.ST/0607168",
  abstract =     "On the occasion of the 125-th anniversary of Newcomb's
                 paper, a bibliography of academic work related to
                 Benford's law from its year of origin 1881 to 2006 has
                 been compiled.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Law of Anomalous Numbers; Zipf's Law",
  remark =       "This bibliography lists 325 references on the title
                 subject, with these (years) and counts: (1881) 1,
                 (1912) 1, (1916) 1, (1917) 1, (1936) 1, (1938) 1,
                 (1944) 1, (1945) 1, (1948) 2, (1950) 1, (1952) 1,
                 (1953) 1, (1954) 1, (1957) 3, (1960) 1, (1961) 2,
                 (1963) 1, (1964) 2, (1965) 2, (1966) 1, (1967) 1,
                 (1968) 2, (1969) 5, (1970) 1, (1971) 4, (1972) 2,
                 (1973) 7, (1974) 2, (1975) 1, (1976) 5, (1977) 3,
                 (1978) 3, (1979) 2, (1981) 6, (1982) 3, (1983) 4,
                 (1984) 7, (1985) 2, (1986) 7, (1987) 5, (1988) 1,
                 (1988) 5, (1989) 2, (1990) 1, (1991) 4, (1992) 6,
                 (1993) 5, (1994) 5, (1995) 1, (1995) 2, (1996) 4,
                 (1997) 1, (1997) 9, (1998) 1, (1998) 6, (1999) 12,
                 (2000) 10, (2001) 19, (2002) 30, (2003) 22, (2004) 29,
                 (2005) 34, (2006) 18.",
}

@Article{Hurlimann:2006:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      "ArXiv Mathematics e-prints",
  month =        jul,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......7166H",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607166",
  keywords =     "Mathematics - Statistics, Mathematics - Number Theory,
                 11B73, 11B83, 11K31, 62E15, 62E17",
}

@Article{Izsak:2006:MLE,
  author =       "F. Izs{\'a}k",
  title =        "Maximum likelihood estimation for constrained
                 parameters of multinomial distributions --- Application
                 to {Zipf--Mandelbrot} models",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "51",
  number =       "3",
  pages =        "1575--1583",
  day =          "1",
  month =        dec,
  year =         "2006",
  CODEN =        "CSDADW",
  DOI =          "https://doi.org/10.1016/j.csda.2006.05.008",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  MRnumber =     "2307527",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016794730600154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
  keywords =     "Zipf's Law",
}

@TechReport{Judge:2006:DPS,
  author =       "George Judge and Laura Schechter",
  title =        "Detecting problems in survey data using {Benford}'s
                 law",
  type =         "Preprint",
  institution =  "University of California at Berkeley and University of
                 Wisconsin at Madison",
  address =      "Berkeley, CA, USA and Madison, WI, USA",
  pages =        "30",
  day =          "1",
  month =        nov,
  year =         "2006",
  bibdate =      "Sat Feb 16 18:12:29 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.aae.wisc.edu/lschechter/benford.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kossovsky:2006:TBU,
  author =       "Alex Ely Kossovsky",
  title =        "Towards a Better Understanding of the Leading Digits
                 Phenomena",
  journal =      "ArXiv Mathematics e-prints",
  year =         "2006",
  bibdate =      "Mon Nov 21 06:46:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/math/0612627",
  abstract =     "This article on leading digits (Benford's Law)
                 contains the following: (i) An attempt at a
                 comprehensive account on the leading digits phenomena,
                 incorporating many of its existing explanations,
                 proofs, and differing points of view. (ii) The finding
                 that leading digits of random numbers derived from a
                 chain of distributions that are linked via parameter
                 selection are logarithmic in the limit as the number of
                 sequences approaches infinity, and that empirically
                 only around 5 or 6 sequences of such a distribution
                 chain are needed to obtain results that are close
                 enough to the logarithmic (i.e., rapid convergence).
                 (iii) An outright exact logarithmic behavior for a
                 2-sequence chain whenever parametrical density is
                 exactly logarithmic. (iv) An account on the existence
                 of singularities in exponential growth rates with
                 regards to the leading digits distributions of their
                 series. (v) An account on several distributions that
                 are intrinsically logarithmic or approximately so. (vi)
                 A conceptual justification of Flehinger's iterated
                 averaging scheme --- an algorithm that was presented
                 without any clear motivation. (vii) A note on the close
                 relationship of Flehinger's scheme and the chain of
                 distribution to Hill's super distribution. (viii) A
                 conceptual argument justifying the scale invariance
                 principle --- a principle invoked in derivations of
                 Benford's law. (ix) A note on the intimate connection
                 between one-sided tail to the right in density
                 distributions and logarithmic leading digit behavior.",
  acknowledgement = ack-nhfb,
  remark =       "On 18 February 2013, the archive has 17 revisions of
                 this article.",
  xxjournal =    "CoRR",
}

@Article{Kristiansen:2006:BTZ,
  author =       "K. de Lange Kristiansen and G. Helgesen and A. T.
                 Skjeltorp",
  title =        "Braid theory and {Zipf--Mandelbrot} relation used in
                 microparticle dynamics",
  journal =      j-EUR-PHYS-J-B,
  volume =       "51",
  number =       "3",
  pages =        "363--371",
  month =        jun,
  year =         "2006",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1140/epjb/e2006-00241-7",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Sat Sep 8 18:31:14 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
}

@Book{Kuipers:2006:UDS,
  author =       "Lauwerens Kuipers and Harald Niederreiter",
  title =        "Uniform distribution of sequences",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xviii + 390",
  year =         "2006",
  ISBN =         "0-486-45019-8 (paperback)",
  ISBN-13 =      "978-0-486-45019-3 (paperback)",
  LCCN =         "QA292 .K84 2006",
  bibdate =      "Sat Nov 12 15:42:53 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0625/2005056064-d.html;
                 http://www.loc.gov/catdir/toc/fy0612/2005056064.html",
  acknowledgement = ack-nhfb,
  remark =       "Originally published in \cite{Kuipers:1974:UDS}.",
  subject =      "Sequences (Mathematics); Uniform distribution
                 (Probability theory)",
}

@Article{Kulikova:2006:HFD,
  author =       "A. A. Kulikova and Yu. V. Prokhorov and V. I.
                 Khokhlov",
  title =        "{H.F.D.} ({$H$}-function Distribution) and {Benford's
                 Law}. {I}",
  journal =      j-THEORY-PROBAB-APPL,
  volume =       "50",
  number =       "2",
  pages =        "311--315",
  month =        jan,
  year =         "2006",
  CODEN =        "TPRBAU",
  DOI =          "https://doi.org/10.1137/S0040585X97981706",
  ISSN =         "0040-585X (print), 1095-7219 (electronic)",
  ISSN-L =       "0040-585X",
  bibdate =      "Wed May 19 18:14:51 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/TVP/50/2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://epubs.siam.org/tvp/resource/1/tprbau/v50/i2/p311_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of probability and its applications",
  journal-URL =  "http://epubs.siam.org/tvp",
}

@Article{Lagarias:2006:BLF,
  author =       "Jeffrey C. Lagarias and K. Soundararajan",
  title =        "{Benford}'s law for the $ 3 x + 1 $ function",
  journal =      "J. London Math. Soc. (2)",
  volume =       "74",
  number =       "2",
  pages =        "289--303",
  year =         "2006",
  CODEN =        "JLMSAK",
  DOI =          "https://doi.org/10.1112/S0024610706023131",
  ISSN =         "0024-6107 (print), 1469-7750 (electronic)",
  ISSN-L =       "0024-6107",
  MRclass =      "37A45",
  MRnumber =     "2269630 (2007h:37007)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the London Mathematical Society. Second
                 Series",
}

@Article{Leinicke:2006:FFN,
  author =       "Linda M. Leinicke and Joyce A. Ostrosky and W. Max
                 Rexroad",
  title =        "Fighting fraud by the numbers: Digital analysis
                 primer",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2006",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:13:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294967620",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
  keywords =     "Benford's Law",
}

@Article{Leydesdorff:2006:CPL,
  author =       "Loet Leydesdorff and Stephen Bensman",
  title =        "Classification and power laws: the logarithmic
                 transformation",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "57",
  number =       "11",
  pages =        "1470--1486",
  month =        sep,
  year =         "2006",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20467",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Sat Feb 16 18:31:04 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  keywords =     "Benford's Law",
}

@Article{Lim:2006:BRB,
  author =       "Nena Lim",
  title =        "Book Review: {{\booktitle{The new forensics:
                 investigating corporate fraud and the theft of
                 intellectual property}}, J. Anastasi. John Wiley \&
                 Sons, New Jersey (2003)}",
  journal =      "Digital Investigation",
  volume =       "3",
  number =       "4",
  pages =        "245--246",
  year =         "2006",
  DOI =          "https://doi.org/10.1016/j.diin.2006.10.002",
  ISSN =         "1742-2876 (print), 1873-202X (electronic)",
  ISSN-L =       "1742-2876",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S174228760600106X",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InCollection{Lu:2006:AFD,
  author =       "Fletcher Lu and J. Efrim Boritz and Dominic Covvey",
  booktitle =    "Advances in artificial intelligence",
  title =        "Adaptive fraud detection using {Benford}'s law",
  volume =       "4013",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "347--358",
  year =         "2006",
  DOI =          "https://doi.org/10.1007/11766247_30",
  MRnumber =     "2280590",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InProceedings{Lu:2006:BCF,
  author =       "F. Lu and J. E. Boritz",
  editor =       "????",
  booktitle =    "{Uncertainty in Artificial Intelligence: Proceedings
                 of the 22nd Conference}",
  title =        "Building a case for fraud using {Benford}'s law with
                 reinforcement learning",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  bibdate =      "Sat Feb 16 18:34:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Manaris:2006:IES,
  author =       "Bill Manaris and Luca Pellicoro and George Pothering
                 and Harland Hodges",
  editor =       "????",
  booktitle =    "{2006 IASTED International Conference on Artificial
                 Intelligence and Applications (AIA 2006), February
                 13--16, 2006, Innsbruck, Austria}",
  title =        "Investigating {Esperanto}'s statistical proportions
                 relative to other languages using neural networks and
                 {Zipf}'s law",
  publisher =    "Acta Press",
  address =      "????",
  pages =        "1--7",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 18:41:37 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.cs.cofc.edu/~manaris/uploads/Main/IASTED2006.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Maslov:2006:BGA,
  author =       "V. P. Maslov",
  title =        "{Bose} gas of anharmonic oscillators and a refinement
                 of {Zipf}'s law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "148",
  number =       "3",
  pages =        "495--496",
  year =         "2006",
  CODEN =        "TMFZAL",
  DOI =          "https://doi.org/10.1007/s11232-006-0117-2",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B10",
  MRnumber =     "2283664",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
  journal-URL =  "http://link.springer.com/journal/11232",
}

@Article{Maslov:2006:NAD,
  author =       "V. P. Maslov",
  title =        "Negative asymptotic dimension, a new condensate, and
                 their relation to the quantized {Zipf} law",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "6",
  pages =        "856--863",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11006-006-0203-7",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "82B10 (20F69 53C23 81S10 91F20)",
  MRnumber =     "2311613 (2008e:82005)",
  MRreviewer =   "Artur E. Ruuge",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
  journal-URL =  "http://link.springer.com/journal/11006",
}

@Article{Maslov:2006:RZM,
  author =       "V. P. Maslov",
  title =        "A refinement of the {Zipf--Mandelbrot} law and
                 lacunarity in an ideal gas",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "147",
  number =       "3",
  pages =        "511--512",
  year =         "2006",
  CODEN =        "TMFZAL",
  DOI =          "https://doi.org/10.1007/s11232-006-0083-8",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B10",
  MRnumber =     "2254729 (2007d:82007)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
  journal-URL =  "http://link.springer.com/journal/11232",
}

@Article{Maslov:2006:ZLR,
  author =       "V. P. Maslov and T. V. Maslova",
  title =        "On {Zipf}'s law and rank distributions in linguistics
                 and semiotics",
  journal =      j-MAT-ZAMETKI,
  volume =       "80",
  number =       "5",
  pages =        "718--732",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11006-006-0189-1",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "60C05 (62-07 62P99)",
  MRnumber =     "2311586 (2008g:60027)",
  MRreviewer =   "Konstantin E. Feldman",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "Zbl 1134.62086",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
  journal-URL =  "http://link.springer.com/journal/11006",
}

@Article{Maslova:2006:ZLM,
  author =       "T. V. Maslova",
  title =        "{Zipf}'s law and {Maslov}'s formula as applied to
                 semiotic systems",
  journal =      j-DOKL-MATH,
  volume =       "74",
  number =       "3",
  pages =        "917--920",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1134/S1064562406060330",
  ISSN =         "1064-5624 (print), 1531-8362 (electronic)",
  ISSN-L =       "1064-5624",
  bibdate =      "Sat Nov 12 11:13:35 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "pre05824774",
  acknowledgement = ack-nhfb,
  classmath =    "62E20 (Asymptotic distribution theory in statistics)
                 82B03 (Foundations of equilibrium statistical
                 mechanics)",
  fjournal =     "Doklady Mathematics",
  journal-URL =  "http://link.springer.com/journal/11472",
  language =     "English. Russian original",
}

@Article{Maslova:2006:ZLV,
  author =       "T. V. Maslova",
  title =        "On the {Zipf} law and the {V. P. Maslov} formula for
                 semiotic systems",
  journal =      j-DOKL-AKAD-NAUK,
  volume =       "411",
  number =       "6",
  pages =        "754--757",
  year =         "2006",
  CODEN =        "DANKAS",
  ISSN =         "0869-5652",
  ISSN-L =       "0869-5652",
  MRclass =      "62E20 (82B03)",
  MRnumber =     "2451374",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Doklady Akademii
                 Nauk",
  journal-URL =  "http://istina.msu.ru/journals/366838/",
}

@InProceedings{Mebane:2006:DAE,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Annual Meeting of the Midwest Political Science
                 Association, April 20--23, Palmer House, Chicago}",
  title =        "Detecting Attempted Election Theft: Vote Counts,
                 Voting Machines and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 50",
  day =          "19",
  month =        apr,
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:14:14 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/mw06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFS,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Feb 15 18:22:27 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www-personal.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2006:EFV,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2006 Summer Meeting of the Political Methodology
                 Society, UC-Davis, July 20--22, 2006}",
  title =        "Election Forensics: Vote Counts and {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "ii + 48",
  day =          "18",
  month =        jul,
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:01:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm06.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Second Digit Benford Law (2BL)",
}

@Article{Mellor:2006:GKZ,
  author =       "Andy Mellor",
  title =        "Book Review: {G. K. Zipf, \booktitle The
                 Psycho-biology of Language (1935) MIT Press, Cambridge,
                 MA}",
  journal =      j-SYSTEM,
  volume =       "34",
  number =       "3",
  pages =        "455--457",
  day =          "20",
  month =        sep,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.system.2006.07.004",
  ISSN =         "0346-251X (print), 1879-3282 (electronic)",
  ISSN-L =       "0346-251X",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0346251X06000674",
  acknowledgement = ack-nhfb,
  fjournal =     "System",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0346251X",
  keywords =     "Zipf's Law",
}

@Article{Metwally:2006:IES,
  author =       "Ahmed Metwally and Divyakant Agrawal and Amr {El
                 Abbadi}",
  title =        "An integrated efficient solution for computing
                 frequent and top-$k$ elements in data streams",
  journal =      j-TODS,
  volume =       "31",
  number =       "3",
  pages =        "1095--1133",
  month =        sep,
  year =         "2006",
  CODEN =        "ATDSD3",
  DOI =          "https://doi.org/10.1145/1166074.1166084",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Tue Oct 17 05:41:01 MDT 2006",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See comments in \cite{Liu:2010:CIE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Database Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
}

@Book{Miller:2006:IMN,
  author =       "Steven J. Miller and Ramin Takloo-Bighash",
  title =        "An Invitation to Modern Number Theory",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xx + 503",
  year =         "2006",
  ISBN =         "0-691-12060-9 (hardcover)",
  ISBN-13 =      "978-0-691-12060-7 (hardcover)",
  LCCN =         "QA241 .M5344 2006",
  bibdate =      "Fri Mar 22 08:57:57 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Number theory",
  tableofcontents = "Part 1. Basic Number Theory \\
                 1. Mod p Arithmetic, Group Theory and Cryptography \\
                 2. Arithmetic Functions \\
                 3. Zeta and L-Functions \\
                 4. Solutions to Diophantine Equations \\
                 Part 2. Continued Fractions and Approximations \\
                 5. Algebraic and Transcendental Numbers \\
                 6. The Proof of Roth's Theorem \\
                 7. Introduction to Continued Fractions \\
                 Part 3. Probabilistic Methods and Equidistribution \\
                 8. Introduction to Probability \\
                 9. Applications of Probability: Benford's Law and
                 Hypothesis Testing \\
                 10. Distribution of Digits of Continued Fractions \\
                 11. Introduction to Fourier Analysis \\
                 12. f n k g and Poissonian Behavior \\
                 Part 4. The Circle Method \\
                 13. Introduction to the Circle Method \\
                 14. Circle Method: Heuristics for Germain Primes \\
                 Part 5. Random Matrix Theory and L-Functions \\
                 15. From Nuclear Physics to L-Functions \\
                 16. Random Matrix Theory: Eigenvalue Densities \\
                 17. Random Matrix Theory: Spacings between Adjacent
                 Eigenvalues \\
                 18. The Explicit Formula and Density Conjectures \\
                 Appendix A. Analysis Review \\
                 Appendix B. Linear Algebra Review \\
                 Appendix C. Hints and Remarks on the Exercises \\
                 Appendix D. Concluding Remarks",
}

@Article{Miller:2006:MCL,
  author =       "Steven J. Miller and M. J. Nigrini",
  title =        "The {Modulo 1 Central Limit Theorem} and {Benford's
                 Law} for Products",
  journal =      "International Journal of Algebra",
  volume =       "3",
  number =       "3",
  pages =        "119--130",
  month =        jul,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "1312-8868 (print), 1314-7595 (electronic)",
  ISSN-L =       "1312-8868",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......7686M;
                 http://arxiv.org/abs/math/0607686",
  abstract =     "We derive a necessary and sufficient condition for the
                 sum of $M$ independent continuous random variables
                 modulo $1$ to converge to the uniform distribution in $
                 L^1 ([0, 1]) $, and discuss generalizations to discrete
                 random variables. A consequence is that if $ X_1,
                 \ldots {}, X_M $ are independent continuous random
                 variables with densities $ f_1, \ldots {}, f_M $, for
                 any base $B$ as $ M \to \infty $ for many choices of
                 the densities the distribution of the digits of $ X_1 *
                 \cdots {} * X_M $ converges to Benford's law base $B$.
                 The rate of convergence can be quantified in terms of
                 the Fourier coefficients of the densities, and provides
                 an explanation for the prevalence of Benford behavior
                 in many diverse systems.",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0607686",
  journal-URL =  "http://www.m-hikari.com/ija/index.html",
  keywords =     "Mathematics - Probability, Mathematics - Classical
                 Analysis and ODEs, 60F05, 60F25, 11K06 (Primary),
                 42A10, 42A61, 62E15 (Secondary)",
}

@Article{Miller:2006:OSB,
  author =       "Steven J. Miller and M. J. Nigrini",
  title =        "Order Statistics and {Benford's Law}",
  journal =      "ArXiv Mathematics e-prints",
  month =        jan,
  year =         "2006",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006math......1344M",
  acknowledgement = ack-nhfb,
  eprint =       "arXiv:math/0601344",
  keywords =     "Mathematics - Probability, Mathematics - Number
                 Theory, 11K06, 60A10 (Primary), 46F12, 60F05, 42A16
                 (Secondary)",
}

@Article{Moret:2006:NBL,
  author =       "M. A. Moret and V. de Senna and M. G. Pereira and G.
                 F. Zebende",
  title =        "{Newcomb--Benford} Law in Astrophysical Sources",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "17",
  number =       "11",
  pages =        "1597--1604",
  month =        "????",
  year =         "2006",
  CODEN =        "IJMPEO",
  DOI =          "https://doi.org/10.1142/S0129183106010054",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  ISSN-L =       "0129-1831",
  bibdate =      "Mon Nov 14 17:37:59 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2006IJMPC..17.1597M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
}

@TechReport{Morrow:2006:BLF,
  author =       "John Morrow",
  title =        "{Benford's Law}, Families of Distributions and a Test
                 Basis",
  type =         "Report",
  institution =  "University of Wisconsin--Madison",
  address =      "Madison, WI, USA",
  month =        "????",
  year =         "2006",
  bibdate =      "Tue Nov 22 20:44:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Revised draft of 9 October 2010.",
  URL =          "http://www.johnmorrow.info/projects/benford/benfordMain.pdf",
  acknowledgement = ack-nhfb,
  lastaccess =   "22 November 2011",
}

@Article{Moura:2006:ZLB,
  author =       "Newton J. {Moura, Jr.} and Marcelo B. Ribeiro",
  title =        "{Zipf} law for {Brazilian} cities",
  journal =      j-J-THEOR-BIOL,
  volume =       "219",
  number =       "4",
  pages =        "441--448",
  day =          "15",
  month =        jul,
  year =         "2006",
  CODEN =        "JTBIAP",
  DOI =          "https://doi.org/10.1016/j.physa.2005.11.038",
  ISSN =         "0022-5193 (print), 1095-8541 (electronic)",
  ISSN-L =       "0022-5193",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437105012422",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Biology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00225193",
  keywords =     "Zipf's Law",
}

@TechReport{Nigrini:2006:BLA,
  author =       "M. J. Nigrini and Steven J. Miller",
  title =        "{Benford}'s law applied to hydrology data --- results
                 and relevance to other geophysical data",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2006",
  bibdate =      "Sat Feb 16 18:58:34 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Ogasawara:2006:ZLH,
  author =       "Osamu Ogasawara and Shoko Kawamoto and Kousaku Okubo",
  title =        "{Zipf}'s law and human transcriptomes: an explanation
                 with an evolutionary model",
  journal =      j-C-R-BIOL,
  volume =       "326",
  number =       "10--11",
  pages =        "1097--1101",
  day =          "1",
  month =        jul,
  year =         "2006",
  CODEN =        "CRBOCM",
  DOI =          "https://doi.org/10.1016/j.crvi.2003.09.031",
  ISSN =         "1631-0691 (print), 1768-3238 (electronic)",
  ISSN-L =       "1631-0691",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1631069103002294",
  acknowledgement = ack-nhfb,
  fjournal =     "Comptes Rendus Biologies",
  journal-URL =  "http://sciencedirect.com/science/journal/16310691",
  keywords =     "Zipf's Law",
}

@Article{Pocheau:2006:SDL,
  author =       "A. Pocheau",
  title =        "The significant digit law: a paradigm of statistical
                 scale symmetries",
  journal =      j-EUR-PHYS-J-B,
  volume =       "49",
  number =       "4",
  pages =        "491--511",
  month =        feb,
  year =         "2006",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1140/epjb/e2006-00084-2",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Sat Feb 16 15:06:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1140/epjb/e2006-00084-2",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
}

@Article{Posch:2006:ADP,
  author =       "Peter N. Posch and Welf A. Kreiner",
  title =        "Analysing digits for portfolio formation and index
                 tracking",
  journal =      j-J-ASSET-MANAGE,
  volume =       "7",
  number =       "1",
  pages =        "69--80",
  month =        may,
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1057/palgrave.jam.2240203",
  ISSN =         "1470-8272 (print), 1479-179X (electronic)",
  ISSN-L =       "1470-8272",
  bibdate =      "Fri Nov 25 11:19:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A general methodology is proposed for using digit
                 distributions as an approach to examining arbitrary
                 datasets. With the Newcomb--Benford law as a starting
                 point, a more general framework for digital analysis is
                 developed. A new measure is proposed based on this
                 framework, namely the Digital-Fit Factor (DFF). The use
                 of index comparison on the S\&P500 and the Dow Jones
                 Industrial Average is demonstrated. The DFF is then
                 used to construct portfolios and measure their
                 performance compared with that of the index. The
                 average returns using the measure exceed the index
                 composition by 6--14 percentage points per year by
                 being more stable at the same time. Furthermore, these
                 measures require only a very small proportion of the
                 available information and are thus very efficient.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Asset Management",
  keywords =     "Benford's Law",
}

@Article{Ree:2006:PLD,
  author =       "Suhan Ree",
  title =        "Power-law distributions from additive preferential
                 redistributions",
  journal =      j-PHYS-REV-E,
  volume =       "73",
  number =       "??",
  pages =        "026115",
  day =          "15",
  month =        feb,
  year =         "2006",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.73.026115",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.73.026115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@InProceedings{Sanches:2006:IRU,
  author =       "Jo{\~a}o M. Sanches and Jorge S. Marques",
  booktitle =    "{2006 IEEE International Conference on Image
                 Processing, Atlanta, Georgia, 8--11 October 2006}",
  title =        "Image Reconstruction using the {Benford Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2029--2032",
  year =         "2006",
  DOI =          "https://doi.org/10.1109/ICIP.2006.312845",
  ISBN =         "1-4244-0480-0",
  ISBN-13 =      "978-1-4244-0480-3",
  ISSN =         "1522-4880",
  bibdate =      "Tue Nov 15 09:03:24 2011",
  bibsource =    "DBLP;
                 http://dblp.uni-trier.de/db/conf/icip/icip2006.html#SanchesM06;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Tt has been claimed that the first digit of real
                 signals follows a logarithmic distribution, called
                 Benford law. This paper shows that this distribution is
                 a natural prior for the gradient of several types of
                 medical images (MRI, CT, ultrasound) and proposes a
                 reconstruction algorithm based on the Benford law which
                 does not require any parameter tuning. Experimental
                 results are presented to illustrate the performance of
                 the reconstruction algorithm",
  acknowledgement = ack-nhfb,
}

@Article{Saville:2006:UBL,
  author =       "Adrian D. Saville",
  title =        "Using {Benford's} Law to detect data error and fraud:
                 An examination of companies listed on the {Johannesburg
                 Stock Exchange}",
  journal =      "South African Journal of Economic and Management
                 Sciences",
  volume =       "9",
  number =       "3",
  pages =        "341--354",
  month =        "????",
  year =         "2006",
  CODEN =        "????",
  ISSN =         "1015-8812 (print), 2222-3436 (electronic)",
  ISSN-L =       "1015-8812",
  bibdate =      "Fri Mar 22 09:12:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  journal-URL =  "http://sajems.org/index.php/sajems/issue/archive",
  keywords =     "Benford's Law",
  remark =       "No issues online before volume 10, number 1, 2007.",
}

@Article{Schneider:2006:RAS,
  author =       "Reto U. Schneider",
  title =        "{Das R{\"a}tsel der abgegriffenen Seiten: Vor {\"u}ber
                 hundert Jahren stiess ein Astronom auf ein
                 merkw{\"u}rdiges statistisches Gesetz, das heute
                 Steuerbetr{\"u}ger entlarven soll}. ({German}) [{The}
                 puzzle of the worn pages: More than a hundred years ago
                 an astronomer came across a strange statistical law
                 that will now expose tax cheats]",
  journal =      "{NZZ Folio: Die Zeitschrift der Neuen Z{\"u}rcher
                 Zeitung}",
  volume =       "??",
  number =       "1/06",
  month =        "????",
  year =         "2006",
  bibdate =      "Fri Nov 18 12:18:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www-x.nzz.ch/folio/curr/articles/schneider_2.html;
                 http://www.nzzfolio.ch/www/d80bd71b-b264-4db4-afd0-277884b93470/showarticle/4c9a5444-883e-4e6b-8a4c-6c31f32c02f3.aspx",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Schuette:2006:TFZ,
  author =       "Paul Schuette and Marcus C. Spruill",
  title =        "Tail fit and the {Zipf--Pareto} law",
  journal =      "Extremes",
  volume =       "9",
  number =       "3--4",
  pages =        "243--261",
  year =         "2006",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10687-007-0030-6",
  ISSN =         "1386-1999",
  ISSN-L =       "1386-1999",
  MRnumber =     "2367837",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Extremes. Statistical Theory and Applications in
                 Science, Engineering and Economics",
  xxyear =       "2007",
}

@Article{Sugimoto:2006:AFP,
  author =       "Toyoaki Sugimoto and Naoto Miyoshi",
  title =        "On the asymptotics of fault probability in
                 least-recently-used caching with {Zipf}-type request
                 distribution",
  journal =      j-RAND-STRUCT,
  volume =       "29",
  number =       "3",
  pages =        "296--323",
  year =         "2006",
  CODEN =        "RSALFD",
  DOI =          "https://doi.org/10.1002/rsa.20098",
  ISSN =         "1042-9832 (print), 1098-2418 (electronic)",
  ISSN-L =       "1042-9832",
  MRclass =      "68N25 (60C05 62E20 62P30 68P05 68U35)",
  MRnumber =     "2254493 (2008h:68028)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Random Structures and Algorithms",
  keywords =     "distributional tail asymptotics; least-recently-used
                 caching; move-to-front algorithm; negative association;
                 Zipf-type distribution",
}

@MastersThesis{TorresNunez:2006:NBL,
  author =       "David A. {Torres N{\'u}{\~n}ez}",
  title =        "{Newcomb--Benford's Law}: Applications to Electoral
                 Processes, Bioinformatics, and the Stock Index",
  type =         "{M.S.} thesis",
  school =       "Center for Bioststatistics and Bioinformatics,
                 University of Puerto Rico, R{\'\i}o Piedras Campus",
  address =      "PO Box 23355, San Juan, PR 00931-3355",
  month =        may,
  year =         "2006",
  bibdate =      "Fri Feb 15 18:34:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  advisor =      "Luis R{\'a}ul Pericchi Guerra",
}

@Article{VandeWalle:2006:ZGK,
  author =       "J. {Van de Walle} and K. Willems",
  title =        "{Zipf, George Kingsley (1902--1950)}",
  journal =      j-J-ECON-DYN-CONTROL,
  volume =       "31",
  number =       "7",
  pages =        "756--757",
  day =          "15",
  month =        jul,
  year =         "2006",
  CODEN =        "JEDCDH",
  DOI =          "https://doi.org/10.1016/B0-08-044854-2/04726-X",
  ISSN =         "0165-1889 (print), 1879-1743 (electronic)",
  ISSN-L =       "0165-1889",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B008044854204726X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Economic Dynamics and Control",
  keywords =     "Zipf's Law",
}

@Article{Wilkinson:2006:RPC,
  author =       "Leland Wilkinson",
  title =        "Revising the {Pareto} Chart",
  journal =      j-AMER-STAT,
  volume =       "60",
  number =       "4",
  pages =        "332--334",
  month =        nov,
  year =         "2006",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/000313006X152243",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Thu Aug 26 21:48:27 MDT 2010",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Ackermann:2007:DMB,
  author =       "Heiner Ackermann and Alantha Newman and Heiko
                 R{\"o}glin and Berthold V{\"o}cking",
  title =        "Decision-making based on approximate and smoothed
                 {Pareto} curves",
  journal =      j-THEOR-COMP-SCI,
  volume =       "378",
  number =       "3",
  pages =        "253--270",
  day =          "9",
  month =        jun,
  year =         "2007",
  CODEN =        "TCSCDI",
  ISSN =         "0304-3975 (print), 1879-2294 (electronic)",
  ISSN-L =       "0304-3975",
  bibdate =      "Tue Mar 29 08:55:49 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/03043975",
  acknowledgement = ack-nhfb,
  fjournal =     "Theoretical Computer Science",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03043975",
}

@Article{Amin:2007:TVA,
  author =       "Zeinab H. Amin",
  title =        "Tests for the Validity of the Assumption that the
                 Underlying Distribution of Life is {Pareto}",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "2",
  pages =        "195--201",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Misc{Anonymous:2007:ZL,
  author =       "Anonymous",
  key =          "Zipf's Law",
  title =        "{Zipf}'s law",
  year =         "2007",
  bibdate =      "Sat Jan 26 12:46:16 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib",
  URL =          "http://en.wikipedia.org/wiki/Zipf's_law",
  acknowledgement = ack-ds,
  lastaccess =   "27 January 2013",
  rawdata =      "Zipf's Law (2007)
                 |http://en.wikipedia.org/wiki/Zipf's_law|",
}

@Article{Bakulina:2007:AZL,
  author =       "M. P. Bakulina",
  title =        "Application of {Zipf}'s law for text compression",
  journal =      "Diskretn. Anal. Issled. Oper. Ser. 2",
  volume =       "14",
  number =       "2",
  pages =        "3--13",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1560-9901",
  ISSN-L =       "1560-9901",
  MRclass =      "94A15",
  MRnumber =     "2542308 (2010i:94076)",
  MRreviewer =   "I. Vajda",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Diskretny{\u\i} Analiz i Issledovanie Operatsi{\u\i}.
                 Seriya 2",
}

@Article{Baskerville:2007:GAS,
  author =       "Kim Baskerville and Peter Grassberger and Maya
                 Paczuski",
  title =        "Graph animals, subgraph sampling, and motif search in
                 large networks",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "036107",
  day =          "11",
  month =        sep,
  year =         "2007",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.76.036107",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.76.036107",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Beeli:2007:FCG,
  author =       "Gian Beeli and Michaela Esslen and Lutz J{\"a}ncke",
  title =        "Frequency Correlates in Grapheme-Color Synaesthesia",
  journal =      "Psychological Science",
  volume =       "18",
  number =       "9",
  pages =        "788--792",
  year =         "2007",
  DOI =          "https://doi.org/10.1111/j.1467-9280.2007.01980.x",
  bibdate =      "Sat Sep 10 10:35:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pss.sagepub.com/content/18/9/788.abstract",
  abstract =     "Individuals with synaesthesia experience certain
                 stimuli in more than one sensory modality. Most common
                 is the linkage of letters and digits (graphemes) to
                 colors. Whereas synaesthesia might be partly
                 genetically determined, the linkages to specific colors
                 are assumed to be learned. We present a systematic
                 statistical analysis of synaesthetic color perception
                 based on subjects' reproduction of individual colors
                 for each grapheme, instead of simple verbal
                 categorizations. The statistical analysis revealed that
                 the color perceptions, measured with the HSL (hue,
                 saturation, and luminance) scale, varied systematically
                 among the different digits and letters. The frequencies
                 of the digits and letters (in the German language)
                 partly explained these systematic variations. However,
                 digit frequency was more strongly related to color
                 perception in the synaesthetes than was letter
                 frequency. The results for digit and letter frequency
                 indicate that experience with graphemes may shape
                 synaesthetic color perception.",
  acknowledgement = ack-nhfb,
  eprint =       "http://pss.sagepub.com/content/18/9/788.full.pdf+html",
  keywords =     "Benford's Law",
}

@Article{Benguigui:2007:DMC,
  author =       "Lucien Benguigui and Efrat Blumenfeld-Lieberthal",
  title =        "A dynamic model for city size distribution beyond
                 {Zipf}'s law",
  journal =      j-PHYSICA-A,
  volume =       "384",
  number =       "2",
  pages =        "613--627",
  day =          "15",
  month =        oct,
  year =         "2007",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2007.05.059",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437107006061",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Berger:2007:DMN,
  author =       "A. Berger and S. Siegmund",
  title =        "On the distribution of mantissae in nonautonomous
                 difference equations",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "13",
  number =       "8--9",
  pages =        "829--845",
  month =        "????",
  year =         "2007",
  CODEN =        "JDEAEA",
  DOI =          "https://doi.org/10.1080/10236190701388039",
  ISSN =         "1023-6198 (print), 1563-5120 (electronic)",
  ISSN-L =       "1023-6198",
  MRclass =      "37A45 (37B55 39A11)",
  MRnumber =     "2343033 (2008j:37010)",
  MRreviewer =   "Reinhard Winkler",
  bibdate =      "Tue Feb 19 09:37:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Second Memorial Issue in Honour of Bernd Aulbach.",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/berger_siegmund_07.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Difference Equations and Applications",
  journal-URL =  "http://www.informaworld.com/1023-6198",
}

@Article{Berger:2007:NMO,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Newton}'s Method Obeys {Benford}'s Law",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "114",
  number =       "7",
  pages =        "588--601",
  month =        aug # "\slash " # sep,
  year =         "2007",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "65G50 (37N30)",
  MRnumber =     "2341322 (2008h:65016)",
  MRreviewer =   "Uwe Sch{\"a}fer",
  bibdate =      "Mon Jan 30 12:00:29 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i27642270;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/27642274",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}

@Article{Bernik:2007:BLA,
  author =       "V. I. Bernik and N. I. Kalosha",
  title =        "{Benford}'s law and the approximation of logarithms of
                 natural numbers by rational numbers",
  journal =      "Vests{\=\i} Nats. Akad. Navuk Belarus{\=\i} Ser.
                 F{\=\i}z.-Mat. Navuk",
  volume =       "??",
  number =       "3",
  pages =        "68--73, 127",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0002-3574",
  ISSN-L =       "0002-3574",
  MRclass =      "11J83 (11A63 11K36)",
  MRnumber =     "2398318 (2008j:11084)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Vests{\=\i} Natsyyanal\cprime na{\u\i}
                 Akad{\`e}m{\=\i} {\=\i} Navuk Belarus{\=\i}. Seryya
                 F{\=\i}z{\=\i}ka-Mat{\`e}matychnykh Navuk. Izvestiya
                 Natsional\cprime no{\u\i} Akademii Nauk Belarusi.
                 Seriya Fiziko-Matematicheskikh Nauk. Proceedings of the
                 National Academy of Sciences of Belarus. Physics and
                 Mathematics Series",
}

@Article{Brown:2007:UZL,
  author =       "R. J. C. Brown",
  title =        "The use of {Zipf}'s law in the screening of analytical
                 data: a step beyond {Benford}",
  journal =      j-ANALYST,
  volume =       "132",
  number =       "4",
  pages =        "344",
  year =         "2007",
  CODEN =        "ANALAO",
  DOI =          "https://doi.org/10.1039/b618255k",
  ISSN =         "0003-2654 (print), 1364-5528 (electronic)",
  ISSN-L =       "0003-2654",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007Ana...132..344B",
  abstract =     "This study shows for the first time the effectiveness
                 of Zipf's law in screening analytical data sets for
                 outliers, data formatting and data transcription
                 errors, particularly when the data sets are small. In
                 the case of pollutant concentrations in ambient air,
                 the multivariate nature of the measurement, and the
                 relationship between the measured values of these
                 multivariant quantities are the characteristics that
                 allow a Zipf's law approach to data screening to be
                 successful. Furthermore, it has been shown that Zipf's
                 law has advantages over other novel data screening
                 techniques, such as Benford's law, in terms of
                 sensitivity and scope",
  acknowledgement = ack-nhfb,
  fjournal =     "The Analyst",
  journal-URL =  "http://pubs.rsc.org/en/journals/journalissues/an",
}

@Article{Chacko:2007:EPB,
  author =       "Manoj Chacko and P. Yageen Thomas",
  title =        "Estimation of a Parameter of Bivariate {Pareto}
                 Distribution by Ranked Set Sampling",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "6",
  pages =        "703--714",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  bibdate =      "Wed Aug 25 11:41:54 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Cho:2007:BBL,
  author =       "Wendy K. Tam Cho and Brian J. Gaines",
  title =        "Breaking the ({Benford}) law: statistical fraud
                 detection in campaign finance",
  journal =      j-AMER-STAT,
  volume =       "61",
  number =       "3",
  pages =        "218--223",
  month =        aug,
  year =         "2007",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/000313007X223496",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2393725",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pubs.amstat.org/doi/pdfplus/10.1198/000313007X223496;
                 http://www.tandfonline.com/doi/abs/10.1198/000313007X223496",
  abstract =     "Benford's law is seeing increasing use as a diagnostic
                 tool for isolating pockets of large datasets with
                 irregularities that deserve closer inspection. Popular
                 and academic accounts of campaign finance are rife with
                 tales of corruption, but the complete dataset of
                 transactions for federal campaigns is enormous.
                 Performing a systematic sweep is extremely arduous;
                 hence, these data are a natural candidate for initial
                 screening by comparison to Benford's distributions.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Clauset:2007:FST,
  author =       "Aaron Clauset and Maxwell Young and Kristian Skrede
                 Gleditsch",
  title =        "On the Frequency of Severe Terrorist Events",
  journal =      j-J-CONFL-RESOLUT,
  volume =       "51",
  number =       "1",
  pages =        "58--87",
  month =        feb,
  year =         "2007",
  CODEN =        "JCFRAL",
  DOI =          "https://doi.org/10.1177/0022002706296157",
  ISSN =         "0022-0027 (print), 1552-8766 (electronic)",
  ISSN-L =       "0022-0027",
  bibdate =      "Thu Nov 24 14:07:17 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jcr.sagepub.com;
                 http://jcr.sagepub.com/content/51/1/58.abstract;
                 http://www.jstor.org/journals/00220027.html",
  abstract =     "In the spirit of Lewis Richardson's original study of
                 the statistics of deadly conflicts, we study the
                 frequency and severity of terrorist attacks worldwide
                 since 1968. We show that these events are uniformly
                 characterized by the phenomenon of ``scale
                 invariance,'' that is, the frequency scales as an
                 inverse power of the severity, $ P(x) \approx x{-
                 \alpha } $. We find that this property is a robust
                 feature of terrorism, persisting when we control for
                 economic development of the target country, the type of
                 weapon used, and even for short time scales. Further,
                 we show that the center of the distribution oscillates
                 slightly with a period of roughly 13 years, that there
                 exist significant temporal correlations in the
                 frequency of severe events, and that current models of
                 event incidence cannot account for these variations or
                 the scale invariance property of global terrorism.
                 Finally, we describe a simple toy model for the
                 generation of these statistics and briefly discuss its
                 implications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Conflict Resolution",
}

@Article{Clauset:2007:PLDa,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "7",
  month =        jun,
  year =         "2007",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  URL =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "27",
}

@Article{Clauset:2007:PLDb,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-law distributions in empirical data",
  journal =      "ArXiv Physics e-prints",
  day =          "2",
  month =        feb,
  year =         "2009",
  DOI =          "https://doi.org/10.1137/070710111",
  bibdate =      "Thu Feb 28 08:52:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "arXiv:0706.1062.",
  URL =          "http://arxiv.org/abs/0706.1062v1",
  acknowledgement = ack-nhfb,
  pagecount =    "43",
}

@Article{Decker:2007:GPC,
  author =       "Ethan H. Decker and Andrew J. Kerkhoff and Melanie E.
                 Moses",
  title =        "Global Patterns of City Size Distributions and Their
                 Fundamental Drivers",
  journal =      j-PLOS-ONE,
  volume =       "2",
  number =       "9",
  pages =        "e934",
  month =        sep,
  year =         "2007",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0000934",
  ISSN =         "1932-6203",
  bibdate =      "Wed Feb 27 06:29:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000934",
  abstract =     "Urban areas and their voracious appetites are
                 increasingly dominating the flows of energy and
                 materials around the globe. Understanding the size
                 distribution and dynamics of urban areas is vital if we
                 are to manage their growth and mitigate their negative
                 impacts on global ecosystems. For over 50 years, city
                 size distributions have been assumed to universally
                 follow a power function, and many theories have been
                 put forth to explain what has become known as Zipf's
                 law (the instance where the exponent of the power
                 function equals unity). Most previous studies, however,
                 only include the largest cities that comprise the tail
                 of the distribution. Here we show that national,
                 regional and continental city size distributions,
                 whether based on census data or inferred from cluster
                 areas of remotely-sensed nighttime lights, are in fact
                 lognormally distributed through the majority of cities
                 and only approach power functions for the largest
                 cities in the distribution tails. To explore generating
                 processes, we use a simple model incorporating only two
                 basic human dynamics, migration and reproduction, that
                 nonetheless generates distributions very similar to
                 those found empirically. Our results suggest that
                 macroscopic patterns of human settlements may be far
                 more constrained by fundamental ecological principles
                 than more fine-scale socioeconomic factors.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
  keywords =     "Zipf's Law",
  pagecount =    "6",
}

@Article{Diekmann:2007:FDU,
  author =       "Andreas Diekmann",
  title =        "Not the First Digit! {Using} {Benford's Law} to Detect
                 Fraudulent Scientific Data",
  journal =      j-J-APPL-STAT,
  volume =       "34",
  number =       "3--4",
  pages =        "321--329",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/02664760601004940",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRnumber =     "2380543",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.tandf.co.uk/journals/routledge/02664763.html",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/02664760601004940",
  abstract =     "Digits in statistical data produced by natural or
                 social processes are often distributed in a manner
                 described by `Benford's law'. Recently, a test against
                 this distribution was used to identify fraudulent
                 accounting data. This test is based on the supposition
                 that first, second, third, and other digits in real
                 data follow the Benford distribution while the digits
                 in fabricated data do not. Is it possible to apply
                 Benford tests to detect fabricated or falsified
                 scientific data as well as fraudulent financial data?
                 We approached this question in two ways. First, we
                 examined the use of the Benford distribution as a
                 standard by checking the frequencies of the nine
                 possible first and ten possible second digits in
                 published statistical estimates. Second, we conducted
                 experiments in which subjects were asked to fabricate
                 statistical estimates (regression coefficients). The
                 digits in these experimental data were scrutinized for
                 possible deviations from the Benford distribution.
                 There were two main findings. First, both digits of the
                 published regression coefficients were approximately
                 Benford distributed or at least followed a pattern of
                 monotonic decline. Second, the experimental results
                 yielded new insights into the strengths and weaknesses
                 of Benford tests. Surprisingly, first digits of faked
                 data also exhibited a pattern of monotonic decline,
                 while second, third, and fourth digits were distributed
                 less in accordance with Benford's law. At least in the
                 case of regression coefficients, there were indications
                 that checks for digit-preference anomalies should focus
                 less on the first (i.e., leftmost) and more on later
                 digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
  keywords =     "Benford's Law; data fabrication; digital analysis;
                 distribution of digits from regression coefficients;
                 first digit law; Zipf's Law",
}

@Article{Dumbgen:2007:EBA,
  author =       "L. D{\"u}mbgen and C. Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007arXiv0705.4488D",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0705.4488",
  keywords =     "Mathematics - Probability, 60E15, 60F99",
  primaryclass = "math.PR",
}

@Article{Egghe:2007:UHL,
  author =       "Leo Egghe",
  title =        "Untangling {Herdan's Law} and {Heaps' Law}:
                 Mathematical and informetric arguments",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "58",
  number =       "5",
  pages =        "702--709",
  month =        mar,
  year =         "2007",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20524",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:40 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  keywords =     "Heaps' law in information retrieval; Herdan's law in
                 linguistics",
  onlinedate =   "2 Feb 2007",
}

@InProceedings{Fu:2007:GBL,
  author =       "D. Fu and Y. Q. Shi and W. Su",
  editor =       "Edward J. {Delp III} and Ping Wah Wong",
  booktitle =    "{Society of Photo-Optical Instrumentation Engineers
                 (SPIE)} Conference Series",
  title =        "A generalized {Benford}'s law for {JPEG} coefficients
                 and its applications in image forensics",
  volume =       "6505",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  month =        feb,
  year =         "2007",
  DOI =          "https://doi.org/10.1117/12.704723",
  ISSN =         "0277-786X (print), 1996-756X (electronic)",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Society of Photo-Optical Instrumentation Engineers
                 (SPIE) Conference Series",
  URL =          "http://adsabs.harvard.edu/abs/2007SPIE.6505E..55F",
  acknowledgement = ack-nhfb,
}

@InProceedings{Gava:2007:IQF,
  author =       "Alexandre Majola Gava and Luiz {Roque de Souza
                 Vitiello, Jr.}",
  booktitle =    "{EnANPAD 2007: XXXI Encontro da ANPAD. Rio de Janeiro
                 / RJ-22 a 26 de setembro de 2007}",
  title =        "Inflation, Quarterly Financial Statements and Fraud:
                 {Benford's Law} and the {Brazilian} Case",
  publisher =    "????",
  address =      "????",
  pages =        "1--13",
  year =         "2007",
  bibdate =      "Thu Oct 13 07:36:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.anpad.org.br/diversos/trabalhos/EnANPAD/enanpad_2007/CONT/2007_CONA819.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Giles:2007:BLN,
  author =       "D. E. Giles",
  title =        "{Benford's Law} and naturally occurring prices in
                 certain {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "14",
  number =       "3",
  pages =        "157--161",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/13504850500425667",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Wed Nov 16 09:49:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/toc/rael20/current",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  journal-URL =  "http://www.tandfonline.com/loi/rael20",
  keywords =     "Benford's Law; Fibonacci sequences; Lucas sequences",
}

@Article{Grendar:2007:ENP,
  author =       "Marian Grendar and George Judge and Laura Schechter",
  title =        "An empirical non-parametric likelihood family of
                 data-based {Benford}-like distributions",
  journal =      j-PHYSICA-A,
  volume =       "380",
  number =       "0",
  pages =        "429--438",
  day =          "1",
  month =        jul,
  year =         "2007",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2007.02.062",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://adsabs.harvard.edu/abs/2007PhyA..380..429G;
                 http://www.sciencedirect.com/science/article/pii/S0378437107001963",
  abstract =     "A mathematical expression known as Benford's law
                 provides an example of an unexpected relationship among
                 randomly selected sequences of first significant digits
                 (FSDs). Newcomb [Note on the frequency of use of the
                 different digits in natural numbers, Am. J. Math. 4
                 (1881) 39 40], and later Benford [The law of anomalous
                 numbers, Proc. Am. Philos. Soc. 78(4) (1938) 551 572],
                 conjectured that {FSDs} would exhibit a weakly
                 monotonic decreasing distribution and proposed a
                 frequency proportional to the logarithmic rule.
                 Unfortunately, the Benford {FSD} function does not hold
                 for a wide range of scale-invariant multiplicative
                 data. To confront this problem we use
                 information-theoretic methods to develop a data-based
                 family of alternative Benford-like exponential
                 distributions that provide null hypotheses for testing
                 purposes. Two data sets are used to illustrate the
                 performance of generalized Benford-like
                 distributions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Empirical likelihood; First significant
                 digit phenomenon; Information-theoretic method;
                 Minimum-divergence distance measure; Relative
                 frequencies",
}

@Article{Guo:2007:DIM,
  author =       "Lei Guo and Enhua Tan and Songqing Chen and Zhen Xiao
                 and Xiaodong Zhang",
  title =        "Does {Internet} media traffic really follow
                 {Zipf}-like distribution?",
  journal =      j-SIGMETRICS,
  volume =       "35",
  number =       "1",
  pages =        "359--360",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1254882.1254929",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Fri Jun 27 09:42:48 MDT 2008",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "It is commonly agreed that Web traffic follows the
                 Zipf-like distribution, which is an analytical
                 foundation for improving Web access performance by
                 client-server based proxy caching systems on the
                 Internet. However, some recent studies have observed
                 non-Zipf-like distributions of Internet media traffic
                 in different content delivery systems. Due to the
                 variety of media delivery systems and the diversity of
                 media content, existing studies on media traffic are
                 largely workload specific, and the observed access
                 patterns are often different from or even conflict with
                 each other. For Web media systems, study [3] reports
                 that the access pattern of streaming media is Zipf-like
                 in a university campus network, while study [2] finds
                 that it is not Zipf-like in an enterprise media
                 server.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "media; stretched exponential; Zipf-like",
}

@Article{Gupta:2007:IMS,
  author =       "Arjun K. Gupta and Saralees Nadarajah",
  title =        "Information matrices for some bivariate {Pareto}
                 distributions",
  journal =      j-APPL-MATH-COMP,
  volume =       "184",
  number =       "2",
  pages =        "1069--1079",
  day =          "15",
  month =        jan,
  year =         "2007",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sat Jul 12 09:03:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2005.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@Article{Hand:2007:DDD,
  author =       "David Hand",
  title =        "Deception and Dishonesty with Data: Fraud in Science",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "1",
  pages =        "22--25",
  month =        mar,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1740-9713.2007.00215.x",
  ISSN =         "1740-9705 (print), 1740-9713 (electronic)",
  ISSN-L =       "1740-9705",
  bibdate =      "Thu Nov 17 19:17:58 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/significance.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Signif.",
  fjournal =     "Significance",
  journal-URL =  "https://rss.onlinelibrary.wiley.com/journal/17409713",
  onlinedate =   "02 March 2007",
}

@Article{Hasumi:2007:ITS,
  author =       "Tomohiro Hasumi",
  title =        "Interoccurrence time statistics in the two-dimensional
                 {Burridge--Knopoff} earthquake model",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  number =       "??",
  pages =        "026117",
  day =          "29",
  month =        aug,
  year =         "2007",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.76.026117",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.76.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf--Mandelbrot law",
}

@TechReport{Hungerbuhler:2007:BGF,
  author =       "Norbert H{\"u}ngerb{\"u}hler",
  title =        "{Benfords Gesetz {\"u}ber f{\"u}hrende Ziffern. Wie
                 die Mathematik Steuers{\"u}ndern das F{\"u}rchten
                 lehrt} [{Benford's Law} on leading digits. Mathematics
                 teaches tax evaders to fear]",
  type =         "Report",
  institution =  "EducETH",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "24",
  day =          "2",
  month =        mar,
  year =         "2007",
  bibdate =      "Fri Nov 18 12:02:21 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.educ.ethz.ch/unt/um/mathe/ana/benford/Benford_Fuehrende_Ziffern.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
  lastaccess =   "18 November 2011",
  remark =       "This report has several nice figures, including
                 photographs of Newcomb, Benford, and worn pages of log
                 tables, and an amazing plot of the agreement of
                 200,125,088 mathematical constants with Benford's
                 Law.",
}

@Article{Kumar:2007:DDD,
  author =       "Kuldeep Kumar and Sukanto Bhattacharya",
  title =        "Detecting the dubious digits: {Benford}'s law in
                 forensic accounting",
  journal =      j-SIGNIF,
  volume =       "4",
  number =       "2",
  pages =        "81--83",
  month =        jun,
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1740-9713.2007.00234.x",
  ISSN =         "1740-9705 (print), 1740-9713 (electronic)",
  ISSN-L =       "1740-9705",
  MRnumber =     "2380610",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/significance.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Signif.",
  fjournal =     "Significance",
  journal-URL =  "https://rss.onlinelibrary.wiley.com/journal/17409713",
  onlinedate =   "07 June 2007",
}

@Article{Loetscher:2007:ENS,
  author =       "T. Loetscher and P. Brugger",
  title =        "Exploring Number Space by Random Digit Generation",
  journal =      "Experimental Brain Research",
  volume =       "180",
  number =       "4",
  pages =        "655--665",
  month =        jul,
  year =         "2007",
  CODEN =        "EXBRAP",
  DOI =          "https://doi.org/10.1007/s00221-007-0889-0",
  ISSN =         "0014-4819 (print), 1432-1106 (electronic)",
  ISSN-L =       "0014-4819",
  bibdate =      "Sat Sep 10 13:10:08 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s00221-007-0889-0",
  acknowledgement = ack-nhfb,
  ajournal =     "Exp. Brain Res.",
  journal-URL =  "http://link.springer.com/journal/221",
  keywords =     "Benford's Law",
}

@InProceedings{Lu:2007:UFD,
  author =       "Fletcher Lu",
  booktitle =    "{Knowledge Discovery in Databases: PKDD 2007}",
  title =        "Uncovering Fraud in Direct Marketing Data with a Fraud
                 Auditing Case Builder",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "540--547",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-74976-9_56",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-540-74976-9_56",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Mansury:2007:EZL,
  author =       "Yuri Mansury and L{\'a}szl{\'o} Guly{\'a}s",
  title =        "The emergence of {Zipf's Law} in a system of cities:
                 an agent-based simulation approach",
  journal =      j-J-ECON-DYN-CONTROL,
  volume =       "31",
  number =       "7",
  pages =        "2438--2460",
  day =          "15",
  month =        jul,
  year =         "2007",
  CODEN =        "JEDCDH",
  DOI =          "https://doi.org/10.1016/j.jedc.2006.08.002",
  ISSN =         "0165-1889 (print), 1879-1743 (electronic)",
  ISSN-L =       "0165-1889",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165188906001527",
  ZMnumber =     "1163.91504",
  abstract =     "This paper develops a spatial agent-based model to
                 generate a system of cities that exhibits the
                 statistical properties of the Zipf's Law. The numerical
                 results suggest that the combination of bounded
                 rationality and maximum heterogeneity of agents can
                 produce a generic power-law relationship in the size
                 distribution of cities, but does not always generate
                 the Zipf's Law. We found sufficient conditions on the
                 probability distribution of spatial reach to generate
                 the Zipf's Law associated with unit power coefficient.
                 Our model also indicates that the Zipf's Law breaks
                 down unless the extent of agglomeration economies
                 overwhelms the negative disagglomerating forces.",
  acknowledgement = ack-nhfb,
  classmath =    "91B72 (Spatial models)",
  fjournal =     "Journal of Economic Dynamics and Control",
  keywords =     "complex systems; power laws; spatial agent based
                 models; Zipf's Law",
}

@Article{Maslov:2007:PTZ,
  author =       "V. P. Maslov",
  title =        "Phase transitions of the zeroth kind and the
                 quantization of the {Zipf} law",
  journal =      j-TEORET-MATH-FIZ,
  volume =       "150",
  number =       "1",
  pages =        "118--142",
  year =         "2007",
  CODEN =        "TMFZAL",
  DOI =          "https://doi.org/10.1007/s11232-007-0008-1",
  ISSN =         "0564-6162",
  ISSN-L =       "0564-6162",
  MRclass =      "82B26 (82B03)",
  MRnumber =     "2325869 (2008g:82037)",
  MRreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Teoreticheskaya i
                 Matematicheskaya Fizika",
  journal-URL =  "http://link.springer.com/journal/11232",
}

@InProceedings{Mebane:2007:SD,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2007 Summer Meeting of the Political Methodology
                 Society, Pennsylvania State University, July 18--21,
                 2007}",
  title =        "Statistics for Digits",
  publisher =    "????",
  address =      "????",
  pages =        "1--21",
  day =          "2",
  month =        jul,
  year =         "2007",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:03:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm07.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Morris:2007:MRT,
  author =       "Steven A. Morris and Michel L. Goldstein",
  title =        "Manifestation of research teams in journal literature:
                 a growth model of papers, authors, collaboration,
                 coauthorship, weak ties, and {Lotka's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "58",
  number =       "12",
  pages =        "1764--1782",
  month =        oct,
  year =         "2007",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.20661",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:37 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "24 Aug 2007",
}

@Article{Nadarajah:2007:CPG,
  author =       "Saralees Nadarajah and Samuel Kotz",
  title =        "On the convolution of {Pareto} and gamma
                 distributions",
  journal =      j-COMP-NET-AMSTERDAM,
  volume =       "51",
  number =       "12",
  pages =        "3650--3654",
  day =          "22",
  month =        aug,
  year =         "2007",
  CODEN =        "????",
  ISSN =         "1389-1286 (print), 1872-7069 (electronic)",
  ISSN-L =       "1389-1286",
  bibdate =      "Sat Apr 2 08:42:20 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/13891286",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Networks",
  journal-URL =  "http://www.sciencedirect.com/science/journal/13891286",
}

@Article{Nicolaisen:2007:PPB,
  author =       "Jeppe Nicolaisen and Birger Hj{\o}rland",
  title =        "Practical potentials of {Bradford}'s law: a critical
                 examination of the received view",
  journal =      j-J-DOC,
  volume =       "63",
  number =       "3",
  pages =        "359--377",
  month =        "????",
  year =         "2007",
  CODEN =        "JDOCAS",
  DOI =          "https://doi.org/10.1108/00220410710743298",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 11:58:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Nigrini:2007:BLA,
  author =       "Mark J. Nigrini and Steven J. Miller",
  title =        "{Benford's Law} Applied to Hydrology Data --- Results
                 and Relevance to Other Geophysical Data",
  journal =      j-MATH-GEOL,
  volume =       "39",
  number =       "5",
  pages =        "469--490",
  month =        jul,
  year =         "2007",
  CODEN =        "MATGED",
  DOI =          "https://doi.org/10.1007/s11004-007-9109-5",
  ISSN =         "0882-8121 (print), 1573-8868 (electronic)",
  ISSN-L =       "0882-8121",
  bibdate =      "Sun Feb 17 13:35:42 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11004-007-9109-5;
                 http://www.springerlink.com/content/m2274ng70435u3x6/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Geology",
}

@Article{Nye:2007:PEN,
  author =       "J. Nye and C. Moul",
  title =        "The Political Economy of Numbers: On the Application
                 of {Benford's Law} to International Macroeconomic
                 Statistics",
  journal =      "{B. E.} Journal of Macroeconomics",
  volume =       "7",
  number =       "1",
  pages =        "??--??",
  month =        "????",
  year =         "2007",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2202/1935-1690.1449",
  ISSN =         "1935-1690",
  ISSN-L =       "1935-1690",
  bibdate =      "Tue Nov 22 20:48:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.bepress.com/bejm/vol7/iss1/art17",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "Berkeley Electronic Press Journal of Macroeconomics",
}

@Article{Oteo:2007:DPE,
  author =       "J. A. Oteo and J. Ros",
  title =        "Double precision errors in the logistic map:
                 Statistical study and dynamical interpretation",
  journal =      j-PHYS-REV-E,
  volume =       "76",
  pages =        "036214",
  month =        sep,
  year =         "2007",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.76.036214",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:35:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.76.036214",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  issue =        "3",
  journal-URL =  "http://pre.aps.org/browse",
  pagecount =    "8",
  remark =       "From the abstract: ``a comparison with Benford?s law
                 for the distribution of the leading digit of
                 compilation of numbers is discussed.''",
}

@Article{Paech:2007:ZLN,
  author =       "Kerstin Paech and Wolfgang Bauer and Scott Pratt",
  title =        "{Zipf}'s law in nuclear multifragmentation and
                 percolation theory",
  journal =      j-PHYS-REV-C,
  volume =       "76",
  number =       "??",
  pages =        "054603",
  day =          "15",
  month =        nov,
  year =         "2007",
  CODEN =        "PRVCAN",
  DOI =          "https://doi.org/10.1103/PhysRevC.76.054603",
  ISSN =         "0556-2813 (print), 1089-490X, 1538-4497",
  ISSN-L =       "0556-2813",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevC.76.054603",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review C (Nuclear Physics)",
  journal-URL =  "http://prc.aps.org/browse",
  keywords =     "Zipf's Law",
}

@InProceedings{Perez-Gonzalez:2007:GBL,
  author =       "F. P{\'e}rez-Gonz{\'a}lez and G. L. Heileman and C. T.
                 Abdallah",
  booktitle =    "2007 European Control Conference (ECC)",
  title =        "A generalization of {Benford's Law} and its
                 application to images",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3613--3619",
  month =        jul,
  year =         "2007",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Approximation methods; Benford's law; Benford's law
                 generalization; Convolution; DCT; discrete cosine
                 transform domain; discrete cosine transforms; Discrete
                 cosine transforms; first significant digit; forensics;
                 Fourier expansion; Fourier series; hidden message;
                 Histograms; image forensics; Image forensics; image
                 forensics; modular logarithmic domain; probability;
                 probability density function; Random variables;
                 watermarking",
}

@InProceedings{Perin:2007:CNA,
  author =       "Stephen P{\'e}rin",
  booktitle =    "Constructal Theory of Social Dynamics",
  title =        "The Constructal Nature of the Air Traffic System",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "119--145",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-0-387-47681-0_6",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-0-387-47681-0_6",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Simons:2007:SIP,
  author =       "John L. Simons",
  title =        "A simple (inductive) proof for the non-existence of
                 2-cycles of the $ 3 x + 1 $ problem",
  journal =      j-J-NUMBER-THEORY,
  volume =       "123",
  number =       "1",
  pages =        "10--17",
  month =        mar,
  year =         "2007",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2006.05.011",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X06001223",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Number Theory",
  keywords =     "Benford's Law",
}

@Book{Tijms:2007:UPC,
  author =       "H. C. Tijms",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "x + 442",
  year =         "2007",
  ISBN =         "0-511-34626-3 (e-book), 0-511-35003-1 (e-book),
                 0-521-70172-4 (paperback)",
  ISBN-13 =      "978-0-511-34626-2 (e-book), 978-0-511-35003-0
                 (e-book), 978-0-521-70172-3 (paperback)",
  LCCN =         "QA273 .T48 2007",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Probabilities; Mathematical analysis; Chance;
                 Mathematics; Probability and Statistics; General;
                 Waarschijnlijkheidstheorie;
                 Wahrscheinlichkeitsverteilung",
  tableofcontents = "Probability questions \\
                 The law of large numbers and simulation \\
                 Probabilities in everyday life \\
                 Rare events and lotteries \\
                 Probability and statistics \\
                 Chance trees and Bayes' rule \\
                 Foundations of probability theory \\
                 Conditional probability and Bayes \\
                 Basic rules for discrete random variables \\
                 Continuous random variables \\
                 Jointly distributed random variables \\
                 Multivariate normal distribution \\
                 Conditional distributions \\
                 Generating functions \\
                 Markov chains",
}

@Article{Torres:2007:HDN,
  author =       "J. Torres and S. Fern{\'a}ndez and A. Gamero and A.
                 Sola",
  title =        "How do numbers begin? (the first digit law)",
  journal =      j-EUR-J-PHYS,
  volume =       "28",
  number =       "3",
  pages =        "L17--L25",
  month =        may,
  year =         "2007",
  CODEN =        "EJPHD4",
  DOI =          "https://doi.org/10.1088/0143-0807/28/3/N04",
  ISSN =         "0143-0807 (print), 1361-6404 (electronic)",
  ISSN-L =       "0143-0807",
  bibdate =      "Fri Feb 15 18:37:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://iopscience.iop.org/0143-0807/28/3/N04",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/0143-0807/",
  keywords =     "Benford's Law; Frank Benford; Simon Newcomb",
  remark-1 =     "From page L19: ``He [Newcomb] founded the American
                 Astronomical Society, and was its first president; he
                 was a successful scientist.''.",
  remark-2 =     "From page L19: ``His [Newcomb's] discovery went
                 unnoticed by the scientific community, in spite of the
                 fact that Newcomb was already a famous scientist at the
                 time. He continued working in physical and mathematical
                 astronomy, receiving honours for his career --- a
                 crater of Mars takes his name --- but he was also
                 responsible for a famous funny mistake: he tried to
                 demonstrate that an object heavier than air could not
                 fly, just months before the Wright brothers' first
                 one-man aeroplane flew in 1903. Far from retracting,
                 Newcomb said that an aeroplane for two or more people
                 could not fly, so aeroplanes would not be worthwhile
                 pursuing [3, 4]. He died in 1909, without even
                 remembering the matter of the first significant digit
                 law.''",
  remark-3 =     "From page L19: ``Frank Benford, a physicist working at
                 General Electric (who was the inventor of the electric
                 light pointer), \ldots{}''.",
}

@Article{Wells:2007:QPV,
  author =       "K. Wells and J. Chiverton and M. Partridge and M.
                 Barry and H. Kadhem and B. Ott",
  title =        "Quantifying the Partial Volume Effect in {PET} Using
                 {Benford's Law}",
  journal =      j-IEEE-TRANS-NUCL-SCI,
  volume =       "54",
  number =       "5",
  pages =        "1616--1625",
  month =        oct,
  year =         "2007",
  CODEN =        "IRNSAM",
  DOI =          "https://doi.org/10.1109/TNS.2007.903182",
  ISSN =         "0018-9499 (print), 1558-1578 (electronic)",
  ISSN-L =       "0018-9499",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2007ITNS...54.1616W",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Nuclear Science",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=23",
}

@Article{Yeh:2007:SMD,
  author =       "Hsiaw-Chan Yeh",
  title =        "Some multivariate discrete time series models for
                 dependent multivariate {Zipf} counts",
  journal =      "Bulletin of the Institute of Mathematics. Academia
                 Sinica. New Series",
  volume =       "2",
  number =       "1",
  pages =        "29--53",
  year =         "2007",
  CODEN =        "????",
  ISSN =         "0304-9825",
  ISSN-L =       "0304-9825",
  MRclass =      "62M10 (62H20)",
  MRnumber =     "2294107",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Bull. Inst. Math. Acad. Sin. (N.S.)",
  fjournal =     "Bulletin of the Institute of Mathematics. Academia
                 Sinica. New Series",
}

@Article{Aerts:2008:CDD,
  author =       "Walter Aerts and Geert {Van Campenhout} and Tom {Van
                 Caneghem}",
  title =        "Clustering in dividends: Do managers rely on cognitive
                 reference points?",
  journal =      "Journal of Economic Psychology",
  volume =       "29",
  number =       "3",
  pages =        "276--284",
  year =         "2008",
  DOI =          "https://doi.org/10.1016/j.joep.2007.10.003",
  ISSN =         "0167-4870 (print), 1872-7719 (electronic)",
  ISSN-L =       "0167-4870",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167487007000864",
  abstract =     "Prior studies (see e.g. [Rosch, E. (1975). Cognitive
                 reference points. Cognitive Psychology, {\bf 7},
                 532--547]) indicate that multiples of ten serve as
                 cognitive reference points with a view to perceiving
                 and evaluating numbers. In order to explore whether
                 managers set dividends per share (henceforth DPS) at or
                 just above a cognitive reference point, we perform a
                 digital analysis on {US} firms' {DPS} for the period
                 1995--2004. That is, based on the theory of cognitive
                 reference points, {DPS} of \$2.00 will be viewed as
                 being abnormally larger than {DPS} of \$1.99, whereas
                 the actual difference only amounts to a marginal
                 \$0.01. Results presented in this paper indicate that
                 managers fall back on cognitive reference points when
                 they set DPS, which shows in significantly more (fewer)
                 zeroes (large digits) in the second-from-the-left
                 position of {DPS} than would normally be expected.
                 Overall, results presented in this paper tally with
                 prior findings on odd-ending prices and price
                 clustering documented in related disciplines.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Cognitive psychology; Management",
}

@Article{Aono:2008:ISO,
  author =       "June Y. Aono and Liming Guan",
  title =        "The impact of {Sarbanes--Oxley} act on cosmetic
                 earnings management",
  journal =      "Research in Accounting Regulation",
  volume =       "20",
  number =       "0",
  pages =        "205--215",
  month =        oct,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1052-0457(07)00212-3",
  ISSN =         "1052-0457 (print), 2467-9895 (electronic)",
  ISSN-L =       "1052-0457",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1052045707002123",
  abstract =     "This study examines the mitigating effect of
                 Sarbanes--Oxley Act on cosmetic earnings management,
                 referred by Kinnunen and Koskela (2003) as earnings
                 manipulative behavior to round earnings such that they
                 result in an upward bias. This behavior reports income
                 numbers to achieve key cognitive reference points
                 represented by $ N \times $ 10k. Using Benford's Law,
                 our analysis compares the distribution of second digits
                 in reported annual net income for publicly listed {US}
                 companies between a 2-year periods before and after the
                 year 2002 when Sarbanes--Oxley Act went into effect.
                 Our empirical results suggest that, in the 2-year
                 period prior to the Act, there was evidence of cosmetic
                 earnings management. However, such behavior in
                 manipulating net income has noticeably decreased in the
                 period after the Act. This finding is consistent with
                 the notion that Sarbanes--Oxley Act has a deterring
                 impact on corporate America's manipulative behavior to
                 report earnings that achieve certain key reference
                 points.",
  acknowledgement = ack-nhfb,
  fjournal =     "Research in Accounting Regulation",
  keywords =     "Benford's Law",
}

@Article{Batty:2008:PSS,
  author =       "Michael Batty",
  title =        "Perspective: The Size, Scale, and Shape of Cities",
  journal =      j-SCIENCE,
  volume =       "318",
  number =       "5864",
  pages =        "769--771",
  day =          "8",
  month =        feb,
  year =         "2008",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.1151419",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Wed Feb 27 06:02:28 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/319/5864/769.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "200 tallest buildings in world; US cities of one
                 million (or more) population; Zipf's law",
}

@Article{Berger:2008:SDI,
  author =       "Arno Berger and Theodore P. Hill and Kent E.
                 Morrison",
  title =        "Scale-Distortion Inequalities for Mantissas of Finite
                 Data Sets",
  journal =      j-J-THEOR-PROBAB,
  volume =       "21",
  number =       "1",
  pages =        "97--117",
  month =        mar,
  year =         "2008",
  CODEN =        "JTPREO",
  DOI =          "https://doi.org/10.1007/s10959-007-0112-z",
  ISSN =         "0894-9840 (print), 1572-9230 (electronic)",
  ISSN-L =       "0894-9840",
  bibdate =      "Thu Aug 28 19:04:16 MDT 2014",
  bibsource =    "http://link.springer.com/journal/10959;
                 http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0894-9840&volume=21&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib",
  URL =          "http://link.springer.com/article/10.1007/s10959-007-0112-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Probability",
  journal-URL =  "http://link.springer.com/journal/10959",
}

@Article{Bhattacharya:2008:FAB,
  author =       "S. Bhattacharya and K. Kumar",
  title =        "Forensic Accounting and {Benford's Law} [In the
                 Spotlight]",
  journal =      j-IEEE-SIGNAL-PROCESS-MAG,
  volume =       "25",
  number =       "2",
  pages =        "152--150",
  month =        mar,
  year =         "2008",
  CODEN =        "ISPRE6",
  DOI =          "https://doi.org/10.1109/MSP.2007.914724",
  ISSN =         "1053-5888 (print), 1558-0792 (electronic)",
  ISSN-L =       "1053-5888",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008ISPM...25..152B",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE signal processing magazine",
}

@Article{Brown:2008:CSP,
  author =       "Philip Brown and Jason Mitchell",
  title =        "Culture and stock price clustering: Evidence from {The
                 Peoples' Republic of China}",
  journal =      "Pacific-Basin Finance Journal",
  volume =       "16",
  number =       "1 2",
  pages =        "95--120",
  year =         "2008",
  DOI =          "https://doi.org/10.1016/j.pacfin.2007.04.005",
  ISSN =         "0927-538X (print), 1879-0585 (electronic)",
  ISSN-L =       "0927-538X",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Behavioral Finance in Asia",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0927538X0700025X",
  abstract =     "Price clustering is the tendency of prices to be
                 observed more frequently at some numbers than others.
                 It results from human bias and from haziness or
                 imprecise beliefs about underlying value. To many
                 Chinese, the number 8 is attractive because it is
                 considered lucky, while 4 is unlucky and to be avoided.
                 We conduct a tightly controlled experiment to determine
                 whether a culturally heuristic number preference
                 exists, by studying trading on the Shanghai and
                 Shenzhen stock exchanges, which historically have been
                 relatively segmented along cultural lines. Our results
                 are extremely clear. For much of our sample period
                 (1994 2002), the prices of A-shares (mostly held by
                 Chinese organisations or individuals) traded on the
                 Shanghai stock exchange were more than twice as likely
                 to end in 8, than 4. Similarly, for A-shares traded on
                 the Shenzhen stock exchange a preference for 8 was
                 found. Preference for 8 on both exchanges was initially
                 very strong, but has weakened somewhat over time. It is
                 observed in opening, high and low as well as closing
                 prices, reinforcing its pervasiveness. Overall, the
                 cultural preference manifest in the prices of A-shares
                 is widespread in both markets and its presence is
                 accentuated once other factors that influence price
                 clustering are taken into account. The preference for 8
                 was much weaker for B-shares, which largely have been
                 held by foreigners.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Feng shui; Number preferences; Shanghai
                 and Shenzhen stock exchanges; Stock price clustering",
}

@Article{Chakravorty:2008:TAE,
  author =       "Douglas N. Hales and V. Sridharan and Abirami
                 Radhakrishnan and Satya S. Chakravorty and Samia M.
                 Siha",
  title =        "Testing the accuracy of employee-reported data: An
                 inexpensive alternative approach to traditional
                 methods",
  journal =      j-EUR-J-OPER-RES,
  volume =       "189",
  number =       "3",
  pages =        "583--593",
  day =          "16",
  month =        sep,
  year =         "2008",
  CODEN =        "EJORDT",
  DOI =          "https://doi.org/10.1016/j.ejor.2006.09.092",
  ISSN =         "0377-2217 (print), 1872-6860 (electronic)",
  ISSN-L =       "0377-2217",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Operational Research",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03772217",
  keywords =     "Benford's Law",
  xxauthor =     "S. Chakravorty and Samia M. Siha",
}

@Article{Costas:2008:NCC,
  author =       "Eduardo Costas and Victoria L{\'o}pez-Rodas and F.
                 Javier Toro and Antonio Flores-Moya",
  title =        "The number of cells in colonies of the cyanobacterium
                 {{\em Microcystis aeruginosa\/}} satisfies {Benford}'s
                 law",
  journal =      j-AQUAT-BOT,
  volume =       "89",
  number =       "3",
  pages =        "341--343",
  month =        oct,
  year =         "2008",
  CODEN =        "AQBODS",
  DOI =          "https://doi.org/10.1016/j.aquabot.2008.03.011",
  ISSN =         "0304-3770 (print), 1879-1522 (electronic)",
  ISSN-L =       "0304-3770",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304377008000533",
  abstract =     "Nowadays, numerous power- or scaling-laws are
                 encountered in many fields of biology: an example is
                 Benford's law. According to this law, the first
                 significant digit of any given series of numbers is
                 figure 1 more often than figure 2, which in turn
                 appears more often than 3, and so on. Here we show that
                 number of cells per colony in the cyanobacterium
                 Microcystis aeruginosa (F. T. K{\"u}tzing), randomly
                 isolated from different reservoirs and lakes from
                 Andalusia (S Spain), was very variable (with figures
                 differing up to five orders of magnitude). However, the
                 distribution of the number of cells per colony
                 satisfies Benford's law. This situation could be much
                 more general in colonial cyanobacteria.",
  acknowledgement = ack-nhfb,
  fjournal =     "Aquatic Botany",
  keywords =     "Benford's Law; Colony; Microcystis aeruginosa",
}

@Article{Depken:2008:BZB,
  author =       "Craig A. {Depken II}",
  title =        "{Benford}, {Zipf} and the blogosphere",
  journal =      j-APPL-ECON-LETT,
  volume =       "15",
  number =       "9",
  pages =        "689--692",
  month =        "????",
  year =         "2008",
  DOI =          "https://doi.org/10.1080/13504850600735270",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Sat Jan 07 09:18:33 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504850600735270",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  journal-URL =  "http://www.tandfonline.com/loi/rael20",
  onlinedate =   "04 Jul 2008",
}

@Article{Dumbgen:2008:EBA,
  author =       "Lutz D{\"u}mbgen and Christoph Leuenberger",
  title =        "Explicit bounds for the approximation error in
                 {Benford}'s law",
  journal =      j-ELECTRON-COMMUN-PROBAB,
  volume =       "13",
  pages =        "99--112",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1083-589X",
  ISSN-L =       "1083-589X",
  MRclass =      "60E15 (60F99)",
  MRnumber =     "2386066 (2009b:60056)",
  MRreviewer =   "Pieter C. Allaart",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://arxiv.org/abs/0705.4488;
                 http://weber.math.washington.edu/~ejpecp/ECP/index.php",
  abstract =     "Benford's law states that for many random variables $
                 X > 0 $ its leading digit $ D = D(X) $ satisfies
                 approximately the equation $ P(D = d) = \log_{10}(1 + 1
                 / d) $ for $ d = 1, 2, \ldots {}, 9 $. This phenomenon
                 follows from another, maybe more intuitive fact,
                 applied to $ Y \coloneq \log_{10}(X) $: For many real
                 random variables $Y$, the remainder $ U \coloneq Y -
                 \floor (Y) $ is approximately uniformly distributed on
                 $ [0, 1) $. The present paper provides new explicit
                 bounds for the latter approximation in terms of the
                 total variation of the density of $Y$ or some
                 derivative of it. These bounds are an interesting
                 alternative to traditional Fourier methods which yield
                 mostly qualitative results. As a by-product we obtain
                 explicit bounds for the approximation error in
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Communications in Probability",
  journal-URL =  "http://ecp.ejpecp.org/",
}

@Article{Gauvrit:2008:PLB,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Pourquoi la loi de {Benford} n'est pas
                 myst{\'e}rieuse. ({French}) [{Why} {Benford}'s law is
                 not mysterious]",
  journal =      "Math{\'e}matiques et Sciences Humaines = Mathematics
                 and Social Sciences",
  volume =       "46",
  number =       "182",
  pages =        "7--15",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0987-6936 (print), 1950-6821 (electronic)",
  ISSN-L =       "0987-6936",
  MRclass =      "62A01 (91E10)",
  MRnumber =     "2433183 (2009f:62008)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ehess.fr/revue-msh/pdf/N182R1280.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Sci. Hum. Math. Soc. Sci.",
  fjournal =     "Math{\'e}matiques et Sciences Humaines= Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Grandison:2008:BPK,
  author =       "S. Grandison and R. J. Morris",
  title =        "Biological Pathway Kinetic Rate Constants Are
                 Scale-Invariant",
  journal =      j-BIOINFORMATICS,
  volume =       "24",
  number =       "6",
  pages =        "741--743",
  month =        "????",
  year =         "2008",
  DOI =          "https://doi.org/10.1093/bioinformatics/btn041",
  ISSN =         "1367-4803 (print), 1367-4811 (electronic)",
  ISSN-L =       "1367-4803",
  bibdate =      "Sat Sep 10 11:56:57 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ncbi.nlm.nih.gov/pubmed/18238786",
  acknowledgement = ack-nhfb,
  fjournal =     "Bioinformatics",
  journal-URL =  "http://bioinformatics.oxfordjournals.org/",
  keywords =     "Benford's Law",
}

@Article{Hales:2008:TAE,
  author =       "Douglas N. Hales and V. Sridharan and Abirami
                 Radhakrishnan and Satya S. Chakravorty and Samia M.
                 Siha",
  title =        "Testing the accuracy of employee-reported data: An
                 inexpensive alternative approach to traditional
                 methods",
  journal =      j-EUR-J-OPER-RES,
  volume =       "189",
  number =       "3",
  pages =        "583--593",
  year =         "2008",
  CODEN =        "EJORDT",
  DOI =          "https://doi.org/10.1016/j.ejor.2006.09.092",
  ISSN =         "0377-2217 (print), 1872-6860 (electronic)",
  ISSN-L =       "0377-2217",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377221706011702",
  abstract =     "Although Information Technology (IT) solutions improve
                 the collection and validation of operational data,
                 Operations Managers must often rely on self-reported
                 data from workers to make decisions. The problem with
                 this data is that they are subject to intentional
                 manipulation, thus reducing their suitability for
                 decision-making. A method of identifying manipulated
                 data, digital analysis, addresses this problem at low
                 cost. In this paper, we demonstrate how one uses this
                 method in real-world companies to validate
                 self-reported data from line workers. The results of
                 our study suggest that digital analysis estimates the
                 accuracy of employee reported data in operations
                 management, within limited contexts. These findings
                 lead to improved operating performance by providing a
                 tool for practitioners to exclude inaccurate
                 information.",
  acknowledgement = ack-nhfb,
  fjournal =     "European Journal of Operational Research",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03772217",
  keywords =     "Benford's Law; Digital analysis; Fraud detection;
                 Operations management; Plastics industry",
}

@Article{Hayes:2008:LED,
  author =       "S. J. Hayes",
  title =        "Letter to the {Editor}: Does Terminal Digit Preference
                 Occur in Pathology?",
  journal =      j-J-CLIN-PATHOL,
  volume =       "61",
  number =       "8",
  pages =        "975--976",
  month =        "????",
  year =         "2008",
  CODEN =        "JCPAAK",
  DOI =          "https://doi.org/10.1136/jcp.2008.057851",
  ISSN =         "0021-9746 (print), 1472-4146 (electronic)",
  ISSN-L =       "0021-9746",
  bibdate =      "Sat Sep 10 12:01:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jcp.bmj.com/content/61/8/975.2",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Pathology",
  journal-URL =  "http://jcp.bmj.com/content/by/year",
  keywords =     "Benford's Law",
}

@Article{Hayes:2008:TDP,
  author =       "S. J. Hayes",
  title =        "Terminal Digit Preference Occurs in Pathology
                 Reporting Irrespective of Patient Management
                 Implication",
  journal =      j-J-CLIN-PATHOL,
  volume =       "61",
  number =       "9",
  pages =        "1071--1072",
  month =        "????",
  year =         "2008",
  CODEN =        "JCPAAK",
  DOI =          "https://doi.org/10.1136/jcp.2008.059543",
  ISSN =         "0021-9746 (print), 1472-4146 (electronic)",
  ISSN-L =       "0021-9746",
  bibdate =      "Sat Sep 10 12:05:19 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jcp.bmj.com/content/61/9/1071.extract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Pathology",
  keywords =     "Benford's Law",
}

@Article{Hefeeda:2008:TMP,
  author =       "Mohamed Hefeeda and Osama Saleh",
  title =        "Traffic modeling and proportional partial caching for
                 peer-to-peer systems",
  journal =      j-IEEE-TRANS-NETWORKING,
  volume =       "16",
  number =       "6",
  pages =        "1447--1460",
  month =        dec,
  year =         "2008",
  CODEN =        "IEANEP",
  DOI =          "https://doi.org/10.1109/TNET.2008.918081",
  ISSN =         "1063-6692 (print), 1558-2566 (electronic)",
  ISSN-L =       "1063-6692",
  bibdate =      "Fri Mar 6 16:31:04 MST 2009",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
  abstract =     "Peer-to-peer (P2P) file sharing systems generate a
                 major portion of the Internet traffic, and this portion
                 is expected to increase in the future. We explore the
                 potential of deploying proxy caches in different
                 Autonomous Systems (ASes) with the goal of reducing the
                 cost incurred by Internet service providers and
                 alleviating the load on the Internet backbone. We
                 conduct an eight-month measurement study to analyze the
                 P2P traffic characteristics that are relevant to
                 caching, such as object popularity, popularity
                 dynamics, and object size. Our study shows that the
                 popularity of P2P objects can be modeled by a
                 Mandelbrot-Zipf distribution, and that several
                 workloads exist in P2P traffic. Guided by our findings,
                 we develop a novel caching algorithm for P2P traffic
                 that is based on object segmentation, and proportional
                 partial admission and eviction of objects. Our
                 trace-based simulations show that with a relatively
                 small cache size, a byte hit rate of up to 35\% can be
                 achieved by our algorithm, which is close to the byte
                 hit rate achieved by an off-line optimal algorithm with
                 complete knowledge of future requests. Our results also
                 show that our algorithm achieves a byte hit rate that
                 is at least 40\% more, and at most triple, the byte hit
                 rate of the common web caching algorithms. Furthermore,
                 our algorithm is robust in face of aborted downloads,
                 which is a common case in P2P systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE\slash ACM Transactions on Networking",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J771",
  keywords =     "internet measurement; network protocols; peer-to-peer
                 systems; traffic analysis; traffic modeling",
}

@Article{Huang:2008:IZL,
  author =       "Shi-Ming Huang and David C. Yen and Luen-Wei Yang and
                 Jing-Shiuan Hua",
  title =        "An investigation of {Zipf's Law} for fraud detection
                 {(DSS\# 06-10-1826R(2))}",
  journal =      j-DEC-SUPP-SYS,
  volume =       "46",
  number =       "1",
  pages =        "70--83",
  month =        dec,
  year =         "2008",
  CODEN =        "DSSYDK",
  DOI =          "https://doi.org/10.1016/j.dss.2008.05.003",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923608001073",
  abstract =     "Fraud risk is higher than ever before. Unfortunately,
                 many auditors lack the expertise to deal with the
                 related risks. The objectives of this research are to
                 develop an innovative fraud detection mechanism on the
                 basis of Zipf's Law. The purpose of this technique is
                 to assist auditors in reviewing the overwhelming
                 volumes of datasets and identifying any potential fraud
                 records. The authors conducted Quasi-experiment
                 research on the KDDCUP'99 benchmark intrusion detection
                 dataset to verify the performance of the proposed
                 mechanism. The simulation experimental results
                 demonstrate that Zipf Analysis can assist auditors to
                 locate the source of suspicion and further enhance the
                 resulting audit processes.",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law; Fraud detection; Misclassification cost
                 matrix; Quasi-experiment research; Zipf's Law",
}

@Article{Humenberger:2008:EBB,
  author =       "H. Humenberger",
  title =        "{Eine elementarmathematische Begr{\"u}ndung des
                 Benford-Gesetzes}. ({German}) [{An} elementary
                 mathematical derivation of the {Benford Law}]",
  journal =      "Der Mathematikunterricht",
  volume =       "54",
  number =       "??",
  pages =        "24--34",
  month =        "????",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "0025-5807",
  ISSN-L =       "0025-5807",
  bibdate =      "Fri Nov 18 11:59:44 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.oemg.ac.at/DK/Didaktikhefte/2008%2520Band%252041/VortragHumenberger.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Ipeirotis:2008:CAH,
  author =       "Panagiotis G. Ipeirotis and Luis Gravano",
  title =        "Classification-aware hidden-web text database
                 selection",
  journal =      j-TOIS,
  volume =       "26",
  number =       "2",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2008",
  CODEN =        "ATISET",
  DOI =          "https://doi.org/10.1145/1344411.1344412",
  ISSN =         "1046-8188",
  ISSN-L =       "0734-2047",
  bibdate =      "Thu Jun 12 16:52:34 MDT 2008",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tois/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Many valuable text databases on the web have
                 noncrawlable contents that are ``hidden'' behind search
                 interfaces. Metasearchers are helpful tools for
                 searching over multiple such ``hidden-web'' text
                 databases at once through a unified query interface. An
                 important step in the metasearching process is database
                 selection, or determining which databases are the most
                 relevant for a given user query. The state-of-the-art
                 database selection techniques rely on statistical
                 summaries of the database contents, generally including
                 the database vocabulary and associated word
                 frequencies. Unfortunately, hidden-web text databases
                 typically do not export such summaries, so previous
                 research has developed algorithms for constructing
                 approximate content summaries from document samples
                 extracted from the databases via querying. We present a
                 novel ``focused-probing'' sampling algorithm that
                 detects the topics covered in a database and adaptively
                 extracts documents that are representative of the topic
                 coverage of the database. Our algorithm is the first to
                 construct content summaries that include the
                 frequencies of the words in the database.
                 Unfortunately, Zipf's law practically guarantees that
                 for any relatively large database, content summaries
                 built from moderately sized document samples will fail
                 to cover many low-frequency words; in turn, incomplete
                 content summaries might negatively affect the database
                 selection process, especially for short queries with
                 infrequent words. To enhance the sparse document
                 samples and improve the database selection decisions,
                 we exploit the fact that topically similar databases
                 tend to have similar vocabularies, so samples extracted
                 from databases with a similar topical focus can
                 complement each other. We have developed two database
                 selection algorithms that exploit this observation. The
                 first algorithm proceeds hierarchically and selects the
                 best categories for a query, and then sends the query
                 to the appropriate databases in the chosen categories.
                 The second algorithm uses ``shrinkage,'' a statistical
                 technique for improving parameter estimation in the
                 face of sparse data, to enhance the database content
                 summaries with category-specific words. We describe how
                 to modify existing database selection algorithms to
                 adaptively decide (at runtime) whether shrinkage is
                 beneficial for a query. A thorough evaluation over a
                 variety of databases, including 315 real web databases
                 as well as TREC data, suggests that the proposed
                 sampling methods generate high-quality content
                 summaries and that the database selection algorithms
                 produce significantly more relevant database selection
                 decisions and overall search results than existing
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Information Systems (TOIS)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J779",
  keywords =     "database selection; Distributed information retrieval;
                 web search",
}

@Article{Jager:2008:DAD,
  author =       "Hendrik Jager and Pierre Liardet",
  title =        "Distributions arithm{\'e}tiques des d{\'e}nominateurs
                 de convergents de fractions continues. ({French})
                 [Arithmetic distributions of the denominators of
                 continued fractions]",
  journal =      "Proceedings of the Koninklijke Nederlandse Akademie
                 van Wetenschappen, Series A, Indagationes
                 mathematicae",
  volume =       "91",
  number =       "2",
  pages =        "181--197",
  day =          "20",
  month =        jun,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/S1385-7258(88)80026-X",
  ISSN =         "1385-7258 (print), 1878-5972 (electronic)",
  ISSN-L =       "1385-7258",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S138572588880026X",
  acknowledgement = ack-nhfb,
  fjournal =     "Indagationes Mathematicae (Proceedings)",
  keywords =     "Benford's Law",
  language =     "French",
  xxjournal =    "Indagationes Mathematicae (Proceedings)",
}

@Article{Jang:2008:CDH,
  author =       "Dennis Jang and Jung Uk Kang and Alex Kruckman and Jun
                 Kudo and Steven J. Miller",
  title =        "Chains of Distributions, Hierarchical {Bayesian}
                 Models and {Benford's Law}",
  journal =      "arxiv.org",
  pages =        "1--15",
  day =          "27",
  month =        may,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Thu Oct 13 07:41:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J;
                 http://arxiv.org/abs/0805.4226",
  abstract =     "Kossovsky recently conjectured that the distribution
                 of leading digits of a chain of probability
                 distributions converges to Benford's law as the length
                 of the chain grows. We prove his conjecture in many
                 cases, and provide an interpretation in terms of
                 products of independent random variables and a central
                 limit theorem. An interesting consequence is that in
                 hierarchical Bayesian models priors tend to satisfy
                 Benford's Law as the number of levels of the hierarchy
                 increases, which allows us to develop some simple tests
                 (based on Benford's law) to test proposed models. We
                 give explicit formulas for the error terms as sums of
                 Mellin transforms, which converges extremely rapidly as
                 the number of terms in the chain grows. We may
                 interpret our results as showing that certain Markov
                 chain Monte Carlo processes are rapidly mixing to
                 Benford's law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  pagecount =    "15",
  primaryclass = "math.PR",
}

@Article{Jelenkovic:2008:CMS,
  author =       "Predrag R. Jelenkovi{\'c} and Xiaozhu Kang",
  title =        "Characterizing the miss sequence of the {LRU} cache",
  journal =      j-SIGMETRICS,
  volume =       "36",
  number =       "2",
  pages =        "119--121",
  month =        sep,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1453175.1453203",
  ISSN =         "0163-5999 (print), 1557-9484 (electronic)",
  ISSN-L =       "0163-5999",
  bibdate =      "Wed Aug 25 07:31:09 MDT 2010",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigmetrics.bib",
  abstract =     "Renewed interest in caching systems stems from their
                 wide-spread use for reducing the document download
                 latency over the Internet. Since caches are usually
                 organized in a hierarchical manner, it is important to
                 study the performance properties of tandem caches. The
                 first step in understanding this problem is to
                 characterize the miss stream from one single cache
                 since it represents the input to the next level cache.
                 In this regard, we discover that the miss stream from
                 one single cache is approximated well by the
                 superposition of a number of asymptotically independent
                 renewal processes. Interestingly, when this weakly
                 correlated miss sequence is fed into another cache,
                 this barely observable correlation can lead to
                 measurably different caching performance when compared
                 to the independent reference model. This result is
                 likely to enable the development of a rigorous analysis
                 of the tandem cache performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGMETRICS Performance Evaluation Review",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J618",
  keywords =     "average-case analysis; cache fault probability;
                 hierarchical caching; least-recently-used caching; web
                 caching; Zipf's law",
}

@Article{Kafri:2008:SIS,
  author =       "Oded Kafri",
  title =        "Sociological Inequality and the {Second Law}",
  journal =      "ArXiv e-prints",
  year =         "2008",
  bibdate =      "Mon Nov 21 06:41:29 2011",
  bibsource =    "http://dblp.uni-trier.de;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/0805.3206",
  abstract =     "There are two fair ways to distribute particles in
                 boxes. The first way is to divide the particles equally
                 between the boxes. The second way, which is calculated
                 here, is to score fairly the particles between the
                 boxes. The obtained power law distribution function
                 yields an uneven distribution of particles in boxes. It
                 is shown that the obtained distribution fits well to
                 sociological phenomena, such as the distribution of
                 votes in polls and the distribution of wealth and
                 Benford's law.",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krakar:2008:ABL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Boris Aurer and Miroslav Ba{\'c}a",
  booktitle =    "Proceedings of the 19th Central European Conference on
                 Information and Intelligent Systems (CECIS 2008)",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  publisher =    "Fakultet organizacije i informatike",
  address =      "Vara{\v{z}}din, Croatia",
  pages =        "187--193",
  year =         "2008",
  bibdate =      "Sun Nov 13 11:14:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Krakar:2008:EBL,
  author =       "Zdravko Krakar and Mario {\v{Z}}gela",
  editor =       "Mario Plenkovi{\'c}",
  booktitle =    "Society and Technology 2008",
  title =        "Evaluation of {Benford's Law}: application in stock
                 prices and stock turnover",
  publisher =    "Hrvatsko komunikolo{\v{s}}ko dru{\v{s}}tvo",
  address =      "Zagreb, Croatia",
  pages =        "57--71",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Nov 13 11:18:37 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  remark =       "International Federation of Communication Studies,
                 Grafi{\v{c}}ki fakultet Sveu{\v{c}}ili{\v{s}}ta u
                 Zagrebu.",
}

@Article{Linville:2008:PFN,
  author =       "Mark Linville",
  title =        "The Problem of False Negative Results in the Use of
                 Digit Analysis",
  journal =      "Journal of Applied Business Research",
  volume =       "24",
  number =       "1",
  pages =        "17--25",
  month =        "First Quarter",
  year =         "2008",
  DOI =          "https://doi.org/10.19030/jabr.v24i1.1363",
  ISSN =         "0892-7626 (print), 2157-8834 (electronic)",
  ISSN-L =       "0892-7626",
  bibdate =      "Thu Oct 13 07:34:30 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.cluteinstitute.com/ojs/index.php/JABR/article/view/1363",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Appl. Bus. Res.",
  journal-URL =  "http://journals.cluteonline.com/index.php/JABR",
  keywords =     "Benford's Law",
}

@Article{Liu:2008:MNS,
  author =       "Cheng-Shi Liu",
  title =        "Maximal non-symmetric entropy leads naturally to
                 {Zipf}'s law",
  journal =      j-FRACTALS,
  volume =       "16",
  number =       "1",
  pages =        "99--101",
  year =         "2008",
  CODEN =        "FRACEG",
  DOI =          "https://doi.org/10.1142/S0218348X08003788",
  ISSN =         "0218-348X",
  ISSN-L =       "0218-348X",
  MRclass =      "94A17 (94A15)",
  MRnumber =     "2399875 (2009c:94027)",
  MRreviewer =   "Yasuichi Horibe",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Fractals. Complex Geometry, Patterns, and Scaling in
                 Nature and Society",
  journal-URL =  "http://www.worldscientific.com/loi/fractals",
}

@Article{Lolbert:2008:NEG,
  author =       "Tam{\'a}s Lolbert",
  title =        "On the non-existence of a general {Benford}'s law",
  journal =      j-MATH-SOC-SCI,
  volume =       "55",
  number =       "2",
  pages =        "103--106",
  month =        mar,
  year =         "2008",
  CODEN =        "MSOSDD",
  DOI =          "https://doi.org/10.1016/j.mathsocsci.2007.09.001",
  ISSN =         "0165-4896 (print), 1879-3118 (electronic)",
  ISSN-L =       "0165-4896",
  MRclass =      "60A10 (60E10)",
  MRnumber =     "2391902",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165489607000935",
  abstract =     "Benford's law states that in randomly collected
                 numbers certain digits are more often leading digits
                 than others. More formally: the general law states that
                 the mantissae follow the logarithmic distribution in
                 any base. Benford's law was recognized by many
                 mathematicians so that several possible explanations
                 have been derived, but several questions are still
                 open. Applications are widespread, for example an
                 auditing technique (the so-called digital analysis),
                 which is employed around the world by internal revenue
                 services to detect tax fraud, is based on this
                 phenomenon.\par

                 In this paper it will be shown that there exists no
                 probability measure that would obey Benford's law for
                 any base, but if the set of possible bases does not
                 exceed a given upper limit, most real-life
                 distributions obey, or can be transformed to obey
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Social Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01654896",
  keywords =     "Benford's Law; Characteristic function; Mantissa;
                 Numeral base",
}

@Article{Luque:2008:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of primes and {Riemann}
                 zeta zeros tend to uniformity following a
                 size-dependent generalized {Benford}'s law",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2008",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See published paper \cite {Luque:2009:FDF}.",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0811.3302L;
                 http://arxiv.org/abs/0811.3302",
  abstract =     "Prime numbers seem to distribute among the natural
                 numbers with no other law than that of chance, however
                 its global distribution presents a quite remarkable
                 smoothness. Such interplay between randomness and
                 regularity has motivated scientists of all ages to
                 search for local and global patterns in this
                 distribution that eventually could shed light into the
                 ultimate nature of primes. In this work we show that a
                 generalization of the well known first-digit Benford's
                 law, which addresses the rate of appearance of a given
                 leading digit $d$ in data sets, describes with
                 astonishing precision the statistical distribution of
                 leading digits in the prime numbers sequence. Moreover,
                 a reciprocal version of this pattern also takes place
                 in the sequence of the nontrivial Riemann zeta zeros.
                 We prove that the prime number theorem is, in the last
                 analysis, the responsible of these patterns. Some new
                 relations concerning the prime numbers distribution are
                 also deduced, including a new approximation to the
                 counting function $ \pi (n) $. Furthermore, some
                 relations concerning the statistical conformance to
                 this generalized Benford's law are derived. Some
                 applications are finally discussed.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0811.3302",
  keywords =     "Mathematics - Number Theory, Mathematics -
                 Probability, Mathematics - Statistics",
  pagecount =    "20",
  primaryclass = "math.NT",
}

@Article{Maillart:2008:ETZ,
  author =       "T. Maillart and D. Sornette and S. Spaeth and G. von
                 Krogh",
  title =        "Empirical Tests of {Zipf's Law} Mechanism in Open
                 Source {Linux} Distribution",
  journal =      j-PHYS-REV-LET,
  volume =       "101",
  number =       "21",
  pages =        "218701",
  day =          "19",
  month =        nov,
  year =         "2008",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.101.218701",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/linux.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.101.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Manin:2008:ZLA,
  author =       "Dmitrii Y. Manin",
  title =        "{Zipf's Law} and Avoidance of Excessive Synonymy",
  journal =      j-COGN-SCI,
  volume =       "32",
  number =       "7",
  pages =        "1075--1098",
  year =         "2008",
  CODEN =        "COGSD5",
  DOI =          "https://doi.org/10.1080/03640210802020003",
  ISSN =         "0364-0213 (print), 1551-6709 (electronic)",
  ISSN-L =       "0364-0213",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognitive Science",
  keywords =     "Semantics; Synonymy; Word frequency; Word meaning;
                 Zipf's law",
}

@Article{Mayr:2008:EBE,
  author =       "Philipp Mayr",
  title =        "An evaluation of {Bradfordizing} Effects",
  journal =      j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
  volume =       "2",
  number =       "2",
  pages =        "21--27",
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09737766.2008.10700850",
  ISSN =         "0973-7766 (print), 2168-930X (electronic)",
  ISSN-L =       "0973-7766",
  bibdate =      "Thu Sep 10 17:47:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Collnet Journal of Scientometrics and Information
                 Management",
  journal-URL =  "http://www.tandfonline.com/loi/tsim20",
}

@InProceedings{Mebane:2008:EFO,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{The American Electoral Process conference, Center for
                 the Study of Democratic Politics, Princeton University,
                 May 1--3, 2008}",
  title =        "Election Forensics: Outlier and Digit Tests in
                 {America} and {Russia}",
  publisher =    "????",
  address =      "????",
  pages =        "i + 26",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:08:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/aep2008.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Mebane:2008:EFSa,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "R. Michael Alvarez and Thad E. Hall and Susan D.
                 Hyde",
  booktitle =    "{The Art and Science of Studying Election Fraud:
                 Detection, Prevention, and Consequences}",
  title =        "Election Forensics: The Second-digit {Benford's Law}
                 Test and Recent {American Presidential} Elections",
  publisher =    "Brookings Institution",
  address =      "Washington, DC, USA",
  pages =        "ii + 30",
  year =         "2008",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Feb 16 12:04:22 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Preprint dated 3 November 2006.",
  URL =          "http://www.umich.edu/~wmebane/fraud06.pdf",
  acknowledgement = ack-nhfb,
  remark =       "An earlier version of this paper was presented at the
                 Election Fraud Conference, Salt Lake City, Utah,
                 September 29--30, 2006.",
}

@InCollection{Mebane:2008:EFSb,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Election forensics: the second-digit {Benford's Law}
                 test and recent {American} presidential elections",
  crossref =     "Alvarez:2008:EFD",
  pages =        "??--??",
  year =         "2008",
  bibdate =      "Sat Sep 10 14:25:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Miller:2008:MCL,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "The modulo $1$ central limit theorem and {Benford's
                 Law} for products",
  journal =      "International Journal of Algebra",
  volume =       "2",
  number =       "3",
  pages =        "119--130",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1312-8868 (print), 1314-7595 (electronic)",
  ISSN-L =       "1312-8868",
  MRclass =      "60F05 (11K06 42A10)",
  MRnumber =     "2417189 (2009e:60053)",
  MRreviewer =   "Gutti J. Babu",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.m-hikari.com/ija/ija-password-2008/ija-password1-4-2008/millerIJA1-4-2008.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Algebra",
  fjournal =     "International Journal of Algebra",
  journal-URL =  "http://www.m-hikari.com/ija/index.html",
}

@Article{Miller:2008:OSB,
  author =       "Steven J. Miller and Mark J. Nigrini",
  title =        "Order statistics and {Benford}'s law",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "382948:1--382948:19",
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1155/2008/382948",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "62G30 (62E10)",
  MRnumber =     "2461421 (2010c:62168)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 382948.",
  URL =          "http://arxiv.org/abs/math/0601344;
                 https://www.hindawi.com/journals/ijmms/2008/382948/",
  abstract =     "Fix a base $B$ and let zeta have the standard
                 exponential distribution; the distribution of digits of
                 zeta base $B$ is known to be very close to Benford's
                 Law. If there exists a $C$ such that the distribution
                 of digits of $C$ times the elements of some set is the
                 same as that of zeta, we say that set exhibits shifted
                 exponential behavior base $B$ (with a shift of $ \log_B
                 C \bmod 1 $ ). Let $ X_1, \ldots {}, X_N $ be
                 independent identically distributed random variables.
                 If the $ X_i $'s are drawn from the uniform
                 distribution on $ [0, L] $, then as $ N \to \infty $
                 the distribution of the digits of the differences
                 between adjacent order statistics converges to shifted
                 exponential behavior (with a shift of $ \log_B L / N
                 \bmod 1 $ ). By differentiating the cumulative
                 distribution function of the logarithms modulo 1,
                 applying Poisson Summation and then integrating the
                 resulting expression, we derive rapidly converging
                 explicit formulas measuring the deviations from
                 Benford's Law. Fix a delta in $ (0, 1) $ and choose $N$
                 independent random variables from any compactly
                 supported distribution with uniformly bounded first and
                 second derivatives and a second order Taylor series
                 expansion at each point. The distribution of digits of
                 any $ N^\delta $ consecutive differences {\em and\/}
                 all $ N - 1 $ normalized differences of the order
                 statistics exhibit shifted exponential behavior. We
                 derive conditions on the probability density which
                 determine whether or not the distribution of the digits
                 of all the un-normalized differences converges to
                 Benford's Law, shifted exponential behavior, or
                 oscillates between the two, and show that the Pareto
                 distribution leads to oscillating behavior.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  keywords =     "Benford's Law",
  pagecount =    "19",
}

@Article{Mitchell:2008:TST,
  author =       "James G. Mitchell and Laurent Seuront",
  title =        "Towards a seascape topology {II}: {Zipf} analysis of
                 one-dimensional patterns",
  journal =      j-J-MAR-SYST,
  volume =       "69",
  number =       "3--4",
  pages =        "328--338",
  month =        feb,
  year =         "2008",
  CODEN =        "JMASE5",
  DOI =          "https://doi.org/10.1016/j.jmarsys.2006.03.026",
  ISSN =         "0924-7963 (print), 1879-1573 (electronic)",
  ISSN-L =       "0924-7963",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0924796307000632",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Marine Systems",
  keywords =     "Zipf's Law",
}

@Article{Mizuno:2008:PLE,
  author =       "Takayuki Mizuno and Masahiro Toriyama and Takao Terano
                 and Misako Takayasu",
  title =        "{Pareto} law of the expenditure of a person in
                 convenience stores",
  journal =      j-PHYSICA-A,
  volume =       "387",
  number =       "15",
  pages =        "3931--3935",
  year =         "2008",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2008.01.059",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "91B82",
  MRnumber =     "2586890",
  bibdate =      "Mon Feb 18 17:05:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Ni:2008:BLH,
  author =       "D. Ni and Z. Ren",
  title =        "{Benford}'s law and half-lives of unstable nuclei",
  journal =      j-EUR-PHYS-J-A,
  volume =       "38",
  pages =        "251--255",
  month =        dec,
  year =         "2008",
  CODEN =        "EPJAFV",
  DOI =          "https://doi.org/10.1140/epja/i2008-10680-8",
  ISSN =         "1434-6001 (print), 1434-601X (electronic)",
  ISSN-L =       "1434-6001",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008EPJA...38..251N",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
  journal-URL =  "http://www.springerlink.com/content/1434-6001",
}

@Article{Pain:2008:BLC,
  author =       "Jean-Christophe Pain",
  title =        "{Benford}'s law and complex atomic spectra",
  journal =      j-PHYS-REV-E,
  volume =       "77",
  number =       "1",
  pages =        "012102:1--012102:3",
  month =        jan,
  year =         "2008",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.77.012102",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008PhRvE..77a2102P;
                 http://pre.aps.org/abstract/PRE/v77/i1/e012102",
  abstract =     "We found that in transition arrays of complex atomic
                 spectra, the strengths of electric-dipolar lines obey
                 Benford's law, which means that their significant
                 digits follow a logarithmic distribution favoring the
                 smallest values. This indicates that atomic processes
                 result from the superposition of uncorrelated
                 probability laws and that the occurrence of digits
                 reflects the constraints induced by the selection
                 rules. Furthermore, Benford's law can be a useful test
                 of theoretical spectroscopic models. Its applicability
                 to the statistics of electric-dipolar lines can be
                 understood in the framework of random matrix theory and
                 is consistent with the Porter-Thomas law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eid =          "012102",
  eprint =       "0801.0946",
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Probability theory, Oscillator strengths, lifetimes,
                 transition moments, Other topics in the theory of the
                 electronic structure of atoms and molecules",
  pagecount =    "3",
  primaryclass = "quant-ph",
}

@Article{Petek:2008:PNH,
  author =       "Marija Petek",
  title =        "Personal name headings in {COBIB}: Testing {Lotka}'s
                 Law",
  journal =      j-SCIENTOMETRICS,
  volume =       "75",
  number =       "1",
  pages =        "175--188",
  month =        apr,
  year =         "2008",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-007-1829-2",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:03 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-007-1829-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Ravikumar:2008:BND,
  author =       "Bala Ravikumar",
  title =        "The {Benford--Newcomb} Distribution and Unambiguous
                 Context-Free Languages",
  journal =      j-INT-J-FOUND-COMP-SCI,
  volume =       "19",
  number =       "3",
  pages =        "717--727",
  month =        jun,
  year =         "2008",
  CODEN =        "IFCSEN",
  DOI =          "https://doi.org/10.1142/S0129054108005905",
  ISSN =         "0129-0541 (print), 1793-6373 (electronic)",
  ISSN-L =       "0129-0541",
  MRclass =      "68Q42 (68Q25 68Q45)",
  MRnumber =     "2417964 (2009h:68068)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://ejournals.wspc.com.sg/ijfcs/mkt/archive.shtml;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Foundations of Computer
                 Science (IJFCS)",
  journal-URL =  "http://www.worldscientific.com/loi/ijfcs",
}

@Article{Ristic:2008:GSP,
  author =       "Miroslav M. Risti{\'c}",
  title =        "A generalized semi-{Pareto} minification process",
  journal =      j-STAT-PAPERS,
  volume =       "49",
  number =       "2",
  pages =        "343--351",
  month =        apr,
  year =         "2008",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-006-0017-4",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:27 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-006-0017-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{Schurger:2008:EBS,
  author =       "Klaus Sch{\"u}rger",
  title =        "Extensions of {Black--Scholes} processes and
                 {Benford's Law}",
  journal =      j-STOCH-PROC-APPL,
  volume =       "118",
  number =       "7",
  pages =        "1219--1243",
  month =        jul,
  year =         "2008",
  CODEN =        "STOPB7",
  DOI =          "https://doi.org/10.1016/j.spa.2007.07.017",
  ISSN =         "0304-4149 (print), 1879-209X (electronic)",
  ISSN-L =       "0304-4149",
  MRclass =      "60F10 (60G44 91B02 91B28)",
  MRnumber =     "2428715 (2009g:60037)",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0304414907001391",
  abstract =     "Let $Z$ be a stochastic process of the form $ Z (t) =
                 Z (0) \exp (\mu t + X (t) - \langle X \rangle_t / 2) $
                 where $ Z (0) > 0 $, $ \mu $ are constants, and $X$ is
                 a continuous local martingale having a deterministic
                 quadratic variation $ \langle X \rangle $ such that $
                 \langle X \rangle_t \to \infty $ as $ t \to \infty $.
                 We show that the mantissa (base $b$) of $ Z (t)$
                 (denoted by $ M (b) (Z (t))$) converges weakly to
                 Benford's Law as $ t \to \infty $. Supposing that $X$
                 satisfies a certain growth condition, we obtain large
                 deviation results for certain functionals (including
                 occupation time) of ($ M^{(b)} (Z(t))$). Similar
                 results are obtained in the discrete-time case. The
                 latter are used to construct a non-parametric test for
                 nonnegative processes ( $ Z (t)$ ) (based on the
                 observation of significant digits of ( $ Z (n)$ ) ) of
                 the null hypothesis $ H_0 (\sigma_0)$ which says that
                 $Z$ is a general Black--Scholes process having a
                 volatility $ \sigma \geq \sigma_0 ( > 0)$. Finally it
                 is shown that the mantissa of Brownian motion is not
                 even weakly convergent.",
  acknowledgement = ack-nhfb,
  fjournal =     "Stochastic Processes and Their Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03044149",
  keywords =     "Azuma's inequality; Benford's Law; Black Scholes
                 processes; Brownian motion; Exponential local
                 martingales; Large deviations; Leading digits;
                 Non-parametric hypothesis testing for processes;
                 Occupation time; Poisson's summation formula;
                 Significant digits; Strong theorems; Weak theorems",
}

@Article{Semboloni:2008:HCS,
  author =       "F. Semboloni",
  title =        "Hierarchy, cities size distribution and {Zipf}'s law",
  journal =      j-EUR-PHYS-J-B,
  volume =       "63",
  number =       "3",
  pages =        "295--301",
  year =         "2008",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1140/epjb/e2008-00203-1",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  MRclass =      "91D10 (82B99 91D25)",
  MRnumber =     "2421552 (2009f:91111)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "Zbl 1189.91174",
  acknowledgement = ack-nhfb,
  fjournal =     "The European Physical Journal B. Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
}

@Article{Seuront:2008:TST,
  author =       "Laurent Seuront and James G. Mitchell",
  title =        "Towards a seascape typology. {I}. {Zipf} versus
                 {Pareto} laws",
  journal =      j-J-MAR-SYST,
  volume =       "69",
  number =       "3--4",
  pages =        "310--327",
  month =        feb,
  year =         "2008",
  CODEN =        "JMASE5",
  DOI =          "https://doi.org/10.1016/j.jmarsys.2006.03.025",
  ISSN =         "0924-7963 (print), 1879-1573 (electronic)",
  ISSN-L =       "0924-7963",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0924796307000620",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Marine Systems",
  keywords =     "Zipf's Law",
}

@Article{Shaki:2008:RSN,
  author =       "Samuel Shaki and Martin H. Fischer",
  title =        "Reading space into numbers --- a cross-linguistic
                 comparison of the {SNARC} effect",
  journal =      j-COGNITION,
  volume =       "108",
  number =       "2",
  pages =        "590--599",
  month =        aug,
  year =         "2008",
  CODEN =        "CGTNAU",
  DOI =          "https://doi.org/10.1016/j.cognition.2008.04.001",
  ISSN =         "0010-0277 (print), 1873-7838 (electronic)",
  ISSN-L =       "0010-0277",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010027708000978",
  abstract =     "Small numbers are spontaneously associated with left
                 space and larger numbers with right space (the {SNARC}
                 effect), for example when classifying numbers by
                 parity. This effect is often attributed to reading
                 habits but a causal link has so far never been
                 documented. We report that bilingual Russian Hebrew
                 readers show a {SNARC} effect after reading Cyrillic
                 script (from left-to-right) that is significantly
                 reduced after reading Hebrew script (from
                 right-to-left). In contrast, they have similar {SNARC}
                 effects after listening to texts in either language.
                 These results support the view that spatially
                 directional scanning habits contribute to the spatial
                 association of numbers but also emphasize its
                 flexibility.",
  acknowledgement = ack-nhfb,
  fjournal =     "Cognition",
  keywords =     "Benford's Law; Mental number line; Reading direction;
                 Spatial Numerical Association of Response Codes
                 (SNARC); {SNARC}",
}

@Article{Volchenkov:2008:SUC,
  author =       "D. Volchenkov and Ph. Blanchard",
  title =        "Scaling and universality in city space syntax: Between
                 {Zipf} and {Matthew}",
  journal =      j-PHYSICA-A,
  volume =       "387",
  number =       "10",
  pages =        "2353--2364",
  day =          "1",
  month =        apr,
  year =         "2008",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2007.11.049",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437107012630",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Vuko:2008:UBL,
  author =       "Tina Vuko",
  title =        "Using {Benford's Law} to Detect Earnings Management
                 Practice: the Case of Listed Companies in {Croatia}",
  journal =      "Global Business \& Economics Anthology",
  volume =       "1",
  number =       "??",
  pages =        "69--74",
  month =        "????",
  year =         "2008",
  CODEN =        "????",
  ISSN =         "1553-1333",
  ISSN-L =       "1553-1333",
  bibdate =      "Sun Nov 13 11:10:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Watrin:2008:BLI,
  author =       "C. Watrin and R. Struffert and R. Ullmann",
  title =        "{Benford's Law}: An Instrument for Selecting Tax Audit
                 Targets?",
  journal =      "Review of Managerial Science",
  volume =       "2",
  number =       "3",
  pages =        "219--237",
  month =        nov,
  year =         "2008",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11846-008-0019-9",
  ISSN =         "1863-6683 (print), 1863-6691 (electronic)",
  ISSN-L =       "1863-6683",
  bibdate =      "Tue Nov 22 20:58:51 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11846-008-0019-9",
  acknowledgement = ack-nhfb,
}

@Article{Wu:2008:IEP,
  author =       "Shu-Fei Wu",
  title =        "Interval estimation for a {Pareto} distribution based
                 on a doubly type {II} censored sample",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "52",
  number =       "7",
  pages =        "3779--3788",
  day =          "15",
  month =        mar,
  year =         "2008",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:42:27 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947308000030",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Book{Ziliak:2008:CSS,
  author =       "Stephen Thomas Ziliak and Deirdre N. McCloskey",
  title =        "The Cult of Statistical Significance: How the Standard
                 Error Costs Us Jobs, Justice, and Lives",
  publisher =    "University of Michigan Press",
  address =      "Ann Arbor, MI, USA",
  pages =        "xxiii + 321",
  year =         "2008",
  ISBN =         "0-472-07007-X (cloth), 0-472-05007-9 (paperback)",
  ISBN-13 =      "978-0-472-07007-7 (cloth), 978-0-472-05007-9
                 (paperback)",
  LCCN =         "HB137 .Z55 2008",
  bibdate =      "Tue Dec 9 15:55:11 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Economics, cognition, and society",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0809/2007035401-d.html",
  acknowledgement = ack-nhfb,
  remark =       "This book has important comments on the battles among
                 Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
                 Pearson, supplementing the discussion of those
                 conflicts in \cite{McGrayne:2011:TWH}.",
  subject =      "economics; statistical methods; statistics; social
                 aspects; statistical hypothesis testing",
}

@Article{Ainsworth:2009:QSR,
  author =       "Richard Thompson Ainsworth and Urs Hengartner",
  title =        "{Quebec's Sales Recording Module (SRM)}: Fighting the
                 {Zapper}, {Phantomware}, and Tax Fraud with
                 technology",
  journal =      "Canadian Tax Journal",
  volume =       "57",
  number =       "4",
  pages =        "715--761",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0068-9823",
  ISSN-L =       "0068-9823",
  bibdate =      "Fri Mar 22 08:37:54 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.ctf.ca/ctfweb/Documents/PDF/2009ctj/09ctj4-ainsworth.pdf",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  journal-URL =  "https://www.ctf.ca/ctfweb",
  keywords =     "Benford's Law",
}

@TechReport{Alexander:2009:RUB,
  author =       "James C. Alexander",
  title =        "Remarks on the use of {Benford's Law}",
  type =         "Working paper",
  institution =  "Department of Mathematics and Cognitive Science, Case
                 Western Reserve University",
  address =      "Cleveland, OH, USA",
  day =          "23",
  month =        nov,
  year =         "2009",
  bibdate =      "Fri Mar 22 08:40:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1505147",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
}

@InProceedings{Altamirano:2009:GTU,
  author =       "Carlo Altamirano and Alberto Robledo",
  editor =       "J. Zhou",
  booktitle =    "Complex Sciences",
  title =        "Generalized Thermodynamics Underlying the Laws of
                 {Zipf} and {Benford}",
  volume =       "5",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "2232--??",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-3-642-02469-6_100",
  ISBN =         "3-642-02468-8",
  ISBN-13 =      "978-3-642-02468-9",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009cosc.conf.2232A",
  acknowledgement = ack-nhfb,
}

@Article{Anderson:2009:CRC,
  author =       "Thomas Anderson",
  title =        "Conference reviewing considered harmful",
  journal =      j-OPER-SYS-REV,
  volume =       "43",
  number =       "2",
  pages =        "108--116",
  month =        apr,
  year =         "2009",
  CODEN =        "OSRED8",
  DOI =          "https://doi.org/10.1145/1531793.1531815",
  ISSN =         "0163-5980 (print), 1943-586X (electronic)",
  ISSN-L =       "0163-5980",
  bibdate =      "Thu Apr 23 19:43:22 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "This paper develops a model of computer systems
                 research to help prospective authors understand the
                 often obscure workings of conference program
                 committees. We present data to show that the
                 variability between reviewers is often the dominant
                 factor as to whether a paper is accepted. We argue that
                 paper merit is likely to be Zipf distributed, making it
                 inherently difficult for program committees to
                 distinguish between most papers. We use game theory to
                 show that with noisy reviews and Zipf merit, authors
                 have an incentive to submit papers too early and too
                 often. These factors make conference reviewing, and
                 systems research as a whole, less efficient and less
                 effective. We describe some recent changes in
                 conference design to address these issues, and we
                 suggest some further potential improvements.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGOPS Operating Systems Review",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J597",
}

@TechReport{Ansari:2009:PAV,
  author =       "Ali Ansari",
  title =        "Preliminary Analysis of the Voting Figures in {Iran}'s
                 2009 {Presidential} Election",
  type =         "Report",
  number =       "MENAP PP 2009/01",
  institution =  "Chatham House and the Institute of Iranian Studies,
                 University of St Andrews",
  address =      "St Andrews, UK",
  day =          "21",
  month =        jun,
  year =         "2009",
  bibdate =      "Sat Sep 10 10:42:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.chathamhouse.org/sites/files/chathamhouse/public/Research/Middle%20East/iranelection0609.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Battersby:2009:SAH,
  author =       "Stephen Battersby",
  title =        "Statistical analyses hint at fraud in {Iranian}
                 election",
  journal =      j-NEW-SCIENTIST,
  volume =       "202",
  number =       "2714",
  pages =        "10--??",
  day =          "24",
  month =        jun,
  year =         "2009",
  CODEN =        "NWSCAL",
  DOI =          "https://doi.org/10.1016/S0262-4079(09)61682-1",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407909616821",
  abstract =     "Mathematicians add their own concerns to claims that
                 vote may have been rigged",
  acknowledgement = ack-nhfb,
  fjournal =     "The New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law",
  xxISSN =       "0262-4079, 0028-6664",
}

@TechReport{Bauer:2009:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  number =       "??",
  institution =  "Institute of Sociology, LMU Munich",
  address =      "Munich, Germany",
  month =        "????",
  year =         "2009",
  bibdate =      "Fri Nov 18 11:46:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Beber:2009:DD,
  author =       "B. Beber and A. Scacco",
  title =        "The Devil Is in the Digits",
  journal =      j-WASHINGTON-POST,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "20",
  month =        jun,
  year =         "2009",
  ISSN =         "0190-8286",
  bibdate =      "Sat Sep 10 10:28:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Washington Post",
  journal-URL =  "http://www.washingtonpost.com/",
  keywords =     "Benford's Law",
  remark =       "Not found in online newspaper archives.",
}

@TechReport{Berger:2009:BOB,
  author =       "A. Berger and T. P. Hill",
  title =        "{Benford} Online Bibliography",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2009",
  bibdate =      "Sat Nov 12 16:48:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.benfordonline.net",
  acknowledgement = ack-nhfb,
  remark =       "According to \cite{Berger:2011:BLS}, the authors'
                 online bibliography contains more than 600
                 references.",
}

@InProceedings{Berinde:2009:SOH,
  author =       "Radu Berinde and Graham Cormode and Piotr Indyk and
                 Martin J. Strauss",
  title =        "Space-optimal heavy hitters with strong error bounds",
  crossref =     "Paredaens:2009:PTE",
  pages =        "157--166",
  year =         "2009",
  DOI =          "https://doi.org/10.1145/1559795.1559819",
  bibdate =      "Thu Jul 2 14:05:34 MDT 2009",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "The problem of finding heavy hitters and approximating
                 the frequencies of items is at the heart of many
                 problems in data stream analysis. It has been observed
                 that several proposed solutions to this problem can
                 outperform their worst-case guarantees on real data.
                 This leads to the question of whether some stronger
                 bounds can be guaranteed. We answer this in the
                 positive by showing that a class of `counter-based
                 algorithms' (including the popular and very
                 space-efficient FREQUENT and SPACESAVING algorithms)
                 provide much stronger approximation guarantees than
                 previously known. Specifically, we show that errors in
                 the approximation of individual elements do not depend
                 on the frequencies of the most frequent elements, but
                 only on the frequency of the remaining `tail.' This
                 shows that counter-based methods are the most
                 space-efficient (in fact, space-optimal) algorithms
                 having this strong error bound.\par

                 This tail guarantee allows these algorithms to solve
                 the `sparse recovery' problem. Here, the goal is to
                 recover a faithful representation of the vector of
                 frequencies, $f$. We prove that using space $ O(k) $,
                 the algorithms construct an approximation $ f* $ to the
                 frequency vector $f$ so that the L1 error $ ||f -
                 f*||_1 $ is close to the best possible error $ \hbox
                 {min}_{f_2} || f_2 - f ||_1 $, where $f$ 2 ranges over
                 all vectors with at most $k$ non-zero entries. This
                 improves the previously best known space bound of about
                 $ O(k \log n) $ for streams without element deletions
                 (where $n$ is the size of the domain from which stream
                 elements are drawn). Other consequences of the tail
                 guarantees are results for skewed (Zipfian) data, and
                 guarantees for accuracy of merging multiple summarized
                 streams.",
  acknowledgement = ack-nhfb,
  keywords =     "frequency estimation; heavy hitters; streaming
                 algorithms",
}

@Article{Blasius:2009:ZLP,
  author =       "Bernd Blasius and Ralf T{\"o}njes",
  title =        "{Zipf's Law} in the Popularity Distribution of Chess
                 Openings",
  journal =      j-PHYS-REV-LET,
  volume =       "103",
  number =       "21",
  pages =        "218701",
  day =          "16",
  month =        nov,
  year =         "2009",
  CODEN =        "PRLTAO",
  DOI =          "https://doi.org/10.1103/PhysRevLett.103.218701",
  ISSN =         "0031-9007 (print), 1079-7114 (electronic), 1092-0145",
  ISSN-L =       "0031-9007",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevLett.103.218701",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review Letters",
  journal-URL =  "http://prl.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "4",
}

@Article{Bradley:2009:WBL,
  author =       "Jonathan R. Bradley and David L. Farnsworth",
  title =        "What Is {Benford's Law}?",
  journal =      "Teaching Statistics",
  volume =       "31",
  number =       "1",
  pages =        "2--6",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1467-9639.2009.00347.x",
  ISSN =         "0141-982X (print), 1467-9639 (electronic)",
  ISSN-L =       "0141-982X",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Class activity; First significant digit; Goodness of
                 fit; Teaching",
  onlinedate =   "6 Jan 2009",
}

@InProceedings{Burns:2009:SSR,
  author =       "B. D. Burns",
  editor =       "N. Taatgen and H. van Rijn",
  booktitle =    "{Proceedings of the Thirty-First Annual Conference of
                 the Cognitive Science Society, Cognitive Science
                 Society, Austin, TX}",
  title =        "Sensitivity to Statistical Regularities: People
                 (Largely) Follow {Benford's Law}",
  publisher =    "????",
  address =      "????",
  pages =        "2872--2877",
  year =         "2009",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Fri Nov 18 11:57:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Chakravorty:2009:TBL,
  author =       "S. Chakravorty and V. Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: a field experiment",
  journal =      j-DRUG-DISCOVERY-TODAY,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  CODEN =        "DDTOFS",
  DOI =          "https://doi.org/10.1016/j.ijpe.2009.06.017",
  ISSN =         "1359-6446 (print), 1878-5832 (electronic)",
  ISSN-L =       "1359-6446",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  acknowledgement = ack-nhfb,
  fjournal =     "Drug Discovery Today",
  keywords =     "Benford's Law",
}

@InProceedings{Chen:2009:DDM,
  author =       "Wen Chen and Yun Q. Shi",
  booktitle =    "{Digital Watermarking}",
  title =        "Detection of Double {MPEG} Compression Based on First
                 Digit Statistics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "16--30",
  year =         "2009",
  DOI =          "https://doi.org/10.1007/978-3-642-04438-0_2",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-04438-0_2",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Chou:2009:BLN,
  author =       "Mabel C. Chou and Qingxia Kong and Chung-Piaw Teo and
                 Zuozheng Wang and Huan Zheng",
  title =        "{Benford's Law} and Number Selection in Fixed-Odds
                 Numbers Game",
  journal =      j-J-GAMBL-STUD,
  volume =       "25",
  number =       "4",
  pages =        "503--521",
  month =        dec,
  year =         "2009",
  CODEN =        "JGSTEM",
  DOI =          "https://doi.org/10.1007/s10899-009-9145-9",
  ISSN =         "1050-5350 (print), 1573-3602 (electronic)",
  ISSN-L =       "1050-5350",
  bibdate =      "Sat Feb 16 15:35:14 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s10899-009-9145-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Gambling Studies",
}

@Article{Chuang:2009:FPS,
  author =       "Kun-Ta Chuang and Hung-Leng Chen and Ming-Syan Chen",
  title =        "Feature-preserved sampling over streaming data",
  journal =      j-TKDD,
  volume =       "2",
  number =       "4",
  pages =        "15:1--15:??",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1460797.1460798",
  ISSN =         "1556-4681 (print), 1556-472X (electronic)",
  ISSN-L =       "1556-4681",
  bibdate =      "Fri Apr 24 17:59:51 MDT 2009",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tkdd/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "In this article, we explore a novel sampling model,
                 called {\em feature preserved sampling\/} ({\em FPS\/})
                 that sequentially generates a high-quality sample over
                 sliding windows. The sampling quality we consider
                 refers to the degree of consistency between the sample
                 proportion and the population proportion of each
                 attribute value in a window. Due to the time-variant
                 nature of real-world datasets, users are more likely to
                 be interested in the most recent data. However,
                 previous works have not been able to generate a
                 high-quality sample over sliding windows that precisely
                 preserves up-to-date population characteristics.
                 Motivated by this shortcoming, we have developed the
                 {\em FPS\/} algorithm, which has several advantages:
                 (1) it sequentially generates a sample from a
                 time-variant data source over sliding windows; (2) the
                 execution time of {\em FPS\/} is linear with respect to
                 the database size; (3) the {\em relative\/}
                 proportional differences between the sample proportions
                 and population proportions of most distinct attribute
                 values are guaranteed to be below a specified error
                 threshold, $ \epsilon $, while the {\em relative\/}
                 proportion differences of the remaining attribute
                 values are as close to $ \epsilon $ as possible, which
                 ensures that the generated sample is of high quality;
                 (4) the sample rate is close to the user specified rate
                 so that a high quality sampling result can be obtained
                 without increasing the sample size; (5) by a thorough
                 analytical and empirical study, we prove that {\em
                 FPS\/} has acceptable space overheads, especially when
                 the attribute values have Zipfian distributions, and
                 {\em FPS\/} can also excellently preserve the
                 population proportion of multivariate features in the
                 sample; and (6) {\em FPS\/} can be applied to infinite
                 streams and finite datasets equally, and the generated
                 samples can be used for various applications. Our
                 experiments on both real and synthetic data validate
                 that {\em FPS\/} can effectively obtain a high quality
                 sample of the desired size. In addition, while using
                 the sample generated by {\em FPS\/} in various mining
                 applications, a significant improvement in efficiency
                 can be achieved without compromising the model's
                 precision.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Knowledge Discovery from Data
                 (TKDD)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1054",
  keywords =     "sampling; Streaming mining",
}

@Article{Clauset:2009:PLDc,
  author =       "Aaron Clauset and Cosma Rohilla Shalizi and M. E. J.
                 Newman",
  title =        "Power-Law Distributions in Empirical Data",
  journal =      j-SIAM-REVIEW,
  volume =       "51",
  number =       "4",
  pages =        "661--703",
  month =        "????",
  year =         "2009",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/070710111",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Mon May 17 17:56:49 MDT 2010",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIREV/51/4;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
}

@Article{Dlugosz:2009:VLD,
  author =       "Stephan Dlugosz and Ulrich M{\"u}ller-Funk",
  title =        "The value of the last digit: statistical fraud
                 detection with digit analysis",
  journal =      "Advances in Data Analysis and Classification",
  volume =       "3",
  number =       "3",
  pages =        "281--290",
  month =        dec,
  year =         "2009",
  DOI =          "https://doi.org/10.1007/s11634-009-0048-5",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11634-009-0048-5",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/11634",
  keywords =     "Benford's Law",
}

@Article{Docampo:2009:BLA,
  author =       "Silvia Docampo and Mar{\'\i}a {del Mar Trigo} and
                 Mar{\'\i}a Aira and Baltasar Cabezudo and Antonio
                 Flores-Moya",
  title =        "{Benford}'s law applied to aerobiological data and its
                 potential as a quality control tool",
  journal =      j-AEROBIOLOGIA,
  volume =       "25",
  number =       "4",
  pages =        "275--283",
  month =        dec,
  year =         "2009",
  CODEN =        "AROBFT",
  DOI =          "https://doi.org/10.1007/s10453-009-9132-8",
  ISSN =         "0393-5965 (print), 1573-3025 (electronic)",
  ISSN-L =       "0393-5965",
  bibdate =      "Fri Nov 25 10:47:33 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ingentaconnect.com/content/klu/aero/2009/00000025/00000004/00009132",
  acknowledgement = ack-nhfb,
  fjournal =     "Aerobiologia",
}

@Article{Dorfleitner:2009:PBE,
  author =       "Gregor Dorfleitner and Christian Klein",
  title =        "Psychological barriers in {European} stock markets:
                 Where are they?",
  journal =      j-GLOB-FINANCE-J,
  volume =       "19",
  number =       "3",
  pages =        "268--285",
  month =        oct,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.gfj.2008.09.001",
  ISSN =         "1044-0283 (print), 1873-5665 (electronic)",
  ISSN-L =       "1044-0283",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1044028308000549",
  abstract =     "We examine four European stock indices and the prices
                 of eight major German stocks for indications of
                 psychological barriers. The frequency, (expected)
                 returns, intraday volatility and trading volume of
                 these assets are studied contingent on whether the
                 prices lie within a certain range around round numbers.
                 Our results indicate that psychological barriers do not
                 exist on a consistent basis. It seems that some
                 barriers have disappeared after these anomalies have
                 been published. This discovery is consistent with
                 current literature findings about disappearing stock
                 market anomalies.",
  acknowledgement = ack-nhfb,
  fjournal =     "Global Finance Journal",
  keywords =     "Benford's Law; Disappearing anomalies; M-values;
                 Psychological barriers",
}

@Article{Egghe:2009:PRP,
  author =       "Leo Egghe",
  title =        "Performance and its relation with productivity in
                 {Lotkaian} systems",
  journal =      j-SCIENTOMETRICS,
  volume =       "81",
  number =       "2",
  pages =        "567--585",
  month =        nov,
  year =         "2009",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-008-2226-1",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-008-2226-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Fewster:2009:SEB,
  author =       "Rachel M. Fewster",
  title =        "A Simple Explanation of {Benford's Law}",
  journal =      j-AMER-STAT,
  volume =       "63",
  number =       "1",
  pages =        "26--32",
  month =        feb,
  year =         "2009",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2009.0005",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2655700",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pubs.amstat.org/doi/pdfplus/10.1198/tast.2009.0005",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Gauvrit:2009:LBG,
  author =       "Nicolas Gauvrit and Jean-Paul Delahaye",
  title =        "Loi de {Benford} g{\'e}n{\'e}rale. ({French})
                 [{General} {Benford}'s law]",
  journal =      "Math. Sci. Hum. Math. Soc. Sci.",
  volume =       "??",
  number =       "186",
  pages =        "5--15",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0987-6936 (print), 1950-6821 (electronic)",
  ISSN-L =       "0987-6936",
  MRclass =      "62E10 (11A63 37A45)",
  MRnumber =     "2562062 (2010i:62029)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://msh.revues.org/document11034.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Math{\'e}matiques et Sciences Humaines. Mathematics
                 and Social Sciences",
  language =     "French",
}

@Article{Gauvrit:2009:SRI,
  author =       "N. Gauvrit and J.-P. Delahaye",
  title =        "Scatter and regularity imply {Benford}'s law \ldots{}
                 and more",
  journal =      "ArXiv e-prints",
  month =        oct,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0910.1359G;
                 http://arxiv.org/abs/0910.1359",
  abstract =     "A random variable (r.v.) $X$ is said to follow
                 Benford's law if $ \log (X) $ is uniform $ \bmod 1 $.
                 Many experimental data sets prove to follow an
                 approximate version of it, and so do many mathematical
                 series and continuous random variables. This phenomenon
                 received some interest, and several explanations have
                 been put forward. Most of them focus on specific data,
                 depending on strong assumptions, often linked with the
                 log function. Some authors hinted --- implicitly ---
                 that the two most important characteristics of a random
                 variable when it comes to Benford are regularity and
                 scatter. In a first part, we prove two theorems, making
                 up a formal version of this intuition: scattered and
                 regular r.v.'s do approximately follow Benford's law.
                 The proofs only need simple mathematical tools, making
                 the analysis easy. Previous explanations thus become
                 corollaries of a more general and simpler one. These
                 results suggest that Benford's law does not depend on
                 properties linked with the log function. We thus
                 propose and test a general version of the Benford's
                 law. The success of these tests may be viewed as an a
                 posteriori validation of the analysis formulated in the
                 first part.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0910.1359",
  keywords =     "Mathematics - Probability, Statistics - Methodology,
                 G.3",
  primaryclass = "math.PR",
}

@Article{Gisin:2009:EEV,
  author =       "Vladimir Gisin and Andrey Markov and Igor Vinukov",
  title =        "Estimation of extreme values of returns using the
                 {Zipf--Mandelbrot} flow",
  journal =      j-INT-J-PURE-APPL-MATH,
  volume =       "50",
  number =       "2",
  pages =        "245--250",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1311-8080 (print), 1314-3395 (electronic)",
  ISSN-L =       "1314-3395",
  MRclass =      "60G70 (91B28 91B84)",
  MRnumber =     "2488836",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Pure and Applied
                 Mathematics",
  journal-URL =  "http://ijpam.eu/",
}

@TechReport{Gonzales-Garcia:2009:BLM,
  author =       "J. Gonzales-Garcia and G. Pastor",
  title =        "{Benford's Law} and Macroeconomic Data Quality",
  type =         "Working Paper",
  institution =  "International Monetary Fund",
  address =      "Washington, DC, USA",
  year =         "2009",
  bibdate =      "Tue Nov 22 18:53:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1356437",
  acknowledgement = ack-nhfb,
}

@Article{Graham:2009:SFD,
  author =       "Scott D. J. Graham and John Hasseldine and David
                 Paton",
  title =        "Statistical fraud detection in a commercial lobster
                 fishery",
  journal =      "New Zealand Journal of Marine and Freshwater
                 Research",
  volume =       "43",
  number =       "1",
  pages =        "457--463",
  year =         "2009",
  DOI =          "https://doi.org/10.1080/00288330909510014",
  bibdate =      "Sat Sep 10 11:38:12 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Abstract In this study we introduce the first step
                 towards a statistical model for the reliability of
                 fisheries data. We applied Benford's Law to catch data
                 from the Atlantic Canadian lobster ({\em Homarus
                 americanus}) fishery's lobster fishery areas (LFAs) 33
                 and 34 and compared our results to those using
                 observations from the grey zone (a highly regulated
                 lobster fishery shared by Canada and United States) and
                 a fishery with a different regulatory regime (snow
                 crab, {\em Chionoecetes opilio}). Non conformity with
                 Benford's Law is often considered as an indicator of
                 human manipulation of accounting data. We found that
                 observations from the grey zone conformed to the
                 distribution predicted by Benford's Law, whereas
                 observations from snow crab and both lobster fishery
                 areas did not conform.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Gunnel:2009:DBL,
  author =       "S. G{\"u}nnel and K.-H. T{\"o}dter",
  title =        "Does {Benford's Law} Hold in Economic Research and
                 Forecasting?",
  journal =      j-EMPIRICA,
  volume =       "36",
  number =       "3",
  pages =        "273--292",
  month =        aug,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s10663-008-9084-1",
  ISSN =         "0340-8744 (print), 1573-6911 (electronic)",
  ISSN-L =       "0340-8744",
  bibdate =      "Thu Nov 17 19:16:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/content/100261/",
  abstract =     "First and higher order digits in data sets of natural
                 and socio-economic processes often follow a
                 distribution called Benford's law. This phenomenon has
                 been used in business and scientific applications,
                 especially in fraud detection for financial data. In
                 this paper, we analyse whether Benford's law holds in
                 economic research and forecasting. First, we examine
                 the distribution of regression coefficients and
                 standard errors in research papers, published in
                 Empirica and Applied Economics Letters. Second, we
                 analyse forecasts of GDP growth and CPI inflation in
                 Germany, published in Consensus Forecasts. There are
                 two main findings: The relative frequencies of the
                 first and second digits in economic research are
                 broadly consistent with Benford's law. In sharp
                 contrast, the second digits of Consensus Forecasts
                 exhibit a massive excess of zeros and fives, raising
                 doubts on their information content.",
  acknowledgement = ack-nhfb,
  fjournal =     "Empirica",
}

@Article{Hales:2009:TBL,
  author =       "Douglas N. Hales and Satya S. Chakravorty and V.
                 Sridharan",
  title =        "Testing {Benford's Law} for improving supply chain
                 decision-making: A field experiment",
  journal =      j-INT-J-PROD-ECON,
  volume =       "122",
  number =       "2",
  pages =        "606--618",
  month =        dec,
  year =         "2009",
  CODEN =        "JPCEYE",
  DOI =          "https://doi.org/10.1016/j.ijpe.2009.06.017",
  ISSN =         "0925-5273 (print), 1873-7579 (electronic)",
  ISSN-L =       "0925-5273",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0925527309002163",
  abstract =     "Supply chain managers must often trust data reported
                 from suppliers to make decisions about sourcing and
                 product reliability due to the costs or complexity of
                 implementing traditional monitoring systems. Without
                 some form of monitoring, these types of data are
                 vulnerable to manipulation, thus making their
                 suitability for decision-making ambiguous and creating
                 an opportunity for supplier opportunism. Recent
                 practitioner literature suggests one solution to this
                 problem they refer to as trust-but-verify . The purpose
                 of this empirical study is to scientifically examine
                 the feasibility and cost of implementing one
                 trust-but-verify method in a real-world supply chain
                 using a principle called Benford's Law. The results of
                 this two-year study suggest that the technique is
                 feasible and cost effective in identifying supply chain
                 data that have been intentionally manipulated. This
                 finding can allow supply chain managers to segregate
                 suspect data from decision-making until they can be
                 validated and thus mitigate supplier opportunism.",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. j. prod. econ.",
  fjournal =     "International Journal of Production Economics",
  keywords =     "Benford's Law; Digital analysis; Operations
                 management; Supplier opportunism; Supply chain
                 management",
}

@Article{Hartshorn:2009:BRB,
  author =       "Kevin Hartshorn",
  title =        "Book Review: {{\booktitle{The fabulous Fibonacci
                 numbers}} by Alfred Posamentier and Ingmar Lehmann}",
  journal =      j-J-MATH-ARTS,
  volume =       "3",
  number =       "2",
  pages =        "113--116",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/17513470902897569",
  ISSN =         "1751-3472 (print), 1751-3480 (electronic)",
  ISSN-L =       "1751-3480",
  bibdate =      "Sat Jan 07 09:43:47 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/17513470902897569",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematics and the Arts",
  journal-URL =  "http://www.tandfonline.com/loi/tmaa20",
  onlinedate =   "05 Jun 2009",
}

@Article{Hayes:2009:CBL,
  author =       "S. J. Hayes",
  title =        "Correspondence: {Benford's Law} in Relation to
                 Terminal Digit Preference",
  journal =      j-J-CLIN-PATHOL,
  volume =       "62",
  number =       "6",
  pages =        "574--575",
  month =        "????",
  year =         "2009",
  CODEN =        "JCPAAK",
  ISSN =         "0021-9746 (print), 1472-4146 (electronic)",
  ISSN-L =       "0021-9746",
  bibdate =      "Sat Sep 10 12:07:02 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jcp.bmj.com/content/62/6/575.2.extract",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Clinical Pathology",
  keywords =     "Benford's Law",
}

@Article{Hernando:2009:ZLF,
  author =       "A. Hernando and D. Puigdom{\`e}nech and D. Villuendas
                 and C. Vesperinas and A. Plastino",
  title =        "{Zipf}'s law from a {Fisher} variational-principle",
  journal =      j-PHYS-LET-A,
  volume =       "374",
  number =       "1",
  pages =        "18--21",
  day =          "14",
  month =        dec,
  year =         "2009",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/j.physleta.2009.10.027",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0375960109012894",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
  keywords =     "Zipf's Law",
}

@InCollection{Horgan:2009:BL,
  author =       "Jane M. Horgan",
  title =        "{Benford's Law}",
  crossref =     "Horgan:2009:PRI",
  chapter =      "9.4",
  pages =        "142--144",
  year =         "2009",
  bibdate =      "Mon Feb 18 18:46:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Hurlimann:2009:GBL,
  author =       "Werner H{\"u}rlimann",
  title =        "Generalizing {Benford}'s law using power laws:
                 application to integer sequences",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "10",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "60E05 (11B83 62E15)",
  MRnumber =     "2533550 (2010h:60043)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Article ID 970284.",
  URL =          "http://arxiv.org/abs/math/0607166",
  abstract =     "A simple method to derive parametric analytical
                 extensions of Benford's law for first digits of
                 numerical data is proposed. Two generalized Benford
                 distributions are considered, namely the two-sided
                 power Benford distribution and the new Pareto Benford
                 distribution. The fitting capabilities of these
                 generalized Benford distributions are illustrated and
                 compared at some interesting and important integer
                 sequences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
}

@Article{Jang:2009:CDH,
  author =       "D. Jang and J. U. Kang and A. Kruckman and J. Kudo and
                 Steven J. Miller",
  title =        "Chains of distributions, hierarchical {Bayesian}
                 models and {Benford's Law}",
  journal =      "Journal of Algebra, Number Theory: Advances and
                 Applications",
  volume =       "1",
  number =       "1",
  pages =        "37--60",
  month =        mar,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0972-5555",
  ISSN-L =       "0972-5555",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2008arXiv0805.4226J",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0805.4226",
  keywords =     "Mathematics - Probability, Mathematics - Statistics
                 Theory, 11K06, 60A10 (Primary), 62F99 (Secondary)",
  primaryclass = "math.PR",
}

@Article{Janvresse:2009:BL,
  author =       "Elise Janvresse and Thierry de la Rue",
  title =        "{Benford}'s law",
  journal =      "Butl. Soc. Catalana Mat.",
  volume =       "24",
  number =       "1",
  pages =        "5--12",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "0214-316X",
  ISSN-L =       "0214-316X",
  MRclass =      "62-01",
  MRnumber =     "2567485",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translated by Frederic Utzet",
  acknowledgement = ack-nhfb,
  fjournal =     "Butllet{\'\i}n de la Societat Catalana de
                 Matem{\`a}tiques",
}

@Article{Jin:2009:AUR,
  author =       "Jang C. Jin",
  title =        "{Asian} University Rankings in International and
                 Development Economics: An Application of {Zipf's Law}",
  journal =      j-REV-INT-ECON,
  volume =       "17",
  number =       "1",
  pages =        "137--143",
  year =         "2009",
  DOI =          "https://doi.org/10.1111/j.1467-9396.2008.00790.x",
  ISSN =         "0965-7576 (print), 1467-9396 (electronic)",
  ISSN-L =       "0965-7576",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Review of International Economics",
}

@Article{Jin:2009:PME,
  author =       "Jang C. Jin",
  title =        "Publications in mathematical economics and
                 econometrics: ranking of {Asian} universities and an
                 application of {Zipf's Law}",
  journal =      "{Asian-Pacific} Economic Literature",
  volume =       "23",
  number =       "2",
  pages =        "116--122",
  year =         "2009",
  DOI =          "https://doi.org/10.1111/j.1467-8411.2009.01233.x",
  ISSN =         "0818-9935 (print), 1467-8411 (electronic)",
  ISSN-L =       "0818-9935",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/%28ISSN%291467-8411",
}

@Article{Jolissaint:2009:LBR,
  author =       "Paul Jolissaint",
  title =        "Loi de {Benford}, relations de r{\'e}currence et
                 suites {\'e}quidistribu{\'e}es. {II}. ({French})
                 [{Benford}'s Law, recurrence relations, and
                 equidistributed sequences. {II}]",
  journal =      j-ELEM-MATH,
  volume =       "64",
  number =       "1",
  pages =        "21--36",
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4171/EM/112",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "62E10 (11A63 37A45)",
  MRnumber =     "2471593 (2010f:62032)",
  MRreviewer =   "Denys Pommeret",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{Judge:2009:DPS,
  author =       "G. Judge and L. Schechter",
  title =        "Detecting Problems in Survey Data using {Benford's
                 Law}",
  journal =      j-J-HUM-RESOUR,
  volume =       "44",
  number =       "1",
  pages =        "1--24",
  month =        "Winter",
  year =         "2009",
  CODEN =        "JHREA9",
  DOI =          "https://doi.org/10.3368/jhr.44.1.1",
  ISSN =         "0022-166X (print), 1548-8004 (electronic)",
  ISSN-L =       "0022-166X",
  bibdate =      "Tue Nov 22 18:55:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://jhr.uwpress.org/content/44/1/1.abstract;
                 http://www.ssc.wisc.edu/jhr/2009ab/judge1.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Human Resources",
}

@Article{Kafri:2009:DNE,
  author =       "Oded Kafri",
  title =        "The Distributions in Nature and Entropy Principle",
  journal =      "ArXiv e-prints",
  day =          "28",
  month =        jul,
  year =         "2009",
  bibdate =      "Mon Nov 21 07:26:11 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/0907.4852",
  abstract =     "The derivation of the maximum entropy distribution of
                 particles in boxes yields two kinds of distributions: a
                 ``bell-like'' distribution and a long-tail
                 distribution. The first one is obtained when the ratio
                 between particles and boxes is low, and the second one
                 when the ratio is high. The obtained long tail
                 distribution yields correctly the empirical Zipf law,
                 Pareto's 20:80 rule and Benford's law. Therefore, it is
                 concluded that the long tail and the ``bell-like''
                 distributions are outcomes of the tendency of
                 statistical systems to maximize entropy.",
  acknowledgement = ack-nhfb,
  pagecount =    "19",
}

@Article{Kafri:2009:EPD,
  author =       "Oded Kafri",
  title =        "Entropy Principle in Direct Derivation of {Benford's
                 Law}",
  journal =      "ArXiv e-prints",
  month =        jan,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0901.3047K;
                 http://arxiv.org/abs/0901.3047",
  abstract =     "The uneven distribution of digits in numerical data,
                 known as Benford's law, was discovered in 1881. Since
                 then, this law has been shown to be correct in copious
                 numerical data relating to economics, physics and even
                 prime numbers. Although it attracts considerable
                 attention, there is no a priori probabilistic criterion
                 when a data set should or should not obey the law. Here
                 a general criterion is suggested, namely that any file
                 of digits in the Shannon limit (namely, having maximum
                 entropy) has a Benford's law distribution of digits.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0901.3047",
  keywords =     "Computer Science - Discrete Mathematics, Physics -
                 Data Analysis, Statistics and Probability",
  primaryclass = "cs.DM",
}

@Article{Kim:2009:ITA,
  author =       "Hyo-Jeong Kim and Michael Mannino and Robert J.
                 Nieschwietz",
  title =        "Information technology acceptance in the internal
                 audit profession: Impact of technology features and
                 complexity",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "10",
  number =       "4",
  pages =        "214--228",
  year =         "2009",
  CODEN =        "IJAIA7",
  DOI =          "https://doi.org/10.1016/j.accinf.2009.09.001",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Ninth International Research Symposium on Accounting
                 Information Systems (IRSAIS)",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089509000360",
  abstract =     "Although various information technologies have been
                 studied using the technology acceptance model (TAM),
                 the study of acceptance of specific technology features
                 for professional groups employing information
                 technologies such as internal auditors (IA) has been
                 limited. To address this gap, we extended the {TAM} for
                 technology acceptance among {IA} professionals and
                 tested the model using a sample of internal auditors
                 provided by the Institute of Internal Auditors (IIA).
                 System usage, perceived usefulness, and perceived ease
                 of use were tested with technology features and
                 complexity. Through the comparison of {TAM} variables,
                 we found that technology features were accepted by
                 internal auditors in different ways. The basic features
                 such as database queries, ratio analysis, and audit
                 sampling were more accepted by internal auditors while
                 the advanced features such as digital analysis,
                 regression/ANOVA, and classification are less accepted
                 by internal auditors. As feature complexity increases,
                 perceived ease of use decreased so that system usage
                 decreased. Through the path analysis between {TAM}
                 variables, the results indicated that path magnitudes
                 were significantly changed by technology features and
                 complexity. Perceived usefulness had more influence on
                 feature acceptance when basic features were used, and
                 perceived ease of use had more impact on feature
                 acceptance when advanced features were used.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law; Information technology adoption;
                 Internal auditing; System acceptance; {IS} features",
}

@Article{Krakar:2009:ABL,
  author =       "Mario {\v{Z}}gela and Zdravko Krakar",
  title =        "Application of {Benford's Law} in Payment System
                 Auditing",
  journal =      j-J-INFO-ORG-SCI,
  volume =       "33",
  number =       "1",
  pages =        "39--51",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1846-3312 (print), 1846-9418 (electronic)",
  ISSN-L =       "1846-3312",
  bibdate =      "Sun Nov 13 11:12:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bib.irb.hr/datoteka/457819.04_Application_of_Benford_s_Law_in_Payment_Systems_Auditing1.pdf;
                 http://jios.foi.hr/index.php/jios/article/view/108/66;
                 http://jios.foi.hr/index.php/jios/issue/view/13",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informational and Organizational Sciences",
  journal-URL =  "http://jios.foi.hr/index.php/jios/index",
  xxjournal =    "Journal of Information Ethics and Organisational
                 Science (wrong!)",
}

@Article{Krishna:2009:DBD,
  author =       "Hare Krishna and Pramendra Singh Pundir",
  title =        "Discrete {Burr} and discrete {Pareto} distributions",
  journal =      j-STAT-METHODOL,
  volume =       "6",
  number =       "2",
  pages =        "177--188",
  month =        mar,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:36 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S157231270800052X",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@MastersThesis{Krygier:2009:PRB,
  author =       "J. Krygier",
  title =        "Psychological Relevance of {Benford's Law}:
                 Sensitivity to Statistical Regularities and
                 Implications for Theories of Number Representation",
  type =         "Honours thesis",
  school =       "University of Sydney",
  address =      "Sydney, NSW, Australia",
  year =         "2009",
  bibdate =      "Sat Sep 10 12:48:34 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Lansey:2009:ISR,
  author =       "Jonathan C. Lansey and Bruce Bukiet",
  title =        "{Internet} Search Result Probabilities: {Heaps' Law}
                 and Word Associativity",
  journal =      j-J-QUANT-LINGUISTICS,
  volume =       "16",
  number =       "1",
  pages =        "40--66",
  month =        "????",
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09296170802514153",
  ISSN =         "0929-6174 (print), 1744-5035 (electronic)",
  ISSN-L =       "0929-6174",
  bibdate =      "Sat Jan 07 09:36:17 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/09296170802514153",
  abstract =     "We study the number of internet search results
                 returned from multi-word queries based on the number of
                 results returned when each word is searched for
                 individually. We derive a model to describe search
                 result values for multi-word queries using the total
                 number of pages indexed by Google and by applying the
                 Zipf power law to the words per page distribution on
                 the internet and Heaps' law for unique word counts.
                 Based on data from 351 word pairs each with exactly one
                 hit when searched for together, and a Zipf law
                 coefficient determined in other studies, we approximate
                 the Heaps' law coefficient for the indexed worldwide
                 web (about 8 billion pages) to be $ \beta = 0.52 $.
                 Previous studies used under 20,000 pages. We
                 demonstrate through examples how the model can be used
                 to analyse automatically the relatedness of word pairs
                 assigning each a value we call ``strength of
                 associativity''. We demonstrate the validity of our
                 method with word triplets and through two experiments
                 conducted 8 months apart. We then use our model to
                 compare the index sizes of competing search giants
                 Yahoo and Google.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Linguistics",
  keywords =     "Benford's Law; Heaps' Law; Zipf's Law",
  onlinedate =   "25 Feb 2009",
  remark =       "From page 65: ``We mention that tests we have
                 conducted show that internet searches for random
                 numbers return approximately log-normally distributed
                 results and sorting by first digits yields results that
                 follow Benford's law (1938).''",
}

@Article{Li:2009:PDD,
  author =       "Weihai Li and Yuan Yuan and Nenghai Yu",
  title =        "Passive detection of doctored {JPEG} image via block
                 artifact grid extraction",
  journal =      j-SIG-PROC,
  volume =       "89",
  number =       "9",
  pages =        "1821--1829",
  year =         "2009",
  CODEN =        "SPRODR",
  DOI =          "https://doi.org/10.1016/j.sigpro.2009.03.025",
  ISSN =         "0165-1684 (print), 1872-7557 (electronic)",
  ISSN-L =       "0165-1684",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165168409001315",
  abstract =     "It has been noticed that the block artifact grids
                 (BAG), caused by the blocking processing during {JPEG}
                 compression, are usually mismatched when interpolating
                 or concealing objects by copy paste operations. In this
                 paper, the {BAGs} are extracted blindly with a new
                 extraction algorithm, and then abnormal {BAGs} can be
                 detected with a marking procedure. Then the phenomenon
                 of grid mismatch or grid blank can be taken as a trail
                 of such forensics. Experimental results show that our
                 method can mark these trails efficiently.",
  acknowledgement = ack-nhfb,
  fjournal =     "Signal Processing",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01651684",
  keywords =     "Benford's Law; Block artifact grid; Doctored image
                 forensic; Grid mismatch; {JPEG} compression",
}

@Article{Lipovetsky:2009:PLD,
  author =       "Stan Lipovetsky",
  title =        "{Pareto} $ 80 / 20 $ law: derivation via random
                 partitioning",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "40",
  number =       "2",
  pages =        "271--277",
  month =        "????",
  year =         "2009",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/00207390802213609",
  ISSN =         "0020-739X (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  bibdate =      "Sat Jan 07 09:22:31 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/00207390802213609",
  abstract =     "The Pareto 80/20 Rule, also known as the Pareto
                 principle or law, states that a small number of causes
                 (20\%) is responsible for a large percentage (80\%) of
                 the effect. Although widely recognized as a heuristic
                 rule, this proportion has not been theoretically based.
                 The article considers derivation of this 80/20 rule and
                 some other standard quotients from the mean and its
                 interval estimation for the total value defined by the
                 product of two variables in the random partitioning
                 model.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  onlinedate =   "19 Feb 2009",
}

@Article{Luque:2009:FDF,
  author =       "Bartolo Luque and Lucas Lacasa",
  title =        "The first digit frequencies of prime numbers and
                 {Riemann} zeta zeros",
  journal =      j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-ENG-SCI,
  volume =       "465",
  number =       "2107",
  pages =        "2197--2216",
  day =          "8",
  month =        jul,
  year =         "2009",
  CODEN =        "PRLAAZ",
  DOI =          "https://doi.org/10.1098/rspa.2009.0126",
  ISSN =         "1364-5021 (print), 1471-2946 (electronic)",
  ISSN-L =       "1364-5021",
  bibdate =      "Mon Feb 25 10:44:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rspa.royalsocietypublishing.org/content/465/2107/2197.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the Royal Society A: Mathematical,
                 Physical, \& Engineering Sciences",
  journal-URL =  "http://rspa.royalsocietypublishing.org/",
  keywords =     "Benford's Law",
  onlinedate =   "22 April 2009",
}

@Article{Mahdian:2009:UNI,
  author =       "Babak Mahdian and Stanislav Saic",
  title =        "Using noise inconsistencies for blind image
                 forensics",
  journal =      j-IMAGE-VIS-COMPUT,
  volume =       "27",
  number =       "10",
  pages =        "1497--1503",
  year =         "2009",
  CODEN =        "IVCODK",
  DOI =          "https://doi.org/10.1016/j.imavis.2009.02.001",
  ISSN =         "0262-8856 (print), 1872-8138 (electronic)",
  ISSN-L =       "0262-8856",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2000.bib",
  note =         "Special Section: Computer Vision Methods for Ambient
                 Intelligence",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262885609000146",
  abstract =     "A commonly used tool to conceal the traces of
                 tampering is the addition of locally random noise to
                 the altered image regions. The noise degradation is the
                 main cause of failure of many active or passive image
                 forgery detection methods. Typically, the amount of
                 noise is uniform across the entire authentic image.
                 Adding locally random noise may cause inconsistencies
                 in the image's noise. Therefore, the detection of
                 various noise levels in an image may signify tampering.
                 In this paper, we propose a novel method capable of
                 dividing an investigated image into various partitions
                 with homogeneous noise levels. In other words, we
                 introduce a segmentation method detecting changes in
                 noise level. We assume the additive white Gaussian
                 noise. Several examples are shown to demonstrate the
                 proposed method's output. An extensive quantitative
                 measure of the efficiency of the noise estimation part
                 as a function of different noise standard deviations,
                 region sizes and various {JPEG} compression qualities
                 is proposed as well.",
  acknowledgement = ack-nhfb,
  fjournal =     "Image and Vision Computing",
  keywords =     "Benford's Law; Digital forgery; Image forensics; Image
                 segmentation; Image tampering; Noise inconsistency",
}

@Article{Mebane:2009:EFR,
  author =       "Walter R. {Mebane, Jr.} and K. Kalinin",
  title =        "Electoral Falsification in {Russia}: Complex
                 Diagnostics Selections 2003--2004, 2007--2008",
  journal =      "Russian Electoral Review",
  volume =       "2",
  number =       "??",
  pages =        "57--70",
  month =        "????",
  year =         "2009",
  bibdate =      "Sat Sep 10 14:30:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  language =     "Russian",
}

@TechReport{Mebane:2009:NPE,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Note on the {Presidential} Election in {Iran}",
  type =         "Report",
  number =       "????",
  institution =  "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  month =        jun,
  year =         "2009",
  bibdate =      "Sat Sep 10 14:17:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/rvwmebane/note29jun2009.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Meintanis:2009:UAT,
  author =       "Simos G. Meintanis",
  title =        "A unified approach of testing for discrete and
                 continuous {Pareto} laws",
  journal =      j-STAT-PAPERS,
  volume =       "50",
  number =       "3",
  pages =        "569--580",
  month =        jun,
  year =         "2009",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-007-0103-2",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:30 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-007-0103-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@TechReport{Moller:2009:MQA,
  author =       "M. M{\"o}ller",
  title =        "Measuring the Quality of Auditing Services with the
                 Help of {Benford's Law} -- An Empirical Analysis and
                 Discussion of this Methodical Approach",
  type =         "Report",
  number =       "??",
  institution =  "Institute for Accounting and Control, University of
                 Z{\"u}rich",
  address =      "Z{\"u}rich, Switzerland",
  pages =        "25",
  day =          "24",
  month =        apr,
  year =         "2009",
  bibdate =      "Tue Nov 22 20:40:12 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ssrn.com/abstract=1529307",
  abstract =     "The so-called Benford's Law describes regularity in
                 the distribution of digits of randomly selected
                 numbers, which states that the relative frequency of
                 the leading digits reduces in a systematic manner from
                 the digit 1 to the digit 9. This distribution
                 hypothesis is being discussed in recent times as an
                 audit instrument in order to gain insights into
                 possible conscious and inadvertent errors in data
                 records. The present paper analyses the closing
                 accounts of 1,373 annual financial statements of
                 companies listed on the German DAX and compares these
                 with the Benford's distribution hypothesis. It can be
                 seen in the process that data pertaining to financial
                 accounts, which have not been audited by the so-called
                 ``Big 4'' audit firms, but by smaller external
                 auditors, deviate to a significant extent from the
                 regularity of Benford's Law, which appears to make the
                 use of Benford's Law suitable as a benchmark to assess
                 the quality of the audit.",
  acknowledgement = ack-nhfb,
}

@Article{Moret:2009:GSA,
  author =       "M. A. Moret and V. de Senna and M. C. Santana and G.
                 F. Zebende",
  title =        "Geometric Structural Aspects of Proteins and
                 {Newcomb--Benford Law}",
  journal =      j-INT-J-MOD-PHYS-C,
  volume =       "20",
  number =       "12",
  pages =        "1981--1988",
  month =        "????",
  year =         "2009",
  CODEN =        "IJMPEO",
  DOI =          "https://doi.org/10.1142/S0129183109014874",
  ISSN =         "0129-1831 (print), 1793-6586 (electronic)",
  ISSN-L =       "0129-1831",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009IJMPC..20.1981M",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Modern Physics C [Physics and
                 Computers]",
  journal-URL =  "http://www.worldscientific.com/loi/ijmpc",
  keywords =     "Hydrophobicity, protein packing, complex systems, Time
                 series analysis, Systems obeying scaling laws, Binary
                 and multiple stars",
}

@Article{Ni:2009:BLD,
  author =       "Dong-Dong Ni and Lai Wei and Zhong-Zhou Ren",
  title =        "{Benford's Law} and $ \beta $-Decay Half-Lives",
  journal =      j-COMM-THEOR-PHYS,
  volume =       "51",
  number =       "4",
  pages =        "713--716",
  month =        apr,
  year =         "2009",
  CODEN =        "CTPHDI",
  DOI =          "https://doi.org/10.1088/0253-6102/51/4/25",
  ISSN =         "0253-6102 (print), 1572-9494 (electronic)",
  ISSN-L =       "0253-6102",
  bibdate =      "Sun Nov 13 11:01:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009CoTPh..51..713N;
                 http://stacks.iop.org/0253-6102/51/i=4/a=25",
  abstract =     "The experimental values of 2059 $ \beta $-decay
                 half-lives are systematically analyzed and
                 investigated. We have found that they are in
                 satisfactory agreement with Benford's law, which states
                 that the frequency of occurrence of each figure, 1--9,
                 as the first significant digit in a surprisingly large
                 number of different data sets follows a logarithmic
                 distribution favoring the smaller ones. Benford's
                 logarithmic distribution of $ \beta $-decay half-lives
                 can be explained in terms of Newcomb's justification of
                 Benford's law and empirical exponential law of $ \beta
                 $-decay half-lives. Moreover, we test the calculated
                 values of 6721 $ \beta $-decay half-lives with the aid
                 of Benford's law. This indicates that Benford's law is
                 useful for theoretical physicists to test their methods
                 for calculating $ \beta $-decay half-lives.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in theoretical physics",
}

@Article{Nigrini:2009:DDU,
  author =       "Mark J. Nigrini and Steven J. Miller",
  title =        "Data Diagnostics Using Second-Order Tests of
                 {Benford's Law}",
  journal =      j-AUDITING,
  volume =       "28",
  number =       "2",
  pages =        "305--324",
  month =        nov,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.2308/aud.2009.28.2.305",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Tue Nov 15 09:11:56 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaapubs.org/loi/ajpt;
                 http://link.aip.org/link/AJPTXX/v28/i2/p305/s1",
  abstract =     "Auditors are required to use analytical procedures to
                 identify the existence of unusual transactions, events,
                 and trends. Benford's Law gives the expected patterns
                 of the digits in numerical data, and has been advocated
                 as a test for the authenticity and reliability of
                 transaction level accounting data. This paper describes
                 a new second-order test that calculates the digit
                 frequencies of the differences between the ordered
                 (ranked) values in a data set. These digit frequencies
                 approximate the frequencies of Benford's Law for most
                 data sets. The second-order test is applied to four
                 sets of transactional data. The second-order test
                 detected errors in data downloads, rounded data, data
                 generated by statistical procedures, and the inaccurate
                 ordering of data. The test can be applied to any data
                 set and nonconformity usually signals an unusual issue
                 related to data integrity that might not have been
                 easily detectable using traditional analytical
                 procedures",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@InCollection{Nisbet:2009:CFD,
  author =       "Robert Nisbet and John Elder and Gary Miner",
  booktitle =    "Handbook of Statistical Analysis and Data Mining
                 Applications",
  title =        "Chapter 17 --- Fraud Detection",
  publisher =    "Academic Press",
  address =      "Boston",
  pages =        "347--361",
  year =         "2009",
  DOI =          "https://doi.org/10.1016/B978-0-12-374765-5.00017-6",
  ISBN =         "0-12-374765-1",
  ISBN-13 =      "978-0-12-374765-5",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780123747655000176",
  abstract =     "Fraud can be defined as a criminal activity, involving
                 false representations to gain an unjust advantage. It
                 occurs in a wide variety of forms and is ever changing
                 as new technologies and new economic and social systems
                 provide new opportunities for fraudulent activity. This
                 chapter introduces fraud detection, provides a simple
                 example of how to build a fraud model, and directs one
                 to additional references to broaden and deepen the
                 knowledge of the vast scope of fraud detection. Fraud
                 is a form of human response that can be modeled in ways
                 very similar to customer response in business. The
                 temporal dimension of fraud provides a rich source of
                 information related to fraud. The occurrence of a fraud
                 event at a given time may be highly related to the
                 pattern of events that happened in the past. These
                 historical data are the most important source of
                 attributes needed to sufficiently define the fraud
                 signature in the data set. Fraud modeling requires the
                 construction of reference objects based on
                 relationships that are drawn in the past between
                 various conditions and the incidence of fraud. The
                 basic approach to fraud detection with an analytical
                 model is to identify possible predictors of fraud
                 associated with known fraudsters and their actions in
                 the past. The most powerful fraud models are built on
                 historical data.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Rajabpour:2009:SRC,
  author =       "M. A. Rajabpour and S. M. {Vaez Allaei}",
  title =        "Scaling relations for contour lines of rough
                 surfaces",
  journal =      j-PHYS-REV-E,
  volume =       "80",
  number =       "1",
  pages =        "011115",
  day =          "13",
  month =        jul,
  year =         "2009",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.80.011115",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.80.011115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
}

@Article{Ramanana-Rahary:2009:APR,
  author =       "Suzy Ramanana-Rahary and Michel Zitt and Ronald
                 Rousseau",
  title =        "Aggregation properties of relative impact and other
                 classical indicators: Convexity issues and the
                 {Yule--Simpson} paradox",
  journal =      j-SCIENTOMETRICS,
  volume =       "79",
  number =       "2",
  pages =        "311--327",
  month =        may,
  year =         "2009",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-009-0420-4",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:11 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2000.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-009-0420-4",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Romero-Rochin:2009:DBL,
  author =       "V. Romero-Rochin",
  title =        "A derivation of {Benford's Law} \ldots{} and a
                 vindication of {Newcomb}",
  journal =      "ArXiv e-prints",
  month =        sep,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0909.3822R;
                 http://arxiv.org/abs/0909.3822",
  abstract =     "We show how Benford's Law (BL) for first, second,
                 \ldots{}, digits, emerges from the distribution of
                 digits of numbers of the type $ a^R $, with $a$ any
                 real positive number and $R$ a set of real numbers
                 uniformly distributed in an interval $ [P \log_a(10),
                 (P + 1) \log_a(10)) $ for any integer $P$. The result
                 is shown to be number base and scale invariant. A rule
                 based on the mantissas of the logarithms allows for a
                 determination of whether a set of numbers obeys BL or
                 not. We show that BL applies to numbers obtained from
                 the {\em multiplication\/} or {\em division\/} of
                 numbers drawn from any distribution. We also argue that
                 (most of) the real-life sets that obey BL are because
                 they are obtained from such basic arithmetic
                 operations. We exhibit that all these arguments were
                 discussed in the original paper by Simon Newcomb in
                 1881, where he presented Benford's Law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0909.3822",
  keywords =     "Mathematics - Probability, Mathematics - History and
                 Overview",
  pagecount =    "12",
  primaryclass = "math.PR",
}

@Article{Roukema:2009:BLA,
  author =       "Boudewijn F. Roukema",
  title =        "{Benford's Law} anomalies in the 2009 {Iranian}
                 presidential election",
  journal =      "ArXiv e-prints",
  day =          "16",
  month =        jun,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009arXiv0906.2789R;
                 http://arxiv.org/abs/0906.2789",
  abstract =     "The vote count first digit frequencies of the 2009
                 Iranian presidential election are analysed assuming
                 proportionality of candidates' votes to the total vote
                 per voting area. This method is closely related to
                 Benford's Law. A highly significant ($ p \approx 0.0007
                 $ ) excess of vote counts for candidate $K$ that start
                 with the digit 7 is found (41 observed, 21.2--22
                 expected). Using this property as a selection criterion
                 leads to the following coincidences. (i) Among the six
                 most populous voting areas, this criterion selects
                 those three that have greater proportions of votes for
                 A than the other three. The probability that the two
                 sub-groups are drawn from the same distribution is $ p
                 \approx 0.1 $. (ii) $K$'s vote counts for these same
                 three voting areas all have the same second digit. The
                 probability of this is $ p \approx 0.01 $. (iii) Most
                 (75\%) of the vote counts for $K$ in voting areas with
                 70 to 79 votes for $K$ are odd, and every even number
                 occurs exactly once. The probability of the latter is $
                 p \approx 0.0005 $. Interpreting the big city effect
                 (i) +( ii) as an overestimate of the true vote, assumed
                 to be roughly 50\% to match other data, while retaining
                 constant total vote numbers and increasing votes for
                 the other three candidates in proportion to their
                 average voting percentages, would imply that the
                 difference between A's and M's vote totals would drop
                 by about one million votes. These results do not
                 exclude other anomalies.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "0906.2789",
  keywords =     "Statistics - Applications",
  primaryclass = "stat.AP",
  remark =       "It appears the title changed over six updates to this
                 paper to the one in the final journal version
                 \cite{Roukema:2014:FDA}.",
  xxtitle =      "A first-digit anomaly in the 2009 {Iranian}
                 {Presidential} election",
}

@Article{Sambridge:2009:ABL,
  author =       "M. Sambridge and H. Tkalcic and A. Jackson",
  title =        "On the applicability of {Benford's Law} in the
                 Geosciences",
  journal =      "AGU Fall Meeting Abstracts",
  pages =        "A1756--??",
  month =        dec,
  year =         "2009",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Tue Nov 15 06:32:38 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2009AGUFM.S33A1756S",
  acknowledgement = ack-nhfb,
  keywords =     "[1294] GEODESY AND GRAVITY / Instruments and
                 techniques, [1594] GEOMAGNETISM AND PALEOMAGNETISM /
                 Instruments and techniques, [3294] MATHEMATICAL
                 GEOPHYSICS / Instruments and techniques, [7299]
                 SEISMOLOGY / General or miscellaneous",
}

@Article{Shao:2009:FDD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First digit distribution of hadron full width",
  journal =      j-MOD-PHYS-LETT-A,
  volume =       "24",
  number =       "40",
  pages =        "3275--3282",
  month =        "????",
  year =         "2009",
  CODEN =        "MPLAEQ",
  DOI =          "https://doi.org/10.1142/S0217732309031223",
  ISSN =         "0217-7323 (print), 1793-6632 (electronic)",
  ISSN-L =       "0217-7323",
  bibdate =      "Mon Nov 14 16:26:06 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "A phenomenological law, called Benford's law, states
                 that the occurrence of the first digit, i.e., $ 1, 2,
                 \ldots {}, 9 $, of numbers from many real world sources
                 is not uniformly distributed, but instead favors
                 smaller ones according to a logarithmic distribution.
                 We investigate, for the first time, the first digit
                 distribution of the full widths of mesons and baryons
                 in the well defined science domain of particle physics
                 systematically, and find that they agree excellently
                 with the Benford distribution. We also discuss several
                 general properties of Benford's law, i.e., the law is
                 scale-invariant, base-invariant, and power-invariant.
                 This means that the lifetimes of hadrons follow also
                 Benford's law.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1004.3077",
  fjournal =     "Modern Physics Letters A (MPLA)",
  journal-URL =  "http://www.worldscientific.com/loi/mpla",
  primaryclass = "hep-ph",
}

@Article{Shi:2009:FDL,
  author =       "Yun Q. Shi",
  title =        "{First Digit Law} and Its Application to Digital
                 Forensics",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "5450",
  pages =        "448--453",
  year =         "2009",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-04438-0_37",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:32:48 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-04438-0_37",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-04438-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-04438-0",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Speed:2009:YWP,
  author =       "T. Speed",
  title =        "You want proof?",
  journal =      j-BULL-INST-MATH-STAT,
  volume =       "38",
  number =       "??",
  pages =        "11--??",
  month =        "????",
  year =         "2009",
  CODEN =        "SMBCVA",
  ISSN =         "0146-3942",
  ISSN-L =       "0146-3942",
  bibdate =      "Wed Nov 16 07:00:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://bulletin.imstat.org/archive/",
  acknowledgement = ack-nhfb,
  fjournal =     "Bulletin --- Institute of Mathematical Statistics",
  keywords =     "Benford's Law",
  remark =       "As of 16 November 2011, volume 38 is not yet online at
                 the publisher Web site, although there are (broken)
                 links for volumes 31 (2002) to date.",
}

@Article{Stosic:2009:CSM,
  author =       "Borko D. Stosi{\'c} and Tatijana Stosi{\'c}",
  title =        "Comment on {``Ising model on the scale-free network
                 with a Cayley-tree-like structure''}",
  journal =      j-PHYS-REV-E,
  volume =       "79",
  number =       apr,
  pages =        "048101",
  day =          "24",
  month =        apr,
  year =         "2009",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.79.048101",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.79.048101",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "2",
}

@Misc{Tao:2009:BLZ,
  author =       "Terrence Tao",
  title =        "{Benford}'s law, {Zipf}'s law, and the {Pareto}
                 distribution",
  howpublished = "Web document.",
  year =         "2009",
  bibdate =      "Mon Nov 14 16:59:19 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://terrytao.wordpress.com/2009/07/03/benfords-law-zipfs-law-and-the-pareto-distribution/",
  acknowledgement = ack-nhfb,
}

@Article{Todter:2009:BLI,
  author =       "Karl-Heinz T{\"o}dter",
  title =        "{Benford's Law} as an Indicator of Fraud in
                 Economics",
  journal =      j-GER-ECON-REV,
  volume =       "10",
  number =       "3",
  pages =        "339--351",
  month =        aug,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1468-0475.2009.00475.x",
  ISSN =         "1465-6485 (print), 1468-0475 (electronic)",
  ISSN-L =       "1465-6485",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  onlinedate =   "16 Jun 2009",
}

@Article{Villasenor-Alva:2009:BGF,
  author =       "Jos{\'e} A. Villase{\~n}or-Alva and Elizabeth
                 Gonz{\'a}lez-Estrada",
  title =        "A bootstrap goodness of fit test for the generalized
                 {Pareto} distribution",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "53",
  number =       "11",
  pages =        "3835--3841",
  day =          "1",
  month =        sep,
  year =         "2009",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:42:33 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947309001406",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@InProceedings{Wang:2009:UBL,
  author =       "J. Wang and B. H. Cha and S. H. Cho and C. C. J. Kuo",
  editor =       "{IEEE}",
  booktitle =    "2009 IEEE International Conference on Multimedia and
                 Expo",
  title =        "Understanding {Benford's Law} and its vulnerability in
                 image forensics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1568--1571",
  month =        jun,
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ICME.2009.5202811",
  ISSN =         "1945-7871",
  bibdate =      "Sat Sep 10 11:29:36 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Application software; Authentication; Benford law;
                 Benford's law; Digital images; forensic science;
                 Forensics; Gaussian processes; generalized Benford's
                 law; generalized Gaussian function; generalized
                 Laplacian function; histogram manipulation; histogram
                 manipulation attack; Histograms; image authentication;
                 image coding; image forensics; Image processing;
                 Laplace equations; message authentication; probability;
                 Probability density function; probability density
                 function; random processes; random variable; Random
                 variables; Signal processing",
}

@Article{Xie:2009:FAS,
  author =       "Tao Xie and Yao Sun",
  title =        "A file assignment strategy independent of workload
                 characteristic assumptions",
  journal =      j-TOS,
  volume =       "5",
  number =       "3",
  pages =        "10:1--10:??",
  month =        nov,
  year =         "2009",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/1629075.1629079",
  ISSN =         "1553-3077 (print), 1553-3093 (electronic)",
  ISSN-L =       "1553-3077",
  bibdate =      "Tue Mar 16 15:33:57 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tos/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tos.bib",
  abstract =     "The problem of statically assigning nonpartitioned
                 files in a parallel I/O system has been extensively
                 investigated. A basic workload characteristic
                 assumption of most existing solutions to the problem is
                 that there exists a strong inverse correlation between
                 file access frequency and file size. In other words,
                 the most popular files are typically small in size,
                 while the large files are relatively unpopular. Recent
                 studies on the characteristics of Web proxy traces
                 suggested, however, the correlation, if any, is so weak
                 that it can be ignored. Hence, the following two
                 questions arise naturally. First, can existing
                 algorithms still perform well when the workload
                 assumption does not hold? Second, if not, can one
                 develop a new file assignment strategy that is immune
                 to the workload assumption? To answer these questions,
                 we first evaluate the performance of three well-known
                 file assignment algorithms with and without the
                 workload assumption, respectively. Next, we develop a
                 novel static nonpartitioned file assignment strategy
                 for parallel I/O systems, called static round-robin
                 (SOR), which is immune to the workload assumption.
                 Comprehensive experimental results show that SOR
                 consistently improves the performance in terms of mean
                 response time over the existing schemes.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Storage",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J960",
  keywords =     "File assignment; load balancing; parallel I/O;
                 workload characteristics; Zipfian distribution",
}

@Article{Zhang:2009:ZDT,
  author =       "Jianhua Zhang and Qinghua Chen and Yougui Wang",
  title =        "{Zipf} distribution in top {Chinese} firms and an
                 economic explanation",
  journal =      j-PHYSICA-A,
  volume =       "388",
  number =       "10",
  pages =        "2020--2024",
  day =          "15",
  month =        may,
  year =         "2009",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2009.01.027",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437109000806",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@InProceedings{Zhao:2009:IFU,
  author =       "Xi Zhao and A. T. S. Ho and Y. Q. Shi",
  booktitle =    "2009 16th International Conference on Digital Signal
                 Processing",
  title =        "Image forensics using generalised {Benford's Law} for
                 accurate detection of unknown {JPEG} compression in
                 watermarked images",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--8",
  month =        jul,
  year =         "2009",
  DOI =          "https://doi.org/10.1109/ICDSP.2009.5201261",
  ISSN =         "1546-1874",
  bibdate =      "Sat Sep 10 11:42:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Authentication; average QF correct detection rate;
                 data compression; DCT; Digital images; Forensics;
                 generalised Benford law; Generalised Benford's Law;
                 Image Authentication; Image coding; image coding; image
                 forensics technique; Image storage; JPEG Compression;
                 message authentication; object detection; Physics
                 computing; Q factor; Q-factor; quality factors;
                 Semi-fragile Watermarking; semifragile watermarking;
                 Signal processing algorithms; Transform coding; unknown
                 JPEG compression detection; watermarked images;
                 Watermarking; watermarking",
}

@Article{Abourbih:2010:SSD,
  author =       "Jonathan A. Abourbih and Luke Blaney and Alan Bundy
                 and Fiona McNeill",
  title =        "A Single-Significant-Digit Calculus for Semi-Automated
                 Guesstimation",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6173",
  pages =        "354--368",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-14203-1_31",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:43:23 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-14203-1_31",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-14203-1",
  book-URL =     "http://www.springerlink.com/content/978-3-642-14203-1",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Afify:2010:EEP,
  author =       "W. M. Afify",
  title =        "On estimation of the exponentiated {Pareto}
                 distribution under different sample schemes",
  journal =      j-STAT-METHODOL,
  volume =       "7",
  number =       "2",
  pages =        "77--83",
  month =        mar,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:41 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312709000653",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Misc{Alagoz:2010:MDB,
  author =       "Ali Alag{\"o}z and Mustafa Ay",
  title =        "Muhasebe Denetiminde {Benford} Kanunu Temelli Dijital
                 Analiz. ({Turkish}) [{Benford Law}-Based Digital
                 Analysis of Accounting Oversight]",
  pages =        "17",
  day =          "8",
  month =        jan,
  year =         "2010",
  bibdate =      "Mon Feb 18 09:19:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "www.alialagoz.com.tr/doc-dr-alialagoz-makaleleri/muhasebe_denetiminde_benfrod_kanunu_temelli_dijital_analiz.pdf",
  acknowledgement = ack-nhfb,
  language =     "Turkish",
}

@Article{Aldous:2010:WCO,
  author =       "David Aldous and Tung Phan",
  title =        "When Can One Test an Explanation? {Compare} and
                 Contrast {Benford's Law} and the Fuzzy {CLT}",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "3",
  pages =        "221--227",
  month =        aug,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2010.09098",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2757166",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1198/tast.2010.09098",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Altamirano:2010:PTS,
  author =       "Carlo Altamirano and Alberto Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      "ArXiv e-prints",
  day =          "10",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:12:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1008.1614",
  abstract =     "We show that the laws of Zipf and Benford, obeyed by
                 scores of numerical data generated by many and diverse
                 kinds of natural phenomena and human activity are
                 related to the focal expression of a generalized
                 thermodynamic structure. This structure is obtained
                 from a deformed type of statistical mechanics that
                 arises when configurational phase space is incompletely
                 visited in a severe way. Specifically, the restriction
                 is that the accessible fraction of this space has
                 fractal properties. The focal expression is an
                 (incomplete) Legendre transform between two entropy (or
                 Massieu) potentials that when particularized to first
                 digits leads to a previously existing generalization of
                 Benford's law. The inverse functional of this
                 expression leads to Zipf's law; but it naturally
                 includes the bends or tails observed in real data for
                 small and large rank. Remarkably, we find that the
                 entire problem is analogous to the transition to chaos
                 via intermittency exhibited by low-dimensional
                 nonlinear maps. Our results also explain the generic
                 form of the degree distribution of scale-free
                 networks.",
  acknowledgement = ack-nhfb,
  remark =       "To be published in European Physical Journal B.",
}

@Article{Anderson:2010:BLC,
  author =       "Theresa Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford's} Law For Coefficients of Modular Forms and
                 Partition Functions",
  journal =      "ArXiv e-prints",
  day =          "3",
  month =        sep,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:10:51 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1009.0780",
  abstract =     "Here we prove that Benford's law holds for
                 coefficients of an infinite class of modular forms.
                 Expanding the work of Bringmann and Ono on exact
                 formulas for harmonic Maass forms, we derive the
                 necessary asymptotics. This implies that the
                 unrestricted partition function $ p(n) $, as well as
                 other natural partition functions, satisfy Benford's
                 law.",
  acknowledgement = ack-nhfb,
  pagecount =    "10",
}

@Article{Bachmann:2010:APC,
  author =       "Val{\'e}rie Bachmann and Martin H. Fischer and
                 Hans-Peter Landolt and Peter Brugger",
  title =        "Asymmetric prefrontal cortex functions predict
                 asymmetries in number space",
  journal =      j-BRAIN-COGN,
  volume =       "74",
  number =       "3",
  pages =        "306--311",
  month =        dec,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.bandc.2010.08.011",
  ISSN =         "0278-2626 (print), 1090-2147 (electronic)",
  ISSN-L =       "0278-2626",
  bibdate =      "Tue Nov 22 11:28:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0278262610001272",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; small-number bias (SNB); Spatial
                 Numerical Association of Response Codes (SNARC)
                 effect",
}

@Article{Balanzario:2010:SCB,
  author =       "Eugenio P. Balanzario and Jorge S{\'a}nchez-Ortiz",
  title =        "Sufficient conditions for {Benford's Law}",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "23--24",
  pages =        "1713--1719",
  day =          "1--15",
  month =        dec,
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2010.07.014",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "62E10 (62E17)",
  MRnumber =     "2734233 (2011i:62019)",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715210002087",
  abstract =     "We present two sufficient conditions for an absolutely
                 continuous random variable to obey Benford's Law for
                 the distribution of the first significant digit. These
                 two sufficient conditions suggest that Benford's Law
                 will not often be observed in everyday sets of
                 numerical data. On the other hand, we recall that there
                 are two processes by way of which a random variable can
                 come close to following Benford's Law. The first of
                 these is the multiplication of independent random
                 variables and the second is the exponentiation of a
                 random variable to a large power. Our working tool is
                 the Poisson sum formula of Fourier analysis. Like the
                 central limit theorem, Benford's Law has an asymptotic
                 nature.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; First significant digit",
}

@Article{Balaz:2010:BLD,
  author =       "V. Bal{\'a}{\v{z}} and K. Nagasaka and O. Strauch",
  title =        "{Benford}'s law and distribution functions of
                 sequences in $ (0, 1) $",
  journal =      j-MATH-NOTES-ACAD-SCI-USSR,
  volume =       "88",
  number =       "3--4",
  pages =        "449--463",
  month =        oct,
  year =         "2010",
  CODEN =        "MTHNB2",
  DOI =          "https://doi.org/10.1134/S0001434610090178",
  ISSN =         "0001-4346 (print), 1573-8876 (electronic)",
  ISSN-L =       "0001-4346",
  bibdate =      "Fri Nov 25 10:52:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1134/S0001434610090178",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Notes of the {Academy of Sciences of the
                 USSR = Matematicheskie Zametki}",
}

@Article{Balazh:2010:BLD,
  author =       "V. Balazh and K. Nagasaka and O. Shtraukh",
  title =        "{Benford}'s law and distribution functions of
                 sequences in {$ (0, 1) $}",
  journal =      j-MAT-ZAMETKI,
  volume =       "88",
  number =       "4",
  pages =        "485--501",
  year =         "2010",
  DOI =          "https://doi.org/10.1134/S0001434610090178",
  ISSN =         "0025-567X",
  ISSN-L =       "0025-567X",
  MRclass =      "11K06 (60E05)",
  MRnumber =     "2882211",
  MRreviewer =   "Michael Drmota",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi{\u\i}skaya Akademiya Nauk. Matematicheskie
                 Zametki",
  journal-URL =  "http://link.springer.com/journal/11006",
}

@TechReport{Bauer:2010:DDF,
  author =       "J. Bauer and J. Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford's
                 Law} on Regression Tables",
  type =         "Report",
  institution =  "Institute of Sociology,
                 Ludwig-Maximilians-Universit{\"a}t",
  address =      "M{\"u}nchen, Germany",
  pages =        "????",
  year =         "2010",
  bibdate =      "Tue Nov 22 21:15:18 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Beber:2010:WNS,
  author =       "Bernd Beber and Alexandria Scacco",
  title =        "What the Numbers Say: a Digit-Based Test for Election
                 Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "20",
  number =       "2",
  pages =        "211--234",
  month =        "Spring",
  year =         "2010",
  DOI =          "https://doi.org/10.1093/pan/mps003",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 17:29:42 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pan.oxfordjournals.org/content/20/2/211.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@TechReport{Berger:2010:FFFa,
  author =       "A. Berger and T. P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  pages =        "8",
  year =         "2010",
  bibdate =      "Mon Feb 18 17:31:57 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.benfordonline.net/ARTICLES/BergerHill2010.pdf",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for $
                 \log_{10} X $ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion.",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2010:FFFb,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "Fundamental Flaws in {Feller}'s Classical Derivation
                 of {Benford's Law}",
  journal =      "ArXiv e-prints",
  month =        may,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 18:23:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1005.2598B;
                 http://arxiv.org/abs/1005.2598",
  abstract =     "Feller's classic text \booktitle{An Introduction to
                 Probability Theory and its Applications}
                 \cite{Feller:1968:IPT} contains a derivation of the
                 well known significant-digit law called Benford's law.
                 More specifically, Feller gives a sufficient condition
                 (`large spread') for a random variable $X$ to be
                 approximately Benford distributed, that is, for $
                 \log_{10}X $ to be approximately uniformly distributed
                 modulo one. This note shows that the large-spread
                 derivation, which continues to be widely cited and
                 used, contains serious basic errors. Concrete examples
                 and a new inequality clearly demonstrate that large
                 spread (or large spread on a logarithmic scale) does
                 not imply that a random variable is approximately
                 Benford distributed, for any reasonable definition of
                 `spread' or measure of dispersion",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1005.2598",
  keywords =     "Mathematics - Probability, Mathematics - Statistics,
                 62Axx",
  primaryclass = "math.PR",
}

@TechReport{Berger:2010:LSD,
  author =       "A. Berger",
  title =        "Large Spread Does Not Imply {Benford's Law}",
  type =         "Preprint",
  institution =  "Department of Mathematical and Statistical Sciences,
                 University of Alberta",
  address =      "Edmonton, AB, Canada",
  year =         "2010",
  bibdate =      "Sat Nov 12 16:46:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.ualberta.ca/~aberger/Publications.html",
  acknowledgement = ack-nhfb,
}

@Article{Block:2010:GEB,
  author =       "Henry W. Block and Thomas H. Savits",
  title =        "A General Example for {Benford} Data",
  journal =      j-AMER-STAT,
  volume =       "64",
  number =       "4",
  pages =        "335--339",
  month =        nov,
  year =         "2010",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2010.09169",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  MRnumber =     "2758565",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Benford's Law deals, among other things, with the
                 proportion of numbers whose first significant digit is
                 a $1$ (e.g., $ 0.00131 $ and $ 19668 $ both have first
                 significant digit $1$) in a variety of datasets. In
                 these datasets, which arise in various compendiums or
                 as mixtures of various sets of numbers, the proportion
                 of numbers with first significant digit one is $ 0.3010
                 $ which is much higher than the commonsense value of $
                 1 / 9 $. The reasons for this occurrence have been
                 elusive. Mathematical attempts to explain this
                 phenomenon have been relatively fruitless. Methods
                 involving probability have been somewhat more
                 successful. In this article we give some simple reasons
                 for this occurrence and also give an example of a
                 general mixture of distributions which exactly
                 satisfies this Law. Various other examples and
                 counterexamples are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
}

@Article{Bonache:2010:DFL,
  author =       "A. B. Bonache and K. Moris and J. Maurice",
  title =        "{D}{\'e}tection de fraudes et loi de {Benford}:
                 Quelques risques associ{\'e}s. ({French}) [{Fraud}
                 detection and {Benford}'s law: Some risks]",
  journal =      "Revue Fran{\c{c}}aise de Comptabilit{\'e}",
  volume =       "??",
  number =       "431",
  pages =        "24--27",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "0484-8764",
  ISSN-L =       "0484-8764",
  bibdate =      "Mon Feb 18 17:33:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "????",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.experts-comptables.fr/csoec/Publications/RFC",
  language =     "French",
}

@InCollection{Brahler:2010:EMS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Anna-Lena
                 Emke",
  booktitle =    "{Ilmenauer Schriften zur Betriebswirtschaftslehre}.
                 ({German}) [{Illmenauer} writings on economics]",
  title =        "{Der Einsatz mathematisch-statistischer Methoden in
                 der digitalen Betriebspr{\"u}fung}. ({German}) [{The}
                 use of mathematical and statistical methods in the
                 digital audit]",
  volume =       "4/2010",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "48",
  month =        apr,
  year =         "2010",
  ISBN =         "3-940882-23-2",
  ISBN-13 =      "978-3-940882-23-3",
  ISSN =         "1866-2145 (print), 2192-4643 (electronic)",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 17:35:58 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.econstor.eu/dspace/bitstream/10419/55680/1/665348576.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Bravo-Marquez:2010:HLM,
  author =       "Felipe Bravo-Marquez and Gaston L'Huillier and
                 Sebasti{\'a}n A. R{\'\i}os and Juan D. Vel{\'a}squez",
  title =        "Hypergeometric Language Model and {Zipf}-Like Scoring
                 Function for {Web} Document Similarity Retrieval",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6393",
  pages =        "303--308",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-16321-0_32",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:49:42 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-16321-0_32",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-16321-0",
  book-URL =     "http://www.springerlink.com/content/978-3-642-16321-0",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Burns:2010:PL,
  author =       "John Burns",
  title =        "Probably likely",
  journal =      j-NEW-SCIENTIST,
  volume =       "208",
  number =       "2786",
  pages =        "32-",
  year =         "2010",
  CODEN =        "NWSCAL",
  DOI =          "https://doi.org/10.1016/S0262-4079(10)62810-2",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407910628102",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law",
}

@Article{Cartlidge:2010:NNO,
  author =       "Edwin Cartlidge",
  title =        "In nature, number one dominates",
  journal =      "Institute of Physics, Environmental Research Letters",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "25",
  month =        oct,
  year =         "2010",
  DOI =          "????",
  bibdate =      "Mon Feb 18 17:38:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://environmentalresearchweb.org/cws/article/news/44124",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Cifarelli:2010:GSP,
  author =       "D. Michele Cifarelli and R. P. Gupta and K.
                 Jayakumar",
  title =        "On generalized semi-{Pareto} and semi-{Burr}
                 distributions and random coefficient minification
                 processes",
  journal =      j-STAT-PAPERS,
  volume =       "51",
  number =       "1",
  pages =        "193--208",
  month =        jan,
  year =         "2010",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-008-0132-5",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:31 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-008-0132-5",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Misc{Conway:2010:CFM,
  author =       "D. Conway",
  title =        "{Benford's Law} Tests for {Wikileaks} Data",
  howpublished = "Zero Intelligence Agents website.",
  day =          "1",
  month =        aug,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:39:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.drewconway.com/zia/?p=2234",
  acknowledgement = ack-nhfb,
}

@InCollection{Corazza:2010:CFM,
  author =       "Marco Corazza and Andrea Ellero and Alberto Zorzi",
  booktitle =    "Mathematical and statistical methods for actuarial
                 sciences and finance",
  title =        "Checking financial markets via {Benford}'s law: the
                 {S\&P 500} case",
  publisher =    "Springer Italia",
  address =      "Milan, Italy",
  pages =        "93--102",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-88-470-1481-7_10",
  MRclass =      "62P05",
  MRnumber =     "2676191",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/chapter/10.1007/978-88-470-1481-7_10",
  acknowledgement = ack-nhfb,
}

@Article{Corominas-Murtra:2010:UZL,
  author =       "Bernat Corominas-Murtra and Ricard V. Sol{\'e}",
  title =        "Universality of {Zipf}'s law",
  journal =      j-PHYS-REV-E,
  volume =       "82",
  number =       "1",
  pages =        "011102",
  day =          "1",
  month =        jul,
  year =         "2010",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.82.011102",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  MRclass =      "82B03 (62B10)",
  MRnumber =     "2736361 (2011j:82002)",
  MRreviewer =   "N. N. Ganikhodjaev",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.82.011102",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Courtland:2010:CML,
  author =       "Rachel Courtland",
  title =        "Curious mathematical law is rife in nature",
  journal =      j-NEW-SCIENTIST,
  volume =       "208",
  number =       "2782",
  pages =        "10--10",
  day =          "16",
  month =        oct,
  year =         "2010",
  CODEN =        "NWSCAL",
  DOI =          "https://doi.org/10.1016/S0262-4079(10)62497-9",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407910624979",
  abstract =     "Disparate data sets produced by natural phenomena all
                 follow Benford's law, suggesting new ways to detect
                 earthquakes or scientific anomalies",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law; earthquake detection",
  xxISSN =       "0262-4079, 0028-6664",
}

@InCollection{Crato:2010:MB,
  author =       "Nuno Crato",
  booktitle =    "Figuring It Out: Entertaining Encounters with Everyday
                 Math",
  title =        "{Mr. Benford}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "ix + 227",
  pages =        "173--178",
  year =         "2010",
  CODEN =        "LNMAA2",
  DOI =          "https://doi.org/10.1007/978-3-642-04833-3_41",
  ISBN =         "3-642-04832-3 (hardcover)",
  ISBN-13 =      "978-3-642-04832-6 (hardcover)",
  bibdate =      "Wed Aug 12 09:28:13 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-04833-3_41.pdf",
  abstract =     "This is a book of mathematical stories, funny and
                 puzzling mathematical stories. They tell of villains
                 who try to steal secrets, heroes who encode their
                 messages, and mathematicians who spend years on end
                 searching for the best way to pile oranges. There are
                 also stories about highway confusions occurring when
                 the rules of Cartesian geometry are ignored,
                 small-change errors due to ignorance of ancient
                 paradoxes, and mistakes in calendars arising from poor
                 numerical approximations. This book is about the power
                 and beauty of mathematics. It shows mathematics in
                 action, explained in a way that everybody can
                 understand.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-04833-3",
  tableofcontents = "Everyday Matters. \\
                 The dinner table algorithm \\
                 Cutting the Christmas cake \\
                 Oranges and computers \\
                 When two and two don't make four \\
                 Getting more intelligent every day \\
                 The other lane always goes faster \\
                 Shoelaces and neckties \\
                 Number puzzles \\
                 Tossing a coin \\
                 The switch \\
                 Eubulides, the heap and the Euro \\
                 The Earth is Round. \\
                 How GPS works \\
                 Gear wheels \\
                 February 29 \\
                 The Nonius scale \\
                 Pedro Nunes' map \\
                 Lighthouse geometry \\
                 Asteroids and least squares \\
                 The useful man and the genius \\
                 Secret Affairs. \\
                 Alice and Bob \\
                 Inviolate cybersecrets \\
                 Quantum cryptography \\
                 The FBI wavelet \\
                 The enigma machine \\
                 Art and Geometry. \\
                 The Vitruvian man \\
                 The golden number \\
                 The geometry of A4 paper sizes \\
                 The strange worlds of Escher \\
                 Escher and the M{\"o}bius strip \\
                 Picasso, Einstein and the fourth dimension \\
                 Pollock's fractals \\
                 Voronoi diagrams \\
                 The Platonic solids \\
                 Pythagorean mosquitoes \\
                 The most beautiful of all \\
                 Mathematical Objects. \\
                 The power of math \\
                 Doubts in the realm of certainty \\
                 When chance enhances reliability \\
                 The difficulty of chance \\
                 Conjectures and proofs \\
                 Mr. Benford \\
                 Financial fractals \\
                 Turing's test \\
                 DNA computers \\
                 Magical multiplication \\
                 Pi day \\
                 The best job in the world \\
                 Out of This World. \\
                 Electoral paradoxes \\
                 The melon paradox \\
                 The cupcake paradox \\
                 Infinity \\
                 Unfair games \\
                 Monsieur Bertrand \\
                 Boy or girl? \\
                 A puzzle for Christmas \\
                 Crisis time for Easter eggs",
}

@Article{Debreceny:2010:DMJ,
  author =       "Roger S. Debreceny and Glen L. Gray",
  title =        "Data mining journal entries for fraud detection: An
                 exploratory study",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "157--181",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "https://doi.org/10.1016/j.accinf.2010.08.001",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See discussion
                 \cite{Grabski:2010:DDM,Kriel:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000540;
                 http://www.sciencedirect.com/science/journal/14670895",
  abstract =     "Fraud detection has become a critical component of
                 financial audits and audit standards have heightened
                 emphasis on journal entries as part of fraud detection.
                 This paper canvasses perspectives on applying data
                 mining techniques to journal entries. In the past, the
                 impediment to researching journal entry data mining is
                 getting access to journal entry data sets, which may
                 explain why the published research in this area is a
                 null set. For this project, we had access to journal
                 entry data sets for 29 different organizations. Our
                 initial exploratory test of the data sets had
                 interesting preliminary findings. (1) For all 29
                 entities, the distribution of first digits of journal
                 dollar amounts differed from that expected by Benford's
                 Law. (2) Regarding last digits, unlike first digits,
                 which are expected to have a logarithmic distribution,
                 the last digits would be expected to have a uniform
                 distribution. Our test found that the distribution was
                 not uniform for many of the entities. In fact, eight
                 entities had one number whose frequency was three times
                 more than expected. (3) We compared the number of
                 accounts related to the top five most frequently
                 occurring three last digit combinations. Four entities
                 had a very high occurrences of the most frequent three
                 digit combinations that involved only a small set of
                 accounts, one entity had a low occurrences of the most
                 frequent three digit combination that involved a large
                 set of accounts and 24 had a low occurrences of the
                 most frequent three digit combinations that involved a
                 small set of accounts. In general, the first four
                 entities would probably pose the highest risk of fraud
                 because it could indicate that the fraudster is
                 covering up or falsifying a particular class of
                 transactions. In the future, we will apply more data
                 mining techniques to discover other patterns and
                 relationships in the data sets. We also want to seed
                 the dataset with fraud indicators (e.g., pairs of
                 accounts that would not be expected in a journal entry)
                 and compare the sensitivity of the different data
                 mining techniques to find these seeded indicators.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Accounting information systems; Auditing; Benford's
                 Law; Data mining; Fraud; Journal entries; XBRL GL",
  remark =       "2009 Research Symposium on Information Integrity \&
                 Information Systems Assurance.",
}

@TechReport{Deckert:2010:IBL,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "The Irrelevance of {Benford's Law} for Detecting Fraud
                 in Elections",
  type =         "{CALTECH} working paper",
  number =       "9",
  institution =  "California Institute of Technology",
  address =      "Pasadena, CA, USA",
  pages =        "27",
  day =          "9",
  month =        mar,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:40:53 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://vote.caltech.edu/drupal/node/327",
  acknowledgement = ack-nhfb,
  remark =       "From the abstract: ``..., we argue here that Benford's
                 Law is essentially useless as a forensic indicator of
                 fraud.''",
}

@Article{Deligny:2010:RRL,
  author =       "H. Deligny and P. Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford's Law}]",
  journal =      "ArXiv e-prints",
  day =          "23",
  month =        jul,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 18:14:51 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1007.5349D;
                 http://arxiv.org/abs/1007.5349",
  abstract =     "We prove that many sequences of positive numbers $
                 (a_n) $ defined by finite linear difference equations $
                 a_{n + k} = c_{k - 1} a_{n + k - 1} + \ldots {} + c_0
                 a_n $ with suitable nonnegative reals coefficients $
                 c_i $ satisfy Benford's Law on the first digit in many
                 bases $ b > 2 $. Our techniques rely on
                 Perron--Frobenius theory via the companion matrix of
                 the characteristic polynomial of the defining
                 equation.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1007.5349",
  keywords =     "Mathematics - Dynamical Systems, Mathematics - Rings
                 and Algebras, 11A99",
  language =     "French",
  primaryclass = "math.DS",
}

@Article{Diekmann:2010:BLF,
  author =       "Andreas Diekmann and Ben Jann",
  title =        "{Benford's Law} and Fraud Detection: Facts and
                 Legends",
  journal =      j-GER-ECON-REV,
  volume =       "11",
  number =       "3",
  pages =        "397--401",
  month =        aug,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1468-0475.2010.00510.x",
  ISSN =         "1465-6485 (print), 1468-0475 (electronic)",
  ISSN-L =       "1465-6485",
  bibdate =      "Mon Nov 14 17:09:33 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  keywords =     "Benford's law; false negative; false positive; fraud
                 detection; regression coefficients",
  onlinedate =   "6 Apr 2010",
}

@Article{Dixit:2010:EEP,
  author =       "U. J. Dixit and M. Jabbari Nooghabi",
  title =        "Efficient estimation in the {Pareto} distribution",
  journal =      j-STAT-METHODOL,
  volume =       "7",
  number =       "6",
  pages =        "687--691",
  month =        nov,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:44 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312710000419",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Article{Egghe:2010:BCN,
  author =       "Leo Egghe",
  title =        "Brief Communication: A new short proof of {Naranan}'s
                 theorem, explaining {Lotka's Law} and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "61",
  number =       "12",
  pages =        "2581--2583",
  month =        dec,
  year =         "2010",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.21431",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:42:58 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "27 Sep 2010",
}

@Article{Egghe:2010:CSS,
  author =       "L. Egghe",
  title =        "Characteristic scores and scales in a {Lotkaian}
                 framework",
  journal =      j-SCIENTOMETRICS,
  volume =       "83",
  number =       "2",
  pages =        "455--462",
  month =        may,
  year =         "2010",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-009-0009-y",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:20 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-009-0009-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Egghe:2010:NSP,
  author =       "Leo Egghe",
  title =        "A new short proof of {Naranan}'s theorem, explaining
                 {Lotka's Law} and {Zipf's Law}",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "61",
  number =       "12",
  pages =        "2581--2583",
  year =         "2010",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.21431",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@Article{Farkas:2010:SUN,
  author =       "Janos Farkas and Gy{\"o}rgy Gyurky",
  title =        "The significance of using the {Newcomb--Benford} law
                 as a test of nuclear half-life calculations",
  journal =      j-ACTA-PHYS-POL-B,
  volume =       "41",
  number =       "6",
  pages =        "1213--1221",
  year =         "2010",
  CODEN =        "APOBBB",
  ISSN =         "0587-4254 (print), 1509-5770 (electronic)",
  ISSN-L =       "0587-4254",
  bibdate =      "Mon Nov 14 16:21:42 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1006.3615F;
                 http://arxiv.org/abs/1006.3615",
  abstract =     "Half-life number sequences collected from nuclear data
                 charts are found to obey the Newcomb--Benford law.
                 Based on this fact, it has been suggested recently,
                 that this law should be used to test the quality of
                 nuclear decay models. In this paper we briefly recall
                 how, when and why the Newcomb--Benford law can be
                 observed in a set of numbers with a given probability
                 distribution. We investigate the special case of
                 nuclear half-lives, and show that the law provides no
                 additional clue in understanding decay half-lives.
                 Thus, it can play no significant role in testing
                 nuclear decay theories.",
  acknowledgement = ack-nhfb,
  ajournal =     "Acta Phys. Pol. B",
  ajournal-2 =   "Acta Phys. Polon. B",
  archiveprefix = "arXiv",
  eprint =       "1006.3615",
  fjournal =     "Acta Physica Polonica B",
  journal-URL =  "http://www.actaphys.uj.edu.pl/pl/acta_physica_polonica_b",
  primaryclass = "math-ph",
}

@Article{Ferrer-i-Cancho:2010:RTD,
  author =       "Ramon Ferrer-i-Cancho and Brita Elvev{\aa}g",
  title =        "Random Texts Do Not Exhibit the Real {Zipf's Law}-Like
                 Rank Distribution",
  journal =      j-PLOS-ONE,
  volume =       "5",
  number =       "3",
  pages =        "e9411:1--e9411:10",
  month =        mar,
  year =         "2010",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0009411",
  ISSN =         "1932-6203",
  bibdate =      "Wed Aug 12 08:54:42 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0009411",
  abstract =     "Zipf's law states that the relationship between the
                 frequency of a word in a text and its rank (the most
                 frequent word has rank 1, the 2nd most frequent word
                 has rank 2, \ldots{}) is approximately linear when
                 plotted on a double logarithmic scale. It has been
                 argued that the law is not a relevant or useful
                 property of language because simple random texts ---
                 constructed by concatenating random characters
                 including blanks behaving as word delimiters ---
                 exhibit a Zipf's law-like word rank distribution.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
}

@Article{Fischer:2010:HCS,
  author =       "Martin H. Fischer and Richard A. Mills and Samuel
                 Shaki",
  title =        "How to cook a {SNARC}: Number placement in text
                 rapidly changes spatial-numerical associations",
  journal =      j-BRAIN-COGN,
  volume =       "72",
  number =       "3",
  pages =        "333--336",
  month =        apr,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.bandc.2009.10.010",
  ISSN =         "0278-2626 (print), 1090-2147 (electronic)",
  ISSN-L =       "0278-2626",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0278262609002024",
  abstract =     "Most theoreticians believe that reading habits explain
                 why Western adults associate small numbers with left
                 space and large numbers with right space (the {SNARC}
                 effect). We challenge this belief by documenting, in
                 both English and Hebrew, that {SNARC} changes during
                 reading: small and large numbers in our texts appeared
                 near the left or right ends of the lines, positioned
                 either spatially congruent or incongruent with reading
                 habits. In English, the congruent group showed reliable
                 {SNARC} before and after reading and the incongruent
                 group's {SNARC} was significantly reduced. In Hebrew
                 the incongruent reading condition even induced a
                 reverse SNARC. These results show that {SNARC} is a
                 fleeting aspect of number representation that captures
                 multiple spatial associations.",
  acknowledgement = ack-nhfb,
  fjournal =     "Brain and Cognition",
  keywords =     "Benford's Law; Number line; Numerical cognition;
                 Reading; Spatial Numerical Association of Response
                 Codes (SNARC); Spatial numerical associations; {SNARC}
                 effect",
}

@Article{Formann:2010:NBL,
  author =       "Anton K. Formann",
  title =        "The {Newcomb--Benford Law} in Its Relation to Some
                 Common Distributions",
  journal =      j-PLOS-ONE,
  volume =       "5",
  number =       "5",
  pages =        "e10541:1--e10541:13",
  month =        may,
  year =         "2010",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0010541",
  ISSN =         "1932-6203",
  ISSN-L =       "1932-6203",
  bibdate =      "Mon Nov 14 18:19:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010PLoSO...510541F",
  abstract =     "An often reported, but nevertheless persistently
                 striking observation, formalized as the Newcomb-Benford
                 law (NBL), is that the frequencies with which the
                 leading digits of numbers occur in a large variety of
                 data are far away from being uniform. Most spectacular
                 seems to be the fact that in many data the leading
                 digit 1 occurs in nearly one third of all cases.
                 Explanations for this uneven distribution of the
                 leading digits were, among others, scale- and
                 base-invariance. Little attention, however, found the
                 interrelation between the distribution of the
                 significant digits and the distribution of the observed
                 variable. It is shown here by simulation that long
                 right-tailed distributions of a random variable are
                 compatible with the NBL, and that for distributions of
                 the ratio of two random variables the fit generally
                 improves. Distributions not putting most mass on small
                 values of the random variable (e.g. symmetric
                 distributions) fail to fit. Hence, the validity of the
                 NBL needs the predominance of small values and, when
                 thinking of real-world data, a majority of small
                 entities. Analyses of data on stock prices, the areas
                 and numbers of inhabitants of countries, and the
                 starting page numbers of papers from a bibliography
                 sustain this conclusion. In all, these findings may
                 help to understand the mechanisms behind the NBL and
                 the conditions needed for its validity. That this law
                 is not only of scientific interest per se, but that, in
                 addition, it has also substantial implications can be
                 seen from those fields where it was suggested to be put
                 into practice. These fields reach from the detection of
                 irregularities in data (e.g. economic fraud) to
                 optimizing the architecture of computers regarding
                 number representation, storage, and round-off errors.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
}

@Article{Genolini:2010:EIP,
  author =       "Christophe Genolini and Tarak Driss",
  title =        "Eveiller l'int{\'e}r{\^e}t pour la statistique par
                 l'exemple. ({French}) [{Raising} interest in statistics
                 by example]",
  journal =      "Statistique et Enseignement",
  volume =       "1",
  number =       "2",
  pages =        "49--57",
  month =        "????",
  year =         "2010",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "2108-6745",
  ISSN-L =       "2108-6745",
  bibdate =      "Mon Feb 18 17:43:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://publications-sfds.math.cnrs.fr/index.php/StatEns/article/view/16",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.statistique-et-enseignement.fr/",
  keywords =     "Benford's Law",
  language =     "French",
}

@Article{Giuliano:2010:UPI,
  author =       "Rita Giuliano and {\'E}lise Janvresse",
  title =        "A unifying probabilistic interpretation of {Benford}'s
                 law",
  journal =      "Uniform Distribution Theory",
  volume =       "5",
  number =       "2",
  pages =        "169--182",
  year =         "2010",
  CODEN =        "????",
  ISSN =         "1336-913X",
  ISSN-L =       "1336-913X",
  MRclass =      "60J10 (11K99 60A99)",
  MRnumber =     "2781415",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.boku.ac.at/MATH/udt/vol05/no2/91GiulJan10-2.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Unif. Distrib. Theory",
  fjournal =     "Uniform Distribution Theory",
}

@InProceedings{Gonzalez-Jimenez:2010:BLN,
  author =       "D. Gonzalez-Jimenez and E. Argones-Rua and F.
                 Perez-Gonzalez and J. L. Alba-Castro",
  editor =       "IEEE",
  booktitle =    "IEEE International Conference on Image Processing",
  title =        "{Benford's Law} for Natural and Synthetic Images",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1245--1248",
  year =         "2010",
  bibdate =      "Sat Sep 10 11:34:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  remark =       "Not found in IEEE Xplore database??",
}

@Article{Grabski:2010:DDM,
  author =       "Severin Grabski",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "182--185",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "https://doi.org/10.1016/j.accinf.2010.07.008",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Kriel:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000394",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
  remark =       "2009 Research Symposium on Information Integrity \&
                 Information Systems Assurance",
}

@Article{Herron:2010:EPO,
  author =       "Erik S. Herron",
  title =        "The effect of passive observation methods on
                 {Azerbaijan}'s 2008 presidential election and 2009
                 referendum",
  journal =      j-ELECT-STUDIES,
  volume =       "29",
  number =       "3",
  pages =        "417--424",
  year =         "2010",
  DOI =          "https://doi.org/10.1016/j.electstud.2010.03.013",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Special Symposium: Voters and Coalition Governments",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379410000259",
  abstract =     "Election observation is used by domestic and
                 international groups to assess election quality and
                 deter fraud. However, a limited amount of research has
                 assessed its effectiveness. This article adds to the
                 literature by analyzing how a passive monitoring tool
                 affected the process and outcome of voting in two
                 elections in Azerbaijan. The analysis shows that the
                 placement of webcams in polling stations is
                 consistently associated with lower reported turnout and
                 inconsistently associated with lower regime support.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Azerbaijan; Benford's Law; Election observation;
                 Fraud",
}

@Article{Hickman:2010:DAC,
  author =       "Matthew Hickman and Stephen Rice",
  title =        "Digital Analysis of Crime Statistics: Does Crime
                 Conform to {Benford's Law}?",
  journal =      j-J-QUANT-CRIMINOL,
  volume =       "26",
  number =       "3",
  pages =        "333--349",
  month =        sep,
  year =         "2010",
  CODEN =        "JQCRE6",
  DOI =          "https://doi.org/10.1007/s10940-010-9094-6",
  ISSN =         "0748-4518 (print), 1573-7799 (electronic)",
  ISSN-L =       "0748-4518",
  bibdate =      "Fri Nov 25 10:30:30 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Quantitative Criminology",
  keywords =     "Benford distribution; Benford's law; Crime data; Crime
                 statistics; Data errors; Digital analysis; Fabricated
                 data; First digit; Fraud detection; Uniform crime
                 reports",
}

@MastersThesis{Jasak:2010:BZR,
  author =       "Zoran Jasak",
  title =        "Benfordov zakon i reinforcement u{\v{c}}enje.
                 ({Bosnian}) [{Benford's Law} and reinforcement
                 learning]",
  type =         "{Magistarski Rad} ({M.Sc.} Thesis)",
  school =       "Prirodno-Matematicki Fakultet, Odsjek za matematiku,
                 Ju Univerzitet u Tuzla",
  address =      "Tuzla, Bosnia and Herzegovina",
  pages =        "124",
  month =        dec,
  year =         "2010",
  bibdate =      "Mon Feb 18 17:48:33 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.math.ualberta.ca/~aberger/benford_bibliography/jasak_10.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "action; Adaptive Benford's method; Adaptivna
                 Benfordova metoda; akcija; Benford's law; Benfordov
                 zakon; confidence intervals; contamination level;
                 intervali povjerenja; koli{\v{c}}nik; nivo
                 kontaminacije; Q learning; Q u{\v{c}}enje; quotient;
                 reinforcement learning; reinforcement u{\v{c}}enje;
                 Sarsa; stanje; state",
  language =     "Bosnian",
}

@Article{Jiang:2010:NMS,
  author =       "Weina Jiang and Anthony T. S. Ho and Helen Treharne
                 and Yun Q. Shi",
  title =        "A Novel Multi-size Block {Benford's Law} Scheme for
                 Printer Identification",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "6297",
  pages =        "643--652",
  year =         "2010",
  CODEN =        "LNCSD9",
  DOI =          "https://doi.org/10.1007/978-3-642-15702-8_59",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Mon Jan 21 17:47:23 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-15702-8_59",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-15702-8",
  book-URL =     "http://www.springerlink.com/content/978-3-642-15702-8",
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}

@Article{Kaynar:2010:FSM,
  author =       "B. Kaynar and A. Berger and T. P. Hill and A. Ridder",
  title =        "Finite-state {Markov} Chains obey {Benford's Law}",
  journal =      "ArXiv e-prints",
  day =          "2",
  month =        mar,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  MRclass =      "60J22, 11K06, 15B51",
  bibdate =      "Tue Nov 15 06:30:53 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1003.0562K;
                 http://arxiv.org/abs/1003.0562",
  abstract =     "A sequence of real numbers ($ x_n$) is Benford if the
                 significands, i.e. the fraction parts in the
                 floating-point representation of ($ x_n$) are
                 distributed logarithmically. Similarly, a discrete-time
                 irreducible and aperiodic finite-state Markov chain
                 with probability transition matrix $P$ and limiting
                 matrix $ P*$ is Benford if every component of both
                 sequences of matrices $ (P^n - P*)$ and $ (P^{n + 1} -
                 P^n)$ is Benford or eventually zero. Using recent tools
                 that established Benford behavior both for Newton's
                 method and for finite-dimensional linear maps, via the
                 classical theories of uniform distribution modulo $1$
                 and Perron-Frobenius, this paper derives a simple
                 sufficient condition (nonresonant) guaranteeing that
                 $P$, or the Markov chain associated with it, is
                 Benford. This result in turn is used to show that
                 almost all Markov chains are Benford, in the sense that
                 if the transition probabilities are chosen
                 independently and continuously, then the resulting
                 Markov chain is Benford with probability one. Concrete
                 examples illustrate the various cases that arise, and
                 the theory is complemented with several simulations and
                 potential applications.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1003.0562",
  keywords =     "Mathematics - Probability",
  primaryclass = "math.PR",
}

@Article{Kibria:2010:PTE,
  author =       "B. M. Golam Kibria and A. K. Md. E. Saleh",
  title =        "Preliminary test estimation of the parameters of
                 exponential and {Pareto} distributions for censored
                 samples",
  journal =      j-STAT-PAPERS,
  volume =       "51",
  number =       "4",
  pages =        "757--773",
  month =        dec,
  year =         "2010",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-008-0163-y",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:33 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-008-0163-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{Klar:2010:ZLL,
  author =       "B. Klar and P. R. Parthasarathy and N. Henze",
  title =        "{Zipf} and {Lerch} limit of birth and death
                 processes",
  journal =      j-PROB-ENG-INFO-SCI,
  volume =       "24",
  number =       "1",
  pages =        "129--144",
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1017/S0269964809990179",
  ISSN =         "0269-9648 (print), 1469-8951 (electronic)",
  ISSN-L =       "0269-9648",
  MRclass =      "60J27 (91F20)",
  MRnumber =     "2575846 (2010m:60254)",
  bibdate =      "Sat Mar 23 12:53:04 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Probab. Engrg. Inform. Sci.",
  fjournal =     "Probability in the Engineering and Informational
                 Sciences",
  keywords =     "Zipf's Law",
}

@Article{Kriel:2010:DDM,
  author =       "Eckhardt Kriel",
  title =        "Discussion of {``Data mining journal entries for fraud
                 detection: An exploratory study''}",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "11",
  number =       "3",
  pages =        "186--188",
  month =        sep,
  year =         "2010",
  CODEN =        "IJAIA7",
  DOI =          "https://doi.org/10.1016/j.accinf.2010.07.009",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "See \cite{Debreceny:2010:DMJ,Grabski:2010:DDM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089510000400",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Benford's Law",
  remark =       "2009 Research Symposium on Information Integrity \&
                 Information Systems Assurance.",
}

@Book{Lagarias:2010:UCP,
  editor =       "Jeffrey C. Lagarias",
  title =        "The ultimate challenge: the $ 3 x + 1 $ problem",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xiv + 344",
  year =         "2010",
  ISBN =         "0-8218-4940-9",
  ISBN-13 =      "978-0-8218-4940-8",
  LCCN =         "QA292 .U48 2010",
  MRclass =      "11B83; 37A45; 11B37; 68Q99",
  bibdate =      "Sat Sep 10 13:02:05 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "The $ 3 x + 1 $ problem, or Collatz problem, concerns
                 the following seemingly innocent arithmetic procedure
                 applied to integers: If an integer $x$ is odd then
                 ``multiply by three and add one'', while if it is even
                 then ``divide by two''. The $ 3 x + 1$ problem asks
                 whether, starting from any positive integer, repeating
                 this procedure over and over will eventually reach the
                 number 1. Despite its simple appearance, this problem
                 is unsolved. Generalizations of the problem are known
                 to be undecidable, and the problem itself is believed
                 to be extraordinarily difficult. This book reports on
                 what is known on this problem. It consists of a
                 collection of papers, which can be read independently
                 of each other. The book begins with two introductory
                 papers, one giving an overview and current status, and
                 the second giving history and basic results on the
                 problem. These are followed by three survey papers on
                 the problem, relating it to number theory and dynamical
                 systems, to Markov chains and ergodic theory, and to
                 logic and the theory of computation. The next paper
                 presents results on probabilistic models for behavior
                 of the iteration. This is followed by a paper giving
                 the latest computational results on the problem, which
                 verify its truth for $ x < 5.4 \cdot 10^{18}$. The book
                 also reprints six early papers on the problem and
                 related questions, by L. Collatz, J. H. Conway, H. S.
                 M. Coxeter, C. J. Everett, and R. K. Guy, each with
                 editorial commentary. The book concludes with an
                 annotated bibliography of work on the problem up to the
                 year 2000.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Sequences (Mathematics); Polynomials; Harmonic
                 analysis; Number theory -- Sequences and sets --
                 Special sequences and polynomials.; Dynamical systems
                 and ergodic theory -- Ergodic theory -- Relations with
                 number theory and harmonic analysis.; Number theory --
                 Sequences and sets -- Recurrences.; Computer science --
                 Theory of computing -- None of the above, but in this
                 section.",
  tableofcontents = "The $ 3 x + 1 $ problem: an overview \\
                 The $ 3 x + 1 $ problem and its generalizations /
                 Jeffrey C. Lagarias \\
                 Survey papers \\
                 A $ 3 x + 1 $ survey: number theory and dynamical
                 systems / Marc Chamberland \\
                 Generalized $ 3 x + 1 $ mappings: Markov chains and
                 ergodic theory / K. R. Matthews \\
                 Generalized $ 3 x + 1 $ functions and the theory of
                 computation / Pascal Michel and Maurice Margenstern \\
                 Stochastic modelling and computation papers \\
                 Stochastic models for the $ 3 x + 1 $ and $ 5 x + 1$
                 problems and related problems / Alex V. Kontorovich and
                 Jeffrey C. Lagarias \\
                 Empirical verification of the $ 3 x + 1 $ and related
                 conjectures / Tom{\'a}s Oliveira E Silva \\
                 Reprinted early papers \\
                 Cyclic sequences and frieze patterns (The fourth Felix
                 Behrend Memorial Lecture) / H. S. M. Coxeter \\
                 Unpredictable iterations / J. H. Conway \\
                 Iteration of the number-theoretic function: $f(2n) =
                 n$, $f(2n + 1) = 3n + 2$ / C. J. Everett \\
                 Don't try to solve these problems! / Richard K. Guy \\
                 On the motivation and origin of the $(3n + 1)$-problem
                 / Lothar Collatz \\
                 FRACTRAN: a simple universal programming language for
                 arithmetic / J. H. Conway \\
                 The $ 3 x + 1 $ problem: an annotated bibliography
                 (1963--1999) / Jeffrey C. Lagarias",
}

@Article{Lee:2010:SAR,
  author =       "Joanne Lee and Wendy K. Tam Cho and George G. Judge",
  title =        "{Stigler}'s approach to recovering the distribution of
                 first significant digits in natural data sets",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "2",
  pages =        "82--88",
  day =          "15",
  month =        jan,
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2009.09.015",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715209003563",
  abstract =     "Benford's Law can be seen as one of the many first
                 significant digit (FSD) distributions in a family of
                 monotonically decreasing distributions. We examine the
                 interrelationship between Benford and other
                 monotonically decreasing distributions such as those
                 arising from Stigler, Zipf, and the power laws. We
                 examine the theoretical basis of the Stigler
                 distribution and extend his reasoning by incorporating
                 {FSD} first-moment information into
                 information-theoretic methods. We present
                 information-theoretic methods as a way to describe,
                 connect, and unify these related distributions and
                 thereby extend the reach of Benford's Law and {FSD}
                 research more generally.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law",
}

@Article{Liu:2010:CIE,
  author =       "Hongyan Liu and Xiaoyu Wang and Yinghui Yang",
  title =        "Comments on {``An integrated efficient solution for
                 computing frequent and top-$k$ elements in data
                 streams''}",
  journal =      j-TODS,
  volume =       "35",
  number =       "2",
  pages =        "15:1--15:??",
  month =        apr,
  year =         "2010",
  CODEN =        "ATDSD3",
  DOI =          "https://doi.org/10.1145/1735886.1735894",
  ISSN =         "0362-5915 (print), 1557-4644 (electronic)",
  ISSN-L =       "0362-5915",
  bibdate =      "Wed Apr 28 13:44:08 MDT 2010",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tods/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Metwally:2006:IES}.",
  abstract =     "We investigate a well-known algorithm, {\em
                 Space-Saving\/} [Metwally et al. 2006], which has been
                 proven efficient and effective at mining frequent
                 elements in data streams. We discovered an error in one
                 of the theorems in Metwally et al. [2006]. Experiments
                 are conducted to illustrate the error.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Database Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J777",
  keywords =     "approximate queries; data streams; frequent elements;
                 top-$k$ elements; Zipfian distributions",
}

@Article{Lu:2010:BLP,
  author =       "Ocean Fan Lu and David E. Giles",
  title =        "{Benford's Law} and psychological barriers in certain
                 {eBay} auctions",
  journal =      j-APPL-ECON-LETT,
  volume =       "17",
  number =       "10",
  pages =        "1005--1008",
  month =        "????",
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/13504850802631814",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Sat Jan 07 09:10:23 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504850802631814",
  abstract =     "Using generalizations of Benford's Law we test for the
                 absence of psychological barriers at various price
                 levels in eBay auctions for professional football
                 tickets. Our empirical results indicate that this
                 hypothesis cannot be rejected.",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  journal-URL =  "http://www.tandfonline.com/loi/rael20",
  onlinedate =   "16 Jun 2009",
}

@Article{Mahdian:2010:BBM,
  author =       "Babak Mahdian and Stanislav Saic",
  title =        "A bibliography on blind methods for identifying image
                 forgery",
  journal =      j-SIGNAL-PROCESS-IMAGE-COMMUN,
  volume =       "25",
  number =       "6",
  pages =        "389--399",
  month =        jul,
  year =         "2010",
  CODEN =        "SPICEF",
  DOI =          "https://doi.org/10.1016/j.image.2010.05.003",
  ISSN =         "0923-5965 (print), 1879-2677 (electronic)",
  ISSN-L =       "0923-5965",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0923596510000536",
  abstract =     "Verifying the integrity of digital images and
                 detecting the traces of tampering without using any
                 protecting pre-extracted or pre-embedded information
                 have become an important and hot research field. The
                 popularity of this field and the rapid growth in papers
                 published during the last years have put considerable
                 need on creating a complete bibliography addressing
                 published papers in this area. In this paper, an
                 extensive list of blind methods for detecting image
                 forgery is presented. By the word blind we refer to
                 those methods that use only the image function. An
                 attempt has been made to make this paper complete by
                 listing most of the existing references and by
                 providing a detailed classification group.",
  acknowledgement = ack-nhfb,
  fjournal =     "Signal Processing: Image Communication",
  keywords =     "Benford's Law; Blind forgery detection; Digital
                 forgery; Image forensics; Image tampering; Multimedia
                 security",
}

@Article{Manoochehrnia:2010:BLA,
  author =       "P. Manoochehrnia and F. Rachidi and M. Rubinstein and
                 W. Schulz and G. Diendorfer",
  title =        "{Benford's Law} and Its Application to Lightning
                 Data",
  journal =      j-IEEE-TRANS-ELECTROMAGN-COMPAT,
  volume =       "52",
  number =       "4",
  pages =        "956--961",
  month =        nov,
  year =         "2010",
  CODEN =        "IEMCAE",
  DOI =          "https://doi.org/10.1109/TEMC.2010.2067218",
  ISSN =         "0018-9375 (print), 1558-187X (electronic)",
  ISSN-L =       "0018-9375",
  bibdate =      "Mon Nov 21 22:24:43 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electromagnetic Compatibility",
}

@InProceedings{Mebane:2010:EFR,
  author =       "Walter R. {Mebane, Jr.} and K. Kalinin",
  editor =       "????",
  booktitle =    "{Proceedings of the 2010 Annual Meeting of the Midwest
                 Political Science Association, Chicago, IL, April
                 22--25, 2010}",
  title =        "Electoral Fraud in {Russia}: Vote Counts Analysis
                 Using Second-Digit Mean Tests",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2010",
  bibdate =      "Sat Sep 10 14:32:06 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InProceedings{Mebane:2010:EFSa,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Proceedings of the 2010 Annual Meeting of the Midwest
                 Political Science Association, Chicago, IL, April
                 22--25, 2010}",
  title =        "Election Fraud or Strategic Voting?",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2010",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Sat Sep 10 14:19:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InProceedings{Mebane:2010:EFSb,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{2010 Summer Meeting of the Political Methodology
                 Society, University of Iowa, July 22--24, 2010}",
  title =        "Election Fraud or Strategic Voting? {Can} Second-digit
                 Tests Tell the Difference?",
  publisher =    "????",
  address =      "????",
  pages =        "1--49",
  year =         "2010",
  ISBN =         "????",
  ISBN-13 =      "????",
  bibdate =      "Sat Feb 16 11:56:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/pm10.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Mebane:2010:FPE,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Fraud in the {2009 Presidential Election} in {Iran}?",
  journal =      j-CHANCE,
  volume =       "23",
  number =       "1",
  pages =        "6--15",
  month =        mar,
  year =         "2010",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1007/s00144-010-0003-4",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Mon Feb 18 17:50:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/content/0337v415563q0753/abstract/",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
  xxnote =       "Publisher archive at
                 \path=http://amstat.tandfonline.com/loi/ucha20= is
                 missing volumes 18 (2005)--24 (2011). Those volumes are
                 available at
                 \path=http://link.springer.com/journal/144=",
}

@TechReport{Mebane:2010:MSD,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Memo on second-digit tests done on precinct counts for
                 {Democratic Senate} primary in {South Carolina}, 2010",
  type =         "Report",
  institution =  "University of Michigan",
  address =      "Ann Arbor, MI, USA",
  day =          "12",
  month =        jun,
  year =         "2010",
  bibdate =      "Sat Feb 16 12:06:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.umich.edu/~wmebane/SCmemo12jun2010.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Morrison:2010:MG,
  author =       "Kent E. Morrison",
  title =        "The Multiplication Game",
  journal =      j-MATH-MAG,
  volume =       "83",
  number =       "??",
  pages =        "100--110",
  month =        apr,
  year =         "2010",
  CODEN =        "MAMGA8",
  DOI =          "????",
  ISSN =         "0025-570X",
  ISSN-L =       "0025-570X",
  bibdate =      "Mon Feb 18 17:51:50 2013",
  bibsource =    "http://www.maa.org/pubs/mag_apr10_toc.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.calpoly.edu/~kmorriso/Research/multgameMMfinal.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
  keywords =     "Benford's Law",
}

@Book{Newbold:2010:SBE,
  author =       "Paul Newbold and William L. Carlson and Betty Thorne",
  title =        "Statistics for Business and Economics",
  publisher =    "Pearson",
  address =      "Boston, MA, USA",
  edition =      "Seventh",
  pages =        "986 + 16",
  year =         "2010",
  ISBN =         "0-13-507248-4",
  ISBN-13 =      "978-0-13-507248-6",
  LCCN =         "QA276.18 .N49 2010",
  bibdate =      "Fri Mar 22 09:03:48 MDT 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@Book{Nillsen:2010:RRD,
  author =       "Rodney Victor Nillsen",
  title =        "Randomness and recurrence in dynamical systems: a real
                 analysis approach",
  volume =       "31",
  publisher =    pub-MATH-ASSOC-AMER,
  address =      pub-MATH-ASSOC-AMER:adr,
  pages =        "xviii + 357",
  year =         "2010",
  ISBN =         "0-88385-043-5",
  ISBN-13 =      "978-0-88385-043-5",
  LCCN =         "QA614.8 .N55 2010",
  bibdate =      "Mon Feb 18 17:53:28 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "The Carus mathematical monographs",
  acknowledgement = ack-nhfb,
  subject =      "Differentiable dynamical systems; Measure theory",
  tableofcontents = "Background ideas and knowledge \\
                 Irrational numbers and dynamical systems \\
                 Probability and randomness \\
                 Recurrence \\
                 Averaging in time and space",
}

@Article{Novikov:2010:APB,
  author =       "V. P. Novikov",
  title =        "Aspectual Principle, {Benford's Law} and {Russell's
                 Paradox}",
  journal =      "ArXiv e-prints",
  month =        dec,
  year =         "2010",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 18:11:57 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1012.5537N;
                 http://arxiv.org/abs/1012.5537",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1012.5537",
  keywords =     "Mathematics - Classical Analysis and ODEs",
  pagecount =    "5",
  primaryclass = "math.CA",
}

@Book{Oleksy:2010:DMB,
  author =       "Marius Oleksy",
  title =        "{Data Mining und Benford's Law als
                 Controllinginstrumente}. ({German}) [{Data} Mining and
                 {Benford's Law} as controlling instruments]",
  volume =       "45",
  publisher =    "Europ{\"a}ischer Hochschulverlag",
  address =      "Bremen, Germany",
  pages =        "181 (est.)",
  year =         "2010",
  ISBN =         "3-86741-405-X",
  ISBN-13 =      "978-3-86741-405-0",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 17:54:59 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "{Wismarer Schriften zu Management und Recht}",
  URL =          "http://www.amazon.de/Data-Mining-Benfords-Law-Controllinginstrumente/dp/386741405X",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Orita:2010:UBL,
  author =       "Masaya Orita and Ayako Moritomo and Tatsuya Niimi and
                 Kazuki Ohno",
  title =        "Use of {Benford's Law} in drug discovery data",
  journal =      j-DRUG-DISCOVERY-TODAY,
  volume =       "15",
  number =       "9--10",
  pages =        "328--331",
  month =        may,
  year =         "2010",
  CODEN =        "DDTOFS",
  DOI =          "https://doi.org/10.1016/j.drudis.2010.03.003",
  ISSN =         "1359-6446 (print), 1878-5832 (electronic)",
  ISSN-L =       "1359-6446",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1359644610000796",
  abstract =     "Benford's law states that the distribution of the
                 first digit of many data sets is not uniform. The first
                 digit of any random number will be 1 almost 30\% of the
                 time, and larger digits occur as the first digit with
                 lower and lower frequency, to the point where 9 occurs
                 as a first digit only 5\% of the time. Here, we
                 demonstrate that several data sets in the field of drug
                 discovery follow Benford's distribution, whereas
                 doctored data do not. Our findings indicate the
                 applicability of Benford's law in assessing data
                 quality in the field of drug discovery. We also propose
                 a useful index of evaluating data quality based on
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Drug Discovery Today",
  keywords =     "Benford's Law",
}

@Misc{Pan:2010:EJC,
  author =       "Da Pan and Lijing Shao and Bo-Qiang Ma",
  title =        "{Benford's Law} in Statistical Physics",
  howpublished = "Wolfram Online Demonstrations Projects.",
  year =         "2010",
  bibdate =      "Mon Feb 18 18:00:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://demonstrations.wolfram.com/BenfordsLawInStatisticalPhysics/",
  acknowledgement = ack-nhfb,
}

@Article{Peng:2010:SFW,
  author =       "Fei Peng and Re-Si Guo and Chang-Tsun Li and Min
                 Long",
  title =        "A semi-fragile watermarking algorithm for
                 authenticating {$2$D} {CAD} engineering graphics based
                 on log-polar transformation",
  journal =      j-COMPUT-AIDED-DES,
  volume =       "42",
  number =       "12",
  pages =        "1207--1216",
  year =         "2010",
  CODEN =        "CAIDA5",
  DOI =          "https://doi.org/10.1016/j.cad.2010.08.004",
  ISSN =         "0010-4485 (print), 1879-2685 (electronic)",
  ISSN-L =       "0010-4485",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010448510001491",
  abstract =     "Copyright violation and illegal manipulation of
                 digital data have been acute challenges for many
                 sectors since the very same set of enabling techniques
                 for generating and processing digital data started to
                 emerge. Although traditional protective methods, such
                 as encryption and digital signatures, have been in use
                 for decades, their inability to provide protection
                 after decryption and locating tampering has prompted
                 the development of digital watermarking. In this paper,
                 a semi-fragile watermarking algorithm for
                 authenticating 2D {CAD} engineering graphics based on
                 log-polar coordinate mapping is proposed. Firstly, the
                 vertices are divided into groups, and for each group,
                 the vertices for carrying a watermark are mapped to the
                 log-polar coordinate system. Then the watermark is
                 embedded in the mantissa of the real-valued log-polar
                 coordinates via bit substitution. Theoretical analysis
                 and experimental results show that the proposed
                 algorithm is not only robust against incidental global
                 operations such as rotation, translation and scaling,
                 but can also detect and locate malicious attacks such
                 as entity modification and entity addition/deletion.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer-Aided Design",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104485",
  keywords =     "Benford's Law; Content authentication; Data hiding;
                 Engineering graphics; Integrity verification;
                 Semi-fragile watermarking",
}

@Article{Peng:2010:ZLC,
  author =       "Guohua Peng",
  title =        "{Zipf}'s law for {Chinese} cities: {Rolling} sample
                 regressions",
  journal =      j-PHYSICA-A,
  volume =       "389",
  number =       "18",
  pages =        "3804--3813",
  day =          "15",
  month =        sep,
  year =         "2010",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2010.05.004",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037843711000381X",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Perc:2010:ZLL,
  author =       "Matja{\v{z}} Perc",
  title =        "{Zipf}'s law and log-normal distributions in measures
                 of scientific output across fields and institutions: 40
                 years of {Slovenia's} research as an example",
  journal =      j-J-INFORMETRICS,
  volume =       "4",
  number =       "3",
  pages =        "358--364",
  day =          "1",
  month =        jul,
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.joi.2010.03.001",
  ISSN =         "1751-1577 (print), 1875-5879 (electronic)",
  ISSN-L =       "1751-1577",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1751157710000234",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informetrics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/17511577",
  keywords =     "Zipf's Law",
}

@Book{Posch:2010:ZNB,
  author =       "Peter N. Posch",
  title =        "{Ziffernanalyse mit dem Newcomb--Benford Gesetz in
                 Theorie und Praxis}. ({German}) [{Digit} analysis with
                 the {Newcomb--Benford} law in theory and practice]",
  publisher =    "Verlag Europ{\"a}ische Wirtschaft",
  address =      "Munich, Germany",
  edition =      "Second",
  pages =        "105 (est.)",
  year =         "2010",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 18:01:16 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@InProceedings{Qadir:2010:EJC,
  author =       "G. Qadir and X. Zhao and A. T. S. Ho",
  booktitle =    "{Society of Photo-Optical Instrumentation Engineers
                 (SPIE)} Conference Series",
  title =        "Estimating {JPEG2000} compression for image forensics
                 using {Benford's Law}",
  volume =       "7723",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  month =        apr,
  year =         "2010",
  DOI =          "https://doi.org/10.1117/12.855085",
  bibdate =      "Mon Nov 14 18:25:16 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Society of Photo-Optical Instrumentation Engineers
                 (SPIE) Conference Series",
  URL =          "http://adsabs.harvard.edu/abs/2010SPIE.7723E..14Q",
  acknowledgement = ack-nhfb,
}

@Article{Raqab:2010:PPD,
  author =       "Mohammad Z. Raqab and A. Asgharzadeh and R.
                 Valiollahi",
  title =        "Prediction for {Pareto} distribution based on
                 progressively {Type-II} censored samples",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "54",
  number =       "7",
  pages =        "1732--1743",
  day =          "1",
  month =        jul,
  year =         "2010",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:00 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947310000563",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Rezayan:2010:SRG,
  author =       "Hani Rezayan and Mahmoud Reza Delavar and Andrew
                 Ulrich Frank and A. Mansouri",
  title =        "Spatial rules that generate urban patterns: Emergence
                 of the power law in the distribution of axial line
                 length",
  journal =      "International Journal of Applied Earth Observation and
                 Geoinformation",
  volume =       "12",
  number =       "5",
  pages =        "317--330",
  year =         "2010",
  DOI =          "https://doi.org/10.1016/j.jag.2010.04.003",
  ISSN =         "0303-2434",
  ISSN-L =       "0303-2434",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0303243410000413",
  abstract =     "This paper studies emergence/generation of power law
                 in rank-order distribution of axial line length, which
                 is a global pattern observed in real cities, due to
                 interaction of a set of seven simple spatial rules at a
                 local scale. These rules and their interactions form a
                 model expected to simulate the morphological structure
                 of free spaces in unplanned organic pedestrian small
                 cities. Effects of each of the seven rules are
                 discussed through repeated simulations of eight
                 possible combinations of the rules, using a bottom-up
                 process. The results show that the rules generate
                 environments with statistically stable rank-order
                 distribution of axial line length that follows the
                 power law. It means that the axial maps of the
                 simulated environments have a scale-free hierarchical
                 structure such that their distributions lean toward
                 short axial lines. It also represents dominance of
                 local spatial structure, as the model renders a faster
                 rate of growth at a local scale while allowing a steady
                 growth at a global scale.",
  acknowledgement = ack-nhfb,
  keywords =     "Axial line; Axial map; Axial representation; Benford's
                 Law; Emergence; Power law",
}

@Article{Rousseau:2010:AFO,
  author =       "Christiane Rousseau",
  title =        "Apprendre {\`a} frauder ou {\`a} d{\'e}tecter les
                 fraudes. ({French}) [{Learning} to defraud or to detect
                 fraud]",
  journal =      "Accrom$\alpha$th",
  volume =       "5",
  pages =        "2--7",
  month =        "{\'E}t{\'e}--automne",
  year =         "2010",
  ISSN =         "1911-0197",
  bibdate =      "Mon Feb 18 18:07:49 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://accromath.uqam.ca/contents/pdf/Benford.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.accromath.ca/",
  language =     "French",
}

@Book{Saichev:2010:TZL,
  author =       "Alexander Saichev and Yannick Malevergne and Didier
                 Sornette",
  title =        "Theory of {Zipf}'s law and beyond",
  volume =       "632",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xii + 171",
  year =         "2010",
  DOI =          "https://doi.org/10.1007/978-3-642-02946-2",
  ISBN =         "3-642-02945-0",
  ISBN-13 =      "978-3-642-02945-5",
  MRclass =      "91-02 (91B70 91B82)",
  MRnumber =     "2569206 (2011b:91008)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Economics and Mathematical Systems",
  ZMnumber =     "Zbl 1189.91009",
  acknowledgement = ack-nhfb,
}

@Article{Saldana-Zepeda:2010:GFT,
  author =       "Dayna P. Salda{\~n}a-Zepeda and Humberto
                 Vaquera-Huerta and Barry C. Arnold",
  title =        "A goodness of fit test for the {Pareto} distribution
                 in the presence of Type {II} censoring, based on the
                 cumulative hazard function",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "54",
  number =       "4",
  pages =        "833--842",
  day =          "1",
  month =        apr,
  year =         "2010",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:42:57 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947309004071",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Sambridge:2010:BLN,
  author =       "M. Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and A.
                 Jackson",
  title =        "{Benford}'s law in the natural sciences",
  journal =      "Geophysical Research Letters",
  volume =       "37",
  number =       "22",
  pages =        "L22301--L22306",
  month =        "????",
  year =         "2010",
  CODEN =        "GPRLAJ",
  DOI =          "https://doi.org/10.1029/2010GL044830",
  ISSN =         "0094-8276 (print), 1944-8007 (electronic)",
  ISSN-L =       "0094-8276",
  bibdate =      "Sun Nov 13 11:03:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010GeoRL..3722301S;
                 http://www.agu.org/pubs/crossref/2010/2010GL044830.shtml",
  abstract =     "More than 100 years ago it was predicted that the
                 distribution of first digits of real world observations
                 would not be uniform, but instead follow a trend where
                 measurements with lower first digit (1, 2, \ldots {})
                 occur more frequently than those with higher first
                 digits (\ldots {}, 8, 9). This result has long been
                 known but regarded largely as a mathematical curiosity
                 and received little attention in the natural sciences.
                 Here we show that the first digit rule is likely to be
                 a widespread phenomenon and may provide new ways to
                 detect anomalous signals in data. We test 15 sets of
                 modern observations drawn from the fields of physics,
                 astronomy, geophysics, chemistry, engineering and
                 mathematics, and show that Benford's law holds for them
                 all. These include geophysical observables such as the
                 length of time between geomagnetic reversals, depths of
                 earthquakes, models of Earth's gravity, geomagnetic and
                 seismic structure. In addition we find it also holds
                 for other natural science observables such as the
                 rotation frequencies of pulsars; green-house gas
                 emissions, the masses of exoplanets as well as numbers
                 of infectious diseases reported to the World Health
                 Organization. The wide range of areas where it is
                 manifested opens up new possibilities for exploitation.
                 An illustration is given of how seismic energy from an
                 earthquake can be detected from just the first digit
                 distribution of displacement counts on a seismometer,
                 i.e., without actually looking at the details of a
                 seismogram at all. This led to the first ever detection
                 of an earthquake using first digit information alone.",
  acknowledgement = ack-nhfb,
  ajournal =     "Geophys. Res. Lett.",
  fjournal =     "Geophysical research letters",
  keywords =     "earthquakes; large data sets; observational
                 seismology; statistics",
}

@TechReport{Schraepler:2010:BLI,
  author =       "J{\"o}rg-Peter Schraepler",
  title =        "{Benford's Law} as an instrument for fraud detection
                 in surveys using the data of the {Socio-Economic Panel
                 (SOEP)}",
  type =         "{SOEP} paper",
  number =       "273",
  institution =  "Socio-Economic Panel, Deutsches Institut f{\"u}r
                 Wirtschaftsforschung",
  address =      "Berlin, Germany",
  pages =        "ii + 56",
  day =          "2",
  month =        mar,
  year =         "2010",
  ISSN =         "1864-6689",
  ISSN-L =       "1864-6689",
  bibdate =      "Mon Feb 18 18:10:18 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.diw.de/documents/publikationen/73/diw_01.c.349061.de/diw_sp0273.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Shao:2010:EMD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "Empirical Mantissa Distributions of Pulsars",
  journal =      j-ASTROPART-PHYS,
  volume =       "33",
  number =       "4",
  pages =        "255--262",
  month =        may,
  year =         "2010",
  CODEN =        "APHYEE",
  DOI =          "https://doi.org/10.1016/j.astropartphys.2010.02.003",
  ISSN =         "0927-6505 (print), 1873-2852 (electronic)",
  ISSN-L =       "0927-6505",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1005.1702;
                 http://www.sciencedirect.com/science/article/pii/S0927650510000447",
  abstract =     "The occurrence of digits one through nine as the
                 leftmost nonzero digit of numbers from real world
                 sources is often not uniformly distributed, but
                 instead, is distributed according to a logarithmic law,
                 known as Benford's Law. Here, we investigate
                 systematically the mantissa distributions of some
                 pulsar quantities, and find that for most quantities
                 their first digits conform to this law. However, the
                 barycentric period shows significant deviation from the
                 usual distribution, but satisfies a generalized
                 Benford's Law roughly. Therefore pulsars can serve as
                 an ideal assemblage to study the first digit
                 distributions of real world data, and the observations
                 can be used to constrain theoretical models of pulsar
                 behavior.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1005.1702",
  fjournal =     "Astroparticle Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09276505",
  keywords =     "Benford's Law; First digit law; Mantissa distribution;
                 Pulsar",
  primaryclass = "astro-ph.IM",
}

@Article{Shao:2010:FDD,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First Digit Distribution of Hadron Full Width",
  journal =      "ArXiv e-prints",
  day =          "19",
  month =        apr,
  year =         "2010",
  bibdate =      "Mon Nov 21 07:21:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1004.3077",
  abstract =     "A phenomenological law, called Benford's law, states
                 that the occurrence of the first digit, i.e., $ 1, 2,
                 \ldots {}, 9 $, of numbers from many real world sources
                 is not uniformly distributed, but instead favors
                 smaller ones according to a logarithmic distribution.
                 We investigate, for the first time, the first digit
                 distribution of the full widths of mesons and baryons
                 in the well defined science domain of particle physics
                 systematically, and find that they agree excellently
                 with the Benford distribution. We also discuss several
                 general properties of Benford's law, i.e., the law is
                 scale-invariant, base-invariant, and power-invariant.
                 This means that the lifetimes of hadrons follow also
                 Benford's law.",
  acknowledgement = ack-nhfb,
  pagecount =    "8",
}

@Article{Shao:2010:FDLa,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First-Digit Law in Nonextensive Statistics",
  journal =      "ArXiv e-prints",
  year =         "2010",
  bibdate =      "Mon Nov 21 07:09:52 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1010.2699",
  abstract =     "Nonextensive statistics, characterized by a
                 nonextensive parameter $q$, is a promising and
                 practically useful generalization of the Boltzmann
                 statistics to describe power-law behaviors from
                 physical and social observations. We here explore the
                 unevenness of the first digit distribution of
                 nonextensive statistics analytically and numerically.
                 We find that the first-digit distribution follows
                 Benford's law and fluctuates slightly in a periodical
                 manner with respect to the logarithm of the
                 temperature. The fluctuation decreases when $q$
                 increases, and the result converges to Benford's law
                 exactly as $q$ approaches 2. The relevant regularities
                 between nonextensive statistics and Benford's law are
                 also presented and discussed.",
  acknowledgement = ack-nhfb,
}

@Article{Shao:2010:FDLb,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "First-digit law in nonextensive statistics",
  journal =      j-PHYS-REV-E,
  volume =       "82",
  number =       "4",
  pages =        "041110",
  month =        oct,
  year =         "2010",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.82.041110",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Mon Feb 18 18:11:37 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.82.041110;
                 http://pre.aps.org/abstract/PRE/v82/i4/e041110",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
}

@Article{Shao:2010:SDL,
  author =       "Lijing Shao and Bo-Qiang Ma",
  title =        "The significant digit law in statistical physics",
  journal =      j-PHYSICA-A,
  volume =       "389",
  number =       "16",
  pages =        "3109--3116",
  month =        may,
  year =         "2010",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2010.04.021",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "82B03",
  MRnumber =     "2652860 (2011d:82007)",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1005.0660;
                 http://inspirehep.net/record/855898;
                 http://inspirehep.net/record/873155;
                 http://www.sciencedirect.com/science/article/pii/S0378437110003596",
  abstract =     "The occurrence of the nonzero leftmost digit, i.e., $
                 1, 2, \ldots {}, 9 $, of numbers from many real world
                 sources is not uniformly distributed as one might
                 naively expect, but instead, the nature favors smaller
                 ones according to a logarithmic distribution, named
                 Benford's Law. We investigate three kinds of widely
                 used physical statistics, i.e., the Boltzmann--Gibbs
                 (BG) distribution, the Fermi--Dirac (FD) distribution,
                 and the Bose--Einstein (BE) distribution, and find that
                 the BG and FD distributions both fluctuate slightly in
                 a periodic manner around Benford's distribution with
                 respect to the temperature of the system, while the BE
                 distribution conforms to it exactly whatever the
                 temperature is. Thus Benford's Law seems to present a
                 general pattern for physical statistics and might be
                 even more fundamental and profound in nature.
                 Furthermore, various elegant properties of Benford's
                 Law, especially the mantissa distribution of data sets,
                 are discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; First digit law; Mantissa distribution;
                 Statistical physics",
}

@Article{Shebaro:2010:LTC,
  author =       "Bilal Shebaro and Fernando Perez-Gonzalez and Jedidiah
                 R. Crandall",
  title =        "Leaving timing-channel fingerprints in hidden service
                 log files",
  journal =      "Digital Investigation",
  volume =       "7, Supplement",
  number =       "0",
  pages =        "S104--S113",
  year =         "2010",
  DOI =          "https://doi.org/10.1016/j.diin.2010.05.013",
  ISSN =         "1742-2876 (print), 1873-202X (electronic)",
  ISSN-L =       "1742-2876",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The Proceedings of the Tenth Annual {DFRWS}
                 Conference",
  URL =          "http://www.sciencedirect.com/science/article/pii/S174228761000040X",
  abstract =     "Hidden services are anonymously hosted services that
                 can be accessed over an anonymity network, such as Tor.
                 While most hidden services are legitimate, some host
                 illegal content. There has been a fair amount of
                 research on locating hidden services, but an open
                 problem is to develop a general method to prove that a
                 physical machine, once confiscated, was in fact the
                 machine that had been hosting the illegal content. In
                 this paper we assume that the hidden service logs
                 requests with some timestamp, and give experimental
                 results for leaving an identifiable fingerprint in this
                 log file as a timing channel that can be recovered from
                 the timestamps. In 60 min, we are able to leave a
                 36-bit fingerprint that can be reliably recovered. The
                 main challenges are the packet delays caused by the
                 anonymity network that requests are sent over and the
                 existing traffic in the log from the actual clients
                 accessing the service. We give data to characterize
                 these noise sources and then describe an implementation
                 of timing-channel fingerprinting for an Apache web
                 server based hidden service on the Tor network, where
                 the fingerprint is an additive channel that is
                 superencoded with a Reed Solomon code for reliable
                 recovery. Finally, we discuss the inherent tradeoffs
                 and possible approaches to making the fingerprint more
                 stealthy.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Fingerprints; Hidden services;
                 Timestamps; Timing channel; Tor network",
}

@InProceedings{Shengmin:2010:DSC,
  author =       "Z. Shengmin and W. Wenchao",
  editor =       "{IEEE}",
  booktitle =    "{2010 International Conference on Management and
                 Service Science (MASS), 24--26 Aug. 2010, Wuhan,
                 China}",
  title =        "Does [sic] {Chinese} Stock Indices Agree with
                 {Benford's Law}?",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--3",
  year =         "2010",
  DOI =          "https://doi.org/10.1109/ICMSS.2010.5575999",
  ISBN =         "1-4244-5325-9, 1-4244-5326-7",
  ISBN-13 =      "978-1-4244-5325-2, 978-1-4244-5326-9",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 18:12:46 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Singleton:2010:FAF,
  author =       "Tommie Singleton and Aaron J. Singleton",
  title =        "Fraud auditing and forensic accounting",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  edition =      "Fourth",
  pages =        "xiv + 317",
  year =         "2010",
  ISBN =         "0-470-56413-X",
  ISBN-13 =      "978-0-470-56413-4",
  LCCN =         "HV8079.W47 B65 2010",
  bibdate =      "Tue Nov 22 10:31:33 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley corporate F and A",
  URL =          "http://catalogimages.wiley.com/images/db/jimages/9780470564134.jpg;
                 http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1007/2010013504-t.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1011/2010013504-b.html",
  abstract =     "Completely revised and updated, Fraud Auditing and
                 Forensic Accounting, Fourth Edition reveals how to
                 develop an investigative eye toward both internal and
                 external fraud and provides crucial information on how
                 to deal with it when discovered. With new chapters on
                 the physiological aspects of the fraudster and on fraud
                 response, as well as new material on non-financial
                 aspects of fraud investigation, body language,
                 discourse analysis, and interviewing techniques, this
                 authoritative, timely book equips auditors,
                 investigators, corporate attorneys, and accountants to
                 identify the signs of financial fraud and successfully
                 investigate it",
  acknowledgement = ack-nhfb,
  remark =       "Derived from third edition (2006). This book does not
                 discuss Benford's Law, but may be helpful background
                 for application of that law to the detection of
                 fraud.",
  subject =      "White collar crime investigation; United States;
                 Forensic accounting; Fraud investigation",
  tableofcontents = "Background of Fraud Auditing and Forensic
                 Accounting \\
                 Fraud Principles \\
                 Fraud Schemes \\
                 Red Flags \\
                 Fraud Risk Assessment \\
                 Fraud Prevention \\
                 Fraud Detection \\
                 Fraud Response \\
                 Computer Crime \\
                 Fraud and the Accounting Information System \\
                 Gathering Evidence \\
                 Cyber Forensics \\
                 Obtaining and Evaluating Nonfinancial Evidence in a
                 Fraud Examination \\
                 General Criteria and Standards for Establishing an
                 Expert Witness's Qualifications \\
                 The Legal Role and Qualifications of an Expert Witness
                 \\
                 Effective Tactics and Procedures for the Expert Witness
                 in Court \\
                 Fraud and the Public Accounting Profession",
}

@Article{Stalcup:2010:BLH,
  author =       "Ken Stalcup",
  title =        "{Benford's Law}: How a Simple Misconception can Trip
                 up a Fraudster and How a Savvy {CFE} Can Spot It",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2010",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 07:57:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=203",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Article{Strzalka:2010:SPB,
  author =       "Dominik Strza{\l}ka",
  title =        "On some properties of {Benford}'s law",
  journal =      "Journal of the {Korean Mathematical Society}",
  volume =       "47",
  number =       "5",
  pages =        "1055--1075",
  year =         "2010",
  CODEN =        "JKMSDG",
  DOI =          "https://doi.org/10.4134/JKMS.2010.47.5.1055",
  ISSN =         "0304-9914",
  ISSN-L =       "0304-9914",
  MRclass =      "11A63",
  MRnumber =     "2723008",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. {Korean Math. Soc.}",
  fjournal =     "Journal of the {Korean Mathematical Society}",
}

@Article{Sudhier:2010:BLS,
  author =       "K. G. Sudhier",
  title =        "{Bradford's law} of Scattering Revisited: A study
                 based on the References in Doctoral theses in the area
                 of Physics",
  journal =      j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
  volume =       "4",
  number =       "2",
  pages =        "35--47",
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09737766.2010.10700891",
  ISSN =         "0973-7766 (print), 2168-930X (electronic)",
  ISSN-L =       "0973-7766",
  bibdate =      "Thu Sep 10 17:47:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Collnet Journal of Scientometrics and Information
                 Management",
  journal-URL =  "http://www.tandfonline.com/loi/tsim20",
}

@Article{Suh:2010:CAB,
  author =       "Ikseon Suh and T. Christopher Headrick",
  title =        "A comparative analysis of the bootstrap versus
                 traditional statistical procedures applied to digital
                 analysis based on {Benford's Law}",
  journal =      "Journal of Forensic and Investigative Accounting",
  volume =       "2",
  number =       "2",
  pages =        "144--175",
  month =        jul # "\slash " # dec,
  year =         "2010",
  CODEN =        "????",
  DOI =          "????",
  ISSN =         "2165-3755",
  bibdate =      "Mon Feb 18 18:16:07 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://epublications.marquette.edu/account_fac/31;
                 http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/FullText/2010v2n2a7.pdf;
                 http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/Articles/v2n2.htm",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.bus.lsu.edu/accounting/faculty/lcrumbley/jfia/articles.htm",
}

@Article{Szewczak:2010:LTR,
  author =       "Zbigniew S. Szewczak",
  title =        "A limit theorem for random sums modulo $1$",
  journal =      j-STAT-PROB-LETT,
  volume =       "80",
  number =       "9--10",
  pages =        "747--751",
  month =        may,
  year =         "2010",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2010.01.005",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715210000106",
  abstract =     "Residues of partial sums in a class of dependent
                 random variables, including functionals of uniformly
                 recurrent Markov chains, are in the domain of
                 attraction of the uniform distribution. These types of
                 limit theorems arise for example in the multiplication
                 of floating-point numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law",
}

@Article{Uzer:2010:MTC,
  author =       "Ali Uzer",
  title =        "Multiplicative type complex calculus as an alternative
                 to the classical calculus",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "60",
  number =       "10",
  pages =        "2725--2737",
  month =        nov,
  year =         "2010",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/j.camwa.2010.08.089",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Thu Feb 14 05:56:39 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122110006747",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From the paper: ``\ldots{} an important work of
                 Benford that was published 70 years ago implies many
                 physical quantities in the nature are of exponentially
                 varying type.''.",
}

@Misc{Wagon:2010:BLD,
  author =       "S. Wagon",
  title =        "{Benford's Law} and Data Spread",
  year =         "2010",
  bibdate =      "Sat Nov 12 16:59:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Web site.",
  URL =          "http://demonstrations.wolfram.com/BenfordsLawAndDataSpread",
  acknowledgement = ack-nhfb,
}

@Article{Zhao:2010:IFU,
  author =       "Xi Zhao and Anthony Tung Shuen Ho and Yun Q. Shi",
  title =        "Image Forensics Using Generalised {Benford's Law} for
                 Improving Image Authentication Detection Rates in
                 Semi-Fragile Watermarking",
  journal =      "International Journal of Digital Crime and Forensics",
  volume =       "2",
  number =       "2",
  pages =        "1--20",
  month =        "????",
  year =         "2010",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4018/jdcf.2010040101",
  ISSN =         "1941-6210 (print), 1941-6229 (electronic)",
  ISSN-L =       "1941-6210",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/ijdcf/ijdcf2.html#ZhaoHS10",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Digit. Crime Forensics",
  dblp-key =     "journals/ijdcf/ZhaoHS10",
  dblp-mdate =   "2020-08-12",
  fjournal =     "International Journal of Digital Crime and Forensics",
  journal-URL =  "https://www.igi-global.com/gateway/journal/1112",
}

@Article{Abrantes-Metz:2011:TLR,
  author =       "R. M. Abrantes-Metz and S. B. Villas-Boas and G.
                 Judge",
  title =        "Tracking the {Libor} rate",
  journal =      j-APPL-ECON-LETT,
  volume =       "18",
  number =       "10",
  pages =        "893--899",
  month =        "????",
  year =         "2011",
  DOI =          "https://doi.org/10.1080/13504851.2010.515197",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Mon Feb 18 18:17:20 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/13504851.2010.515197",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  journal-URL =  "http://www.tandfonline.com/loi/rael20",
  keywords =     "Benford's Second-Digit Law",
  remark =       "From the abstract: ``Libor rates depart significantly
                 from the expected Benford reference distribution. This
                 raises potential concerns relative to the unbiased
                 nature of the signals coming from the 16 banks from
                 which the Libor is computed and the usefulness of the
                 Libor as a major economic indicator.''",
}

@Article{Adamic:2011:CSU,
  author =       "Lada Adamic",
  title =        "Complex systems: Unzipping {Zipf}'s law",
  journal =      j-NATURE,
  volume =       "474",
  number =       "7350",
  pages =        "164--165",
  day =          "8",
  month =        jun,
  year =         "2011",
  CODEN =        "NATUAS",
  DOI =          "https://doi.org/10.1038/474164a",
  ISSN =         "0028-0836 (print), 1476-4687 (electronic)",
  ISSN-L =       "0028-0836",
  bibdate =      "Tue Nov 15 09:29:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/nature/journal/v474/n7350/full/474164a.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Nature",
  journal-URL =  "http://www.nature.com/nature/archive/",
  onlinedate =   "09 June 2011",
}

@Article{Altamirano:2011:PTS,
  author =       "C. Altamirano and A. Robledo",
  title =        "Possible thermodynamic structure underlying the laws
                 of {Zipf} and {Benford}",
  journal =      j-EUR-PHYS-J-B,
  volume =       "81",
  number =       "3",
  pages =        "345--351",
  month =        jun,
  year =         "2011",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1140/epjb/e2011-10968-5",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Mon Nov 14 17:53:47 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011EPJB...81..345A",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1008.1614",
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
  primaryclass = "cond-mat.stat-mech",
}

@Article{Anderson:2011:BLC,
  author =       "Theresa C. Anderson and Larry Rolen and Ruth Stoehr",
  title =        "{Benford}'s law for coefficients of modular forms and
                 partition functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "139",
  number =       "5",
  pages =        "1533--1541",
  year =         "2011",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/S0002-9939-2010-10577-4",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "11F12 (11F20 11P83)",
  MRnumber =     "2763743",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2010arXiv1009.0780A",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Andrew:2011:OBM,
  author =       "Alex M. Andrew",
  title =        "Obituary: {Beno{\^\i}t Mandelbrot: 20 November
                 1924--14 October 2010}",
  journal =      "Kybernetes",
  volume =       "40",
  number =       "1--2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "KBNTA3",
  ISSN =         "0368-492X (print), 1758-7883 (electronic)",
  ISSN-L =       "0368-492X",
  bibdate =      "Fri Nov 25 07:32:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://en.wikipedia.org/wiki/ernst_von_glasersfeld;
                 http://www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf;
                 http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=1/2&articleid=1921825;
                 http://www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary;
                 http://www.math.yale.edu/mandelbrot/;
                 http://www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/benoit-mandelbrot.html",
  acknowledgement = ack-nhfb,
}

@Misc{Anonymous:2011:BLH,
  author =       "Anonymous",
  title =        "{Benford's Law} --- How mathematics can detect
                 fraud!",
  howpublished = "Web video lecture (10m47s).",
  day =          "9",
  month =        apr,
  year =         "2011",
  bibdate =      "Fri Oct 09 06:40:54 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.youtube.com/watch?v=vIsDjbhbADY",
  acknowledgement = ack-nhfb,
  xxauthor =     "Brady Haran",
}

@Article{Archambault:2011:EMA,
  author =       "J. Archambault and M. Archambault",
  title =        "Earnings management among firms during the pre-{SEC}
                 era: a {Benford}'s law analysis",
  journal =      j-ACCOUNT-HIST-J,
  volume =       "38",
  number =       "2",
  pages =        "145--170",
  month =        "????",
  year =         "2011",
  ISSN =         "0148-4184",
  ISSN-L =       "0148-4184",
  bibdate =      "Mon Feb 18 11:32:23 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Accounting Historians Journal",
  journal-URL =  "http://www.jstor.org/action/showPublication?journalCode=accohistjour;
                 http://www.aahhq.org/",
  remark =       "JSTOR has a 3-year moving wall, so this article is not
                 yet in that archive; the publisher's Web site is poor,
                 and I cannot find the article there.",
}

@Article{Baek:2011:ZLU,
  author =       "Seung Ki Baek and Sebastian Bernhardsson and Petter
                 Minnhagen",
  title =        "{Zipf}'s law unzipped",
  journal =      j-NEW-J-PHYS,
  volume =       "13",
  number =       "4",
  pages =        "043004",
  month =        "????",
  year =         "2011",
  CODEN =        "NJOPFM",
  DOI =          "https://doi.org/10.1088/1367-2630/13/4/043004",
  ISSN =         "1367-2630",
  ISSN-L =       "1367-2630",
  bibdate =      "Tue Nov 15 09:32:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://iopscience.iop.org/1367-2630/13/4/043004",
  abstract =     "Why does Zipf's law give a good description of data
                 from seemingly completely unrelated phenomena? Here it
                 is argued that the reason is that they can all be
                 described as outcomes of a ubiquitous random group
                 division: the elements can be citizens of a country and
                 the groups family names, or the elements can be all the
                 words making up a novel and the groups the unique
                 words, or the elements could be inhabitants and the
                 groups the cities in a country and so on. A random
                 group formation (RGF) is presented from which a
                 Bayesian estimate is obtained based on minimal
                 information: it provides the best prediction for the
                 number of groups with $k$ elements, given the total
                 number of elements, groups and the number of elements
                 in the largest group. For each specification of these
                 three values, the RGF predicts a unique group
                 distribution $ N(k) \propto \exp ( - b k) / k^\gamma $,
                 where the power-law index $ \gamma $ is a unique
                 function of the same three values. The universality of
                 the result is made possible by the fact that no
                 system-specific assumptions are made about the
                 mechanism responsible for the group division. The
                 direct relation between $ \gamma $ and the total number
                 of elements, groups and the number of elements in the
                 largest group is calculated. The predictive power of
                 the RGF model is demonstrated by direct comparison with
                 data from a variety of systems. It is shown that $
                 \gamma $ usually takes values in the interval $ 1 \leq
                 \gamma \leq 2 $ and that the value for a given
                 phenomenon depends in a systematic way on the total
                 size of the dataset. The results are put in the context
                 of earlier discussions on Zipf's and Gibrat's laws, $
                 N(k) \propto k^{-2} $ and the connection between growth
                 models and RGF is elucidated.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Journal of Physics",
  journal-URL =  "http://iopscience.iop.org/1367-2630",
  pagecount =    "21",
}

@Misc{Barnes:2011:LCS,
  author =       "K. Barnes",
  title =        "Letter to {China Shen Zhou Mining and Resources (AMEX:
                 SHZ)} current shareholders and potential investors from
                 {Absaroka Capital}",
  howpublished = "Absaroka Capital Management, LLP, Wyoming, USA.",
  year =         "2011",
  bibdate =      "Fri Mar 22 08:42:58 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
}

@InCollection{Barrale:2011:SID,
  author =       "Tom Barrale and R. Hendel and Michael Sluys",
  booktitle =    "{Proceedings of the 14th international conference on
                 Fibonacci numbers and their applications, Morelia,
                 Mexico, July 5--9, 2010}",
  title =        "Sequences of the initial digits of {Fibonacci}
                 numbers",
  publisher =    "Sociedad Matem\'atica Mexicana",
  address =      "M{\'e}xico, DF, M{\'e}xico",
  pages =        "25--42",
  year =         "2011",
  ISBN =         "607-02-2543-0 (paperback)",
  ISBN-13 =      "978-607-02-2543-7 (paperback)",
  MRnumber =     "11B37 11B39",
  bibdate =      "Sat Sep 10 10:27:11 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "1287.11017",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Fibonacci numbers",
}

@Article{Bauer:2011:DDF,
  author =       "Johannes Bauer and Jochen Gross",
  title =        "Difficulties Detecting Fraud? {The} Use of {Benford?s
                 Law} on Regression Tables",
  journal =      "Journal of Economics and Statistics (Jahrb{\"u}cher
                 f{\"u}r National{\"o}konomie und Statistik)",
  volume =       "231",
  number =       "5--6",
  pages =        "733--748",
  month =        nov,
  year =         "2011",
  DOI =          "????",
  bibdate =      "Mon Feb 18 18:18:45 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ideas.repec.org/a/jns/jbstat/v231y2011i5-6p733-748.html",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://wiwi.uni-giessen.de/home/oekonometrie/Jahrbuecher/",
}

@Article{Bawden:2011:BMS,
  author =       "David Bawden",
  title =        "{Beno{\^\i}t Mandelbrot} and the self-similarity of
                 information",
  journal =      j-J-DOC,
  volume =       "67",
  number =       "2",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "JDOCAS",
  ISSN =         "0022-0418 (print), 1758-7379 (electronic)",
  ISSN-L =       "0022-0418",
  bibdate =      "Fri Nov 25 07:40:34 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.emeraldinsight.com/journals.htm?issn=0022-0418&volume=67&issue=2&articleid=1911717",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Documentation",
  journal-URL =  "http://www.emeraldinsight.com/loi/jd",
}

@Article{Becker:2011:BLC,
  author =       "T. Becker and A. Greaves-Tunnell and Steven J. Miller
                 and R. Ronan and F. W. Strauch",
  title =        "{Benford's Law} and Continuous Dependent Random
                 Variables",
  journal =      "ArXiv e-prints",
  month =        nov,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Mon Nov 14 17:50:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011arXiv1111.0568B;
                 http://arxiv.org/abs/1111.0568",
  abstract =     "Many systems exhibit a digit bias. For example, the
                 first digit base 10 of the Fibonacci numbers, or of $
                 2^n $, equals 1 not 10\% or 11\% of the time, as one
                 would expect if all digits were equally likely, but
                 about 30\% of the time. This phenomenon, known as
                 Benford's Law, has many applications, ranging from
                 detecting tax fraud for the IRS to analyzing round-off
                 errors in computer science.\par

                 The central question is determining which data sets
                 follow Benford's law. Inspired by natural processes
                 such as particle decay, our work examines models for
                 the decomposition of conserved quantities. We prove
                 that in many instances the distribution of lengths of
                 the resulting pieces converges to Benford behavior as
                 the number of divisions grow. The main difficulty is
                 that the resulting random variables are dependent,
                 which we handle by a careful analysis of the
                 dependencies and tools from Fourier analysis to obtain
                 quantified convergence rates.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1111.0568",
  keywords =     "Mathematics - Probability, 11K06, 60A10 (primary),
                 60E10 (secondary)",
  primaryclass = "math.PR",
}

@Article{Berger:2011:BLS,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "{Benford}'s law strikes back: no simple explanation in
                 sight for mathematical gem",
  journal =      j-MATH-INTEL,
  volume =       "33",
  number =       "1",
  pages =        "85--91",
  month =        mar,
  year =         "2011",
  CODEN =        "MAINDC",
  DOI =          "https://doi.org/10.1007/s00283-010-9182-3",
  ISSN =         "0343-6993 (print), 1866-7414 (electronic)",
  ISSN-L =       "0343-6993",
  MRclass =      "62A99 (60E05)",
  MRnumber =     "2774458",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See letter \cite{Hill:2011:LEB}.",
  URL =          "http://link.springer.com/article/10.1007/s00283-010-9182-3",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Intelligencer",
  journal-URL =  "http://link.springer.com/journal/283",
}

@Article{Berger:2011:BTB,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "A basic theory of {Benford's Law}",
  journal =      j-PROBAB-SURV,
  volume =       "8",
  number =       "??",
  pages =        "1--126",
  month =        "????",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1214/11-PS175",
  ISSN =         "1549-5787",
  ISSN-L =       "1549-5787",
  MRclass =      "37A45 (11K06 60-02 60F15 60G57 62E10)",
  MRnumber =     "2846899 (2012h:37015)",
  MRreviewer =   "Steven Joel Miller",
  bibdate =      "Tue Nov 15 11:07:49 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/probabsurv.bib",
  URL =          "http://projecteuclid.org/euclid.ps/1311860830",
  abstract =     "Drawing from a large, diverse body of work, this
                 survey presents a comprehensive and unified
                 introduction to the mathematics underlying the
                 prevalent logarithmic distribution of significant
                 digits and significands, often referred to as {\em
                 Benford's Law\/} (BL) or, in a special case, as the
                 {\em First Digit Law}. The invariance properties that
                 characterize BL are developed in detail. Special
                 attention is given to the emergence of BL in a wide
                 variety of deterministic and random processes. Though
                 mainly expository in nature, the article also provides
                 strengthened versions of, and simplified proofs for,
                 many key results in the literature. Numerous intriguing
                 problems for future research arise naturally.",
  acknowledgement = ack-nhfb,
  fjournal =     "Probability Surveys",
  journal-URL =  "http://projecteuclid.org/all/euclid.ps",
  keywords =     "base-invariance; Benford's Law; difference equation;
                 mixture of distributions; random probability measure;
                 scale-invariance; shadowing; significant digits;
                 sum-invariance; uniform distribution mod 1",
}

@Article{Berger:2011:FSM,
  author =       "Arno Berger and Theodore P. Hill and Bahar Kaynar and
                 Ad Ridder",
  title =        "Finite-state {Markov} Chains Obey {Benford's Law}",
  journal =      j-SIAM-J-MAT-ANA-APPL,
  volume =       "32",
  number =       "3",
  pages =        "665--684",
  month =        "????",
  year =         "2011",
  CODEN =        "SJMAEL",
  DOI =          "https://doi.org/10.1137/100789890",
  ISSN =         "0895-4798 (print), 1095-7162 (electronic)",
  ISSN-L =       "0895-4798",
  MRclass =      "15B51 (11J71 60J22 65C40)",
  MRnumber =     "2825319 (2012h:15058)",
  MRreviewer =   "E. Seneta",
  bibdate =      "Wed Aug 24 11:18:18 MDT 2011",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMAX/32/3;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
  URL =          "http://epubs.siam.org/simax/resource/1/sjmael/v32/i3/p665_s1;
                 https://dblp.org/db/journals/siammax/siammax32.html#BergerHKR11",
  acknowledgement = ack-nhfb,
  dblp-key =     "journals/siammax/BergerHKR11",
  dblp-mdate =   "2020-05-26",
  fjournal =     "SIAM Journal on Matrix Analysis and Applications",
  journal-URL =  "http://epubs.siam.org/simax",
  onlinedate =   "July 21, 2011",
}

@Article{Berger:2011:SDP,
  author =       "Arno Berger",
  title =        "Some dynamical properties of {Benford} sequences",
  journal =      j-J-DIFFERENCE-EQU-APPL,
  volume =       "17",
  number =       "2",
  pages =        "137--159",
  year =         "2011",
  CODEN =        "JDEAEA",
  DOI =          "https://doi.org/10.1080/10236198.2010.549012",
  ISSN =         "1023-6198 (print), 1563-5120 (electronic)",
  ISSN-L =       "1023-6198",
  MRclass =      "37A45 (11K06 37Bxx)",
  MRnumber =     "2783341",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/10236198.2010.549012",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Difference Equ. Appl.",
  fjournal =     "Journal of Difference Equations and Applications",
  journal-URL =  "http://www.informaworld.com/1023-6198",
}

@Article{Bernhardsson:2011:PPM,
  author =       "Sebastian Bernhardsson and Seung Ki Baek and Petter
                 Minnhagen",
  title =        "A paradoxical property of the monkey book",
  journal =      j-J-STAT-MECH-THEORY-EXP,
  volume =       "2011",
  number =       "??",
  pages =        "P07013",
  month =        jul,
  year =         "2011",
  CODEN =        "JSMTC6",
  DOI =          "https://doi.org/10.1088/1742-5468/2011/07/P07013",
  ISSN =         "1742-5468",
  ISSN-L =       "1742-5468",
  bibdate =      "Mon Nov 21 21:57:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1103.2681;
                 http://iopscience.iop.org/1742-5468/2011/07/P07013/",
  abstract =     "A `monkey book' is a book consisting of a random
                 sequence of letters and blanks, where a group of
                 letters surrounded by two blanks is defined as a word.
                 We compare the statistics of the word distribution for
                 a monkey book to real books. It is shown that the word
                 distribution statistics for the monkey book is
                 different and quite distinct from a typical real book.
                 In particular, the monkey book obeys Heaps' power law
                 to an extraordinarily good approximation, in contrast
                 to the word distributions for real books, which deviate
                 from Heaps' law in a characteristic way. This
                 discrepancy is traced to the different properties of a
                 `spiked' distribution and its smooth envelope. The
                 somewhat counter-intuitive conclusion is that a `monkey
                 book' obeys Heaps' power law precisely because its
                 word-frequency distribution is not a smooth power law,
                 contrary to the expectation based on simple
                 mathematical arguments that if one is a power law, so
                 is the other.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Mechanics: Theory and
                 Experiment",
  journal-URL =  "http://iopscience.iop.org/1742-5468/",
  keywords =     "Heaps' Law",
}

@Article{Bhattacharya:2011:ABA,
  author =       "Sukanto Bhattacharya and Dongming Xu and Kuldeep
                 Kumar",
  title =        "An {ANN}-based auditor decision support system using
                 {Benford}'s law",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "576--584",
  month =        feb,
  year =         "2011",
  CODEN =        "DSSYDK",
  DOI =          "https://doi.org/10.1016/j.dss.2010.08.011",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "On quantitative methods for detection of financial
                 fraud",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923610001351",
  abstract =     "While there is a growing professional interest on the
                 application of Benford's law and digit analysis in
                 financial fraud detection, there has been relatively
                 little academic research to demonstrate its efficacy as
                 a decision support tool in the context of an analytical
                 review procedure pertaining to a financial audit. We
                 conduct a numerical study using a genetically optimized
                 artificial neural network. Building on an earlier work
                 by others of a similar nature, we assess the benefits
                 of Benford's law as a useful classifier in segregating
                 naturally occurring (i.e. non-concocted) numbers from
                 those that are made up. Alongside the frequency of the
                 first and second significant digits and their mean and
                 standard deviation, a posited set of non-digit input
                 variables categorized as information theoretic,
                 distance-based and goodness-of-fit measures, help to
                 minimize the critical classification errors that can
                 lead to an audit failure. We come up with the optimal
                 network structure for every instance corresponding to a
                 $ 3 \times 3 $ Manipulation Involvement matrix that is
                 drawn to depict the different combinations of the level
                 of sophistication in data manipulation by the
                 perpetrators of a financial fraud and also the extent
                 of collusive involvement.",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "ANNs; ARPs; Auditor decision support system; Benford's
                 law; Benford's Law; Benford's law; Benford's Law;
                 Genetic optimization; {ANNs}; {ARPs}",
}

@Article{Bose:2011:QMD,
  author =       "Indranil Bose and Selwyn Piramuthu and Michael J.
                 Shaw",
  title =        "Quantitative methods for Detection of Financial
                 Fraud",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "3",
  pages =        "557--558",
  month =        feb,
  year =         "2011",
  CODEN =        "DSSYDK",
  DOI =          "https://doi.org/10.1016/j.dss.2010.08.005",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "On quantitative methods for detection of financial
                 fraud",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923610001296",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law",
}

@InCollection{Brahler:2011:BGS,
  author =       "Gernot Br{\"a}hler and Markus Bensmann and Hans-Ralph
                 Jakobi",
  editor =       "????",
  booktitle =    "Ilmenauer Schriften zur Betriebswirtschaftslehre",
  title =        "{Das Benfordsche Gesetz und seine Anwendbarkeit bei
                 der digitalen Pr{\"u}fung von Fahrtenb{\"u}chern}.
                 ({German}) [{The} {Benford} law and its applicability
                 in the digital examination of logbooks]",
  volume =       "3/2011",
  publisher =    "Verlag proWiWi e.V.",
  address =      "Ilmenau, Germany",
  pages =        "??--??",
  month =        mar,
  year =         "2011",
  ISBN =         "3-940882-28-3",
  ISBN-13 =      "978-3-940882-28-8",
  ISSN =         "1866-2145 (print), 2192-4643 (electronic)",
  LCCN =         "????",
  bibdate =      "Mon Feb 18 18:21:29 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.econstor.eu/dspace/bitstream/10419/55703/1/662518055.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Breunig:2011:SEI,
  author =       "Christian Breunig and Achim Goerres",
  title =        "Searching for electoral irregularities in an
                 established democracy: Applying {Benford's Law} tests
                 to {Bundestag} elections in {Unified Germany}",
  journal =      j-ELECT-STUDIES,
  volume =       "30",
  number =       "3",
  pages =        "534--545",
  month =        sep,
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.electstud.2011.03.005",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "Special Symposium on the Politics of Economic Crisis",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379411000370",
  abstract =     "This article investigates electoral irregularities in
                 the 1990 to 2005 Bundestag elections of unified
                 Germany. Drawing on the Second Digit Benford Law (2BL)
                 by Mebane (2006), the analysis consists of comparing
                 the observed frequencies of numerals of candidate votes
                 and party votes at the precinct level against the
                 expected frequencies according to Benford's Law. Four
                 central findings stand out. First, there is no evidence
                 for systematic fraud or mismanagement with regard to
                 candidate votes from districts where fraud would be
                 most instrumental. Second, at the state level
                 (Bundesland), there are 51 violations in 190 tests of
                 the party list votes. Third, East German states are not
                 more prone to violations than Western ones. This
                 finding refutes the notion that the East's more recent
                 transition to democracy poses problems in electoral
                 management. Fourth, a strong variation in patterns of
                 violation across Bundesl{\"a}nder exists: states with
                 dominant party control are more likely to display
                 irregularities. The article concludes by hypothesizing
                 and exploring the notion that partisan composition of
                 nominees involved in the counting may produce a higher
                 likelihood of violation and be a cause of L{\"a}nder
                 variation. This may especially be the case when a party
                 dominates in a Bundesland or opponents to the former
                 socialist regime party are involved in the counting.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Benford's Law; Bundestag; Fraud; Germany",
}

@TechReport{Bul:2011:BGG,
  author =       "K. Bul",
  title =        "{Das Benford'sche Gesetz}. ({German}) [{Benford's
                 Law}]",
  type =         "Working paper",
  institution =  "Max-von-Laue-gymnasium",
  address =      "Koblenz, Germany",
  year =         "2011",
  bibdate =      "Fri Mar 22 08:44:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  language =     "German",
}

@Article{Campanario:2011:BLC,
  author =       "Juan Campanario and Mar{\'\i}a Coslado",
  title =        "{Benford}'s law and citations, articles and impact
                 factors of scientific journals",
  journal =      j-SCIENTOMETRICS,
  volume =       "88",
  number =       "2",
  pages =        "421--432",
  month =        aug,
  year =         "2011",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-011-0387-9",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Fri Nov 25 10:43:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-011-0387-9",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Cantu:2011:FDA,
  author =       "F. Cantu and S. M. Saiegh",
  title =        "Fraudulent Democracy? {An} Analysis of {Argentina}'s
                 Infamous Decade Using Supervised Machine Learning",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "4",
  pages =        "409--433",
  month =        "Autumn",
  year =         "2011",
  DOI =          "https://doi.org/10.1093/pan/mpr033",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 18:24:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://pan.oxfordjournals.org/content/19/4/409.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  keywords =     "Benford's Law",
}

@Article{Chang:2011:CGR,
  author =       "Harry M. Chang",
  title =        "Constructing $n$-gram rules for natural language
                 models through exploring the limitation of the
                 {Zipf--Mandelbrot} law",
  journal =      j-COMPUTING,
  volume =       "91",
  number =       "3",
  pages =        "241--264",
  month =        mar,
  year =         "2011",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-010-0116-x",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  MRclass =      "68T50",
  MRnumber =     "2776088",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0010-485X&volume=91&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0010-485X&volume=91&issue=3&spage=241",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing. Archives for Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}

@Article{Chida:2011:LSI,
  author =       "Satoshi Chida and Naoto Miyoshi",
  title =        "Limiting size index distributions for ball-bin models
                 with {Zipf}-type frequencies",
  journal =      j-ANN-INST-STAT-MATH-TOKYO,
  volume =       "63",
  number =       "4",
  pages =        "745--768",
  year =         "2011",
  CODEN =        "AISXAD",
  DOI =          "https://doi.org/10.1007/s10463-010-0276-7",
  ISSN =         "0020-3157 (print), 1572-9052 (electronic)",
  ISSN-L =       "0020-3157",
  MRclass =      "60C05 (60F15 60J27)",
  MRnumber =     "2805906 (2012f:60035)",
  MRreviewer =   "Elvira Di Nardo",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of the Institute of Statistical Mathematics
                 (Tokyo)",
  journal-URL =  "http://link.springer.com/journal/10463",
}

@Article{Corominas-Murtra:2011:EZL,
  author =       "Bernat Corominas-Murtra and Jordi Fortuny and Ricard
                 V. Sol{\'e}",
  title =        "Emergence of {Zipf}'s law in the evolution of
                 communication",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "1",
  pages =        "036115",
  day =          "28",
  month =        mar,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.83.036115",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036115",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "9",
}

@Article{Deckert:2011:BLD,
  author =       "Joseph Deckert and Mikhail Myagkov and Peter C.
                 Ordeshook",
  title =        "{Benford's Law} and the Detection of Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "245--268",
  month =        "Summer",
  year =         "2011",
  DOI =          "https://doi.org/10.1093/pan/mpr014",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Mon Feb 18 18:26:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Mebane:2011:CBL} for a rebuttal.",
  URL =          "http://pan.oxfordjournals.org/content/19/3/245.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
  remark =       "The authors argue that application of Benford's Law
                 tests to election results to detect fraud is
                 inconclusive and ``essentially equivalent to a toss of
                 a coin''.",
}

@Article{Dixit:2011:EEP,
  author =       "U. J. Dixit and M. Jabbari Nooghabi",
  title =        "Efficient estimation in the {Pareto} distribution with
                 the presence of outliers",
  journal =      j-STAT-METHODOL,
  volume =       "8",
  number =       "4",
  pages =        "340--355",
  month =        jul,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:47 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312711000141",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Article{Doyle:2011:ITA,
  author =       "Laurance R. Doyle and Brenda McCowan and Simon
                 Johnston and Sean F. Hanser",
  title =        "Information theory, animal communication, and the
                 search for extraterrestrial intelligence",
  journal =      j-ACTA-ASTRONAUT,
  volume =       "68",
  number =       "3--4",
  pages =        "406--417",
  month =        feb # "\slash " # mar,
  year =         "2011",
  CODEN =        "AASTCF",
  DOI =          "https://doi.org/10.1016/j.actaastro.2009.11.018",
  ISSN =         "0094-5765 (print), 1879-2030 (electronic)",
  ISSN-L =       "0094-5765",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  note =         "{SETI} Special Edition",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0094576509005682",
  abstract =     "We present ongoing research in the application of
                 information theory to animal communication systems with
                 the goal of developing additional detectors and
                 estimators for possible extraterrestrial intelligent
                 signals. Regardless of the species, for intelligence
                 (i.e., complex knowledge) to be transmitted certain
                 rules of information theory must still be obeyed. We
                 demonstrate some preliminary results of applying
                 information theory to socially complex marine mammal
                 species (bottlenose dolphins and humpback whales) as
                 well as arboreal squirrel monkeys, because they almost
                 exclusively rely on vocal signals for their
                 communications, producing signals which can be readily
                 characterized by signal analysis. Metrics such as
                 Zipf's Law and higher-order information-entropic
                 structure are emerging as indicators of the
                 communicative complexity characteristic of an
                 intelligent message content within these animals
                 signals, perhaps not surprising given these species
                 social complexity. In addition to human languages, for
                 comparison we also apply these metrics to pulsar
                 signals perhaps (arguably) the most organized of
                 stellar systems as an example of astrophysical systems
                 that would have to be distinguished from an
                 extraterrestrial intelligence message by such
                 information theoretic filters. We also look at a
                 message transmitted from Earth (Arecibo Observatory)
                 that contains a lot of meaning but little information
                 in the mathematical sense we define it here. We
                 conclude that the study of non-human communication
                 systems on our own planet can make a valuable
                 contribution to the detection of extraterrestrial
                 intelligence by providing quantitative general measures
                 of communicative complexity. Studying the complex
                 communication systems of other intelligent species on
                 our own planet may also be one of the best ways to
                 deprovincialize our thinking about extraterrestrial
                 communication systems in general.",
  acknowledgement = ack-nhfb,
  fjournal =     "Acta Astronautica",
  keywords =     "Animal communication; Benford's Law; Information
                 theory; Zipf's Law; {SETI}",
}

@Article{Edwards:2011:LFP,
  author =       "Roderick Edwards and Laura Collins",
  title =        "Lexical Frequency Profiles and {Zipf's Law}",
  journal =      "Language Learning",
  volume =       "61",
  number =       "1",
  pages =        "1--30",
  year =         "2011",
  DOI =          "https://doi.org/10.1111/j.1467-9922.2010.00616.x",
  ISSN =         "0023-8333 (print), 1467-9922 (electronic)",
  ISSN-L =       "0023-8333",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "L2 vocabulary learning; L2 vocabulary size; modeling
                 vocabulary learning; Zipf's law",
}

@Article{Egghe:2011:BLS,
  author =       "Leo Egghe",
  title =        "{Benford}'s law is a simple consequence of {Zipf}'s
                 law",
  journal =      "ISSI Newsletter",
  volume =       "7",
  number =       "3",
  pages =        "55--56",
  month =        sep,
  year =         "2011",
  DOI =          "????",
  bibdate =      "Mon Feb 18 18:27:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.issi-society.info/archives/newsletter27.pdf",
  abstract =     "We show that benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) can be deduced from the
                 classical law of zipf. this explains Bensford's law as
                 a scientometric or informetric law.",
  acknowledgement = ack-nhfb,
}

@TechReport{Eliahou:2011:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  type =         "Preprint",
  institution =  "Universit{\'e} du Littoral C{\^o}te d'Opale",
  address =      "Nord-Pas-de-Calais, France",
  pages =        "14",
  day =          "15",
  month =        nov,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:27:51 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://fr.wikipedia.org/wiki/Universit%C3%A9_du_Littoral_C%C3%B4te_d%27Opale;
                 http://www-lmpa.univ-littoral.fr/publications/articles/lmpa447.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Eliazar:2011:LLZ,
  author =       "Iddo Eliazar",
  title =        "Limit laws for {Zipf}'s law",
  journal =      j-J-PHYS-A,
  volume =       "44",
  number =       "2",
  pages =        "022001",
  year =         "2011",
  CODEN =        "JPHAC5",
  DOI =          "https://doi.org/10.1088/1751-8113/44/2/022001",
  ISSN =         "1751-8113 (print), 1751-8121 (electronic)",
  ISSN-L =       "0305-4470",
  MRclass =      "62G30 (91D20)",
  MRnumber =     "2749082 (2011i:62083)",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  ZMnumber =     "Zbl 1204.62196",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Physics. A. Mathematical and Theoretical",
  journal-URL =  "http://iopscience.iop.org/0305-4470",
  pagecount =    "6",
}

@Misc{Farbaniec:2011:AFD,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  title =        "Application of the first digit law in credibility
                 evaluation of the financial accounting data based on
                 particular cases",
  howpublished = "Lecture slides for 10th International Congress on
                 Internal Control, Internal Audit, Fraud and
                 Anti-Corruption Issues, Krak{\'o}w, September 14--16,
                 2011.",
  pages =        "27",
  year =         "2011",
  bibdate =      "Thu Dec 01 21:27:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://benford.pl/documents/benford_pikw.pdf",
  acknowledgement = ack-nhfb,
}

@InProceedings{Farbaniec:2011:UBL,
  author =       "Marzena Farbaniec and Tadeusz Grabi{\'n}ski and
                 Bart{\l}omiej Zab{\l}ocki and Wac{\l}aw Zaj{\k{a}}c",
  editor =       "????",
  booktitle =    "10th International Congress on Internal Control,
                 Internal Audit, Fraud and Anti-Corruption Issues,
                 Krak{\'o}w, September 14--16, 2011",
  title =        "Using {Benford}'s law to detect irregularities in the
                 collection of data",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2011",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Thu Dec 01 21:32:03 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Garcia:2011:FPA,
  author =       "Juan Manuel Garcia Garcia",
  title =        "A fixed-point algorithm to estimate the {Yule-Simon}
                 distribution parameter",
  journal =      j-APPL-MATH-COMP,
  volume =       "217",
  number =       "21",
  pages =        "8560--8566",
  day =          "1",
  month =        jul,
  year =         "2011",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/j.amc.2011.03.092",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Oct 25 12:05:30 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/science/journal/00963003",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300311004607",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}

@InCollection{Gauvrit:2011:SRI,
  author =       "N. Gauvrit and J-P. Delahaye",
  title =        "Scatter and Regularity Implies {Benford's Law}\ldots{}
                 and More",
  crossref =     "Zenil:2011:RTC",
  pages =        "53--69",
  year =         "2011",
  bibdate =      "Mon Feb 18 18:29:00 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Giuliano:2011:WCS,
  author =       "Rita Giuliano",
  title =        "Weak convergence of sequences from fractional parts of
                 random variables and applications",
  journal =      j-THEORY-PROBAB-MATH-STAT,
  volume =       "83",
  number =       "??",
  pages =        "49--58",
  month =        "????",
  year =         "2011",
  CODEN =        "TPMSCO",
  DOI =          "????",
  ISSN =         "0094-9000 (print), 1547-7363 (electronic)",
  ISSN-L =       "0094-9000",
  MRclass =      "60F05, 60G52, 60G70, 11K06 (62G07, 42A10, 42A61)",
  MRnumber =     "http://www.ams.org/mathscinet-getitem?mr=2768848",
  bibdate =      "Mon Feb 18 17:47:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ams.org/journals/tpms/2011-83-00/S0094-9000-2012-00841-7/S0094-9000-2012-00841-7.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Theory of Probability and Mathematical Statistics",
  journal-URL =  "http://www.ams.org/publications/journals/journalsframework/tpms",
  keywords =     "Benford's Law",
}

@Book{Henriques:2011:WLB,
  author =       "Diana B. Henriques",
  title =        "The wizard of lies: {Bernie Madoff} and the death of
                 trust",
  publisher =    "Times Books/Henry Holt",
  address =      "New York, NY, USA",
  pages =        "xxiv + 419",
  year =         "2011",
  ISBN =         "0-8050-9134-3",
  ISBN-13 =      "978-0-8050-9134-2",
  LCCN =         "HV6692.M33 H46 2011",
  bibdate =      "Fri Mar 22 08:51:50 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Madoff, Bernard L; Swindlers and swindling; United
                 States; Biography; Ponzi schemes; Commercial crimes",
  tableofcontents = "An earthquake on Wall Street \\
                 Becoming bernie \\
                 The hunger for yield \\
                 The big four \\
                 The cash spigot \\
                 What they wanted to believe \\
                 Warning signs \\
                 A near-death experience \\
                 Madoff's world \\
                 The year of living dangerously \\
                 Waking up in the rubble \\
                 Reckoning the damage \\
                 Net winners and net losers \\
                 The sins of the father \\
                 The wheels of justice \\
                 Hope, lost and found",
}

@Article{Hill:2011:LEB,
  author =       "Theodore P. Hill",
  title =        "Letter to the Editor: {Benford's Law} Blunders",
  journal =      j-AMER-STAT,
  volume =       "65",
  number =       "2",
  pages =        "141--141",
  month =        may,
  year =         "2011",
  CODEN =        "ASTAAJ",
  DOI =          "https://doi.org/10.1198/tast.2011.10179",
  ISSN =         "0003-1305 (print), 1537-2731 (electronic)",
  ISSN-L =       "0003-1305",
  bibdate =      "Mon Feb 18 18:34:43 2013",
  bibsource =    "http://www.amstat.org/publications/tas/;
                 https://www.math.utah.edu/pub/tex/bib/amstat2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/pdf/10.1198/tast.2011.11011",
  acknowledgement = ack-nhfb,
  fjournal =     "The American Statistician",
  journal-URL =  "http://www.tandfonline.com/loi/utas20",
  remark =       "Brief comment on a error in Feller's derivation of
                 Benford's Law, with pointer to a corrected proof in
                 \cite{Berger:2011:BLS}.",
}

@Article{Hisano:2011:PVD,
  author =       "Ryohei Hisano and Didier Sornette and Takayuki
                 Mizuno",
  title =        "Predicted and verified deviations from {Zipf}'s law in
                 ecology of competing products",
  journal =      j-PHYS-REV-E,
  volume =       "84",
  number =       "2",
  pages =        "026117",
  day =          "24",
  month =        aug,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.84.026117",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.84.026117",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Zipf's Law",
  pagecount =    "8",
}

@Article{Hui:2011:BLN,
  author =       "Jiang Hui and Shen Jia-Jie and Zhao Yu-Min",
  title =        "{Benford's Law} in Nuclear Structure Physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "32101--32104",
  month =        mar,
  year =         "2011",
  CODEN =        "CPLEEU",
  DOI =          "https://doi.org/10.1088/0256-307X/28/3/032101",
  ISSN =         "0256-307X (print), 1741-3540 (electronic)",
  ISSN-L =       "0256-307X",
  bibdate =      "Fri Nov 25 10:37:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chinese Physics Letters",
}

@Article{Janvresse:2011:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "ArXiv e-prints",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:06:41 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1103.1719",
  abstract =     "Motivated by giving a meaning to ``The probability
                 that a random integer has initial digit $d$'', we
                 define a URI-set as a random set $E$ of natural
                 integers such that each $ n > 0$ belongs to $E$ with
                 probability $ 1 / n$, independently of other integers.
                 This enables us to introduce two notions of densities
                 on natural numbers: The URI-density, obtained by
                 averaging along the elements of $E$, and the local
                 URI-density, which we get by considering the $k$-th
                 element of $E$ and letting $k$ go to infinity. We prove
                 that the elements of $E$ satisfy Benford's law, both in
                 the sense of URI-density and in the sense of local
                 URI-density. Moreover, if $ b_1 $ and $ b_2 $ are two
                 multiplicatively independent integers, then the
                 mantissae of a natural number in base $ b_1 $ and in
                 base $ b_2 $ are independent. Connections of
                 URI-density and local URI-density with other well-known
                 notions of densities are established: Both are stronger
                 than the natural density, and URI-density is equivalent
                 to log-density. We also give a stochastic
                 interpretation, in terms of URI-set, of the $ H_\infty
                 $-density.",
  acknowledgement = ack-nhfb,
}

@Article{Jiang:2011:BLN,
  author =       "Hui Jiang and Jia-Jie Shen and Yu-Min Zhao",
  title =        "{Benford}'s law in nuclear structure physics",
  journal =      j-CHIN-PHYS-LETT,
  volume =       "28",
  number =       "3",
  pages =        "032101",
  month =        "????",
  year =         "2011",
  CODEN =        "CPLEEU",
  DOI =          "https://doi.org/10.1088/0256-307X/28/3/032101",
  ISSN =         "0256-307X (print), 1741-3540 (electronic)",
  ISSN-L =       "0256-307X",
  bibdate =      "Mon Nov 14 16:16:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See also \cite{Ferreira:2015:LPA}.",
  acknowledgement = ack-nhfb,
  ajournal =     "Chin. Phys. Lett.",
  fjournal =     "Chinese Physics Letters",
  pagecount =    "4",
}

@InProceedings{Kalinin:2011:UEF,
  author =       "K. Kalinin and Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Proceedings of the 2011 Annual Meeting of the Midwest
                 Political Science Association, Chicago, IL, March
                 31--April 2, 2011}",
  title =        "Understanding Electoral Frauds through Evolution of
                 {Russian} Federalism: From ``Bargaining Loyalty'' to
                 ``Signaling Loyalty''",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2011",
  bibdate =      "Sat Sep 10 12:37:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kim:2011:ZAS,
  author =       "SeongKi Kim and HaYoon Song and SangYong Han",
  title =        "{ZipfAllocation}: an algorithm for static allocation
                 of movies in a cluster of video servers",
  journal =      j-SPE,
  volume =       "41",
  number =       "6",
  pages =        "695--716",
  month =        may,
  year =         "2011",
  CODEN =        "SPEXBL",
  DOI =          "https://doi.org/10.1002/spe.1027",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Tue Jun 21 17:09:57 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soft{\-}ware\emdash Prac{\-}tice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
  onlinedate =   "25 Nov 2010",
}

@Misc{Li:2011:ZLB,
  author =       "Wentian Li",
  title =        "{Zipf's Law} bibliography",
  howpublished = "Web site.",
  month =        aug,
  year =         "2011",
  bibdate =      "Fri Nov 25 08:58:21 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "The site holds 870 references (in untagged
                 reference-list form) up to 11 August 2011.",
  URL =          "http://www.nslij-genetics.org/wli/zipf/",
  acknowledgement = ack-nhfb,
  lastaccess =   "25 November 2011",
}

@Article{Liu:2011:BLC,
  author =       "X. J. Liu and X. P. Zhang and D. D. Ni and Z. Z. Ren",
  title =        "{Benford}'s law and cross-sections of {$ A(n, \alpha)
                 B $} reactions",
  journal =      j-EUR-PHYS-J-A,
  volume =       "47",
  pages =        "78",
  month =        jun,
  year =         "2011",
  CODEN =        "EPJAFV",
  DOI =          "https://doi.org/10.1140/epja/i2011-11078-3",
  ISSN =         "1434-6001 (print), 1434-601X (electronic)",
  ISSN-L =       "1434-6001",
  bibdate =      "Mon Nov 14 18:00:32 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011EPJA...47...78L",
  acknowledgement = ack-nhfb,
  fjournal =     "European Physical Journal A: Hadrons and Nuclei",
  journal-URL =  "http://www.springerlink.com/content/1434-6001",
}

@InProceedings{Lyons:2011:NSF,
  author =       "M. Lyons and E. Carl-Ludwig Siegel",
  booktitle =    "APS March Meeting Abstracts",
  title =        "{NON-Shor} Factorization via {BEQS BEC}: {Watkins}
                 Number-Theory ``Pure''-Mathematics $ \cup $ with
                 Statistical-Physics: {Benford} Log-Law Inversion to
                 {ONLY} {BEQS} digit $ d = 0 $ {BEC}!!!",
  publisher =    "American Physical Society",
  address =      "????",
  pages =        "K1142",
  month =        mar,
  year =         "2011",
  bibdate =      "Mon Nov 14 18:08:39 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2011APS..MAR.K1142L",
  acknowledgement = ack-nhfb,
}

@Article{Malevergne:2011:TPA,
  author =       "Yannick Malevergne and Vladilen Pisarenko and Didier
                 Sornette",
  title =        "Testing the {Pareto} against the lognormal
                 distributions with the uniformly most powerful unbiased
                 test applied to the distribution of cities",
  journal =      j-PHYS-REV-E,
  volume =       "83",
  number =       "3",
  pages =        "036111",
  day =          "22",
  month =        mar,
  year =         "2011",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.83.036111",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Feb 26 06:40:57 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.83.036111",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  keywords =     "Pareto distribution; Zipf's Law",
  pagecount =    "11",
}

@Article{Martinez-Rodriguez:2011:MUE,
  author =       "A. M. Mart{\'\i}nez-Rodr{\'\i}guez and A. J.
                 S{\'a}ez-Castillo and A. Conde-S{\'a}nchez",
  title =        "Modelling using an extended {Yule} distribution",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "55",
  number =       "1",
  pages =        "863--873",
  day =          "1",
  month =        jan,
  year =         "2011",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:03 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947310002872",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Masse:2011:SWD,
  author =       "Bruno Mass{\'e} and Dominique Schneider",
  title =        "A survey on weighted densities and their connection
                 with the first digit phenomenon",
  journal =      j-ROCKY-MOUNTAIN-J-MATH,
  volume =       "41",
  number =       "5",
  pages =        "1395--1415",
  month =        "????",
  year =         "2011",
  CODEN =        "RMJMAE",
  DOI =          "https://doi.org/10.1216/RMJ-2011-41-5-1395",
  ISSN =         "0035-7596 (print), 1945-3795 (electronic)",
  ISSN-L =       "0035-7596",
  MRclass =      "60B10 (11B05 11K99)",
  MRnumber =     "2838069 (2012k:60009)",
  MRreviewer =   "Radhakrishnan Nair",
  bibdate =      "Mon Feb 18 18:47:30 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rmmc.asu.edu/abstracts/rmj/vol41-5/surv-masspag1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Rocky Mountain Journal of Mathematics",
  journal-URL =  "http://projecteuclid.org/euclid.rmjm",
  keywords =     "Benford's law; first digit phenomenon; hierarchy;
                 mantissa; weighted density",
}

@Book{McGrayne:2011:TWH,
  author =       "Sharon Bertsch McGrayne",
  title =        "The theory that would not die: how {Bayes}' rule
                 cracked the {Enigma} code, hunted down {Russian}
                 submarines, and emerged triumphant from two centuries
                 of controversy",
  publisher =    pub-YALE,
  address =      pub-YALE:adr,
  pages =        "xiii + 320",
  year =         "2011",
  ISBN =         "0-300-16969-8",
  ISBN-13 =      "978-0-300-16969-0",
  LCCN =         "QA279.5 .M415 2011",
  bibdate =      "Wed May 11 14:42:54 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "Bayes' rule appears to be a straightforward, one-line
                 theorem: by updating our initial beliefs with objective
                 new information, we get a new and improved belief. To
                 its adherents, it is an elegant statement about
                 learning from experience. To its opponents, it is
                 subjectivity run amok. In the first-ever account of
                 Bayes' rule for general readers, Sharon Bertsch
                 McGrayne explores this controversial theorem and the
                 human obsessions surrounding it. She traces its
                 discovery by an amateur mathematician in the 1740s
                 through its development into roughly its modern form by
                 French scientist Pierre Simon Laplace. She reveals why
                 respected statisticians rendered it professionally
                 taboo for 150 years --- at the same time that
                 practitioners relied on it to solve crises involving
                 great uncertainty and scanty information, even breaking
                 Germany's Enigma code during World War II, and explains
                 how the advent of off-the-shelf computer technology in
                 the 1980s proved to be a game-changer. Today, Bayes'
                 rule is used everywhere from DNA de-coding to Homeland
                 Security. Drawing on primary source material and
                 interviews with statisticians and other scientists, The
                 Theory That Would Not Die is the riveting account of
                 how a seemingly simple theorem ignited one of the
                 greatest controversies of all time.",
  acknowledgement = ack-nhfb,
  remark =       "This book has important comments on the battles among
                 Sir Ronald Fisher, Jerzy Neyman, Egon Pearson, and Karl
                 Pearson, supplementing the extensive discussion of
                 those conflicts in \cite{Ziliak:2008:CSS}.",
  subject =      "Bayesian statistical decision theory; history; science
                 / history; mathematics / history and philosophy",
}

@Article{Mebane:2011:CBL,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Comment on {Benford's Law} and the Detection of
                 Election Fraud",
  journal =      j-POLIT-ANAL,
  volume =       "19",
  number =       "3",
  pages =        "269--272",
  day =          "18",
  month =        "Summer",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1093/pan/mpr024",
  ISSN =         "1047-1987 (print), 1476-4989 (electronic)",
  ISSN-L =       "1047-1987",
  bibdate =      "Fri Nov 25 11:00:46 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Deckert:2011:BLD}.",
  URL =          "http://pan.oxfordjournals.org/content/19/3/269.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Political Analysis",
}

@Article{Michel:2011:QAC,
  author =       "Jean-Baptiste Michel and Yuan Kui Shen and Aviva
                 Presser Aiden and Adrian Veres and Matthew K. Gray and
                 {The Google Books Team} and Joseph P. Pickett and Dale
                 Hoiberg and Dan Clancy and Peter Norvig and Jon Orwant
                 and Steven Pinker and Martin A. Nowak and Erez
                 Lieberman Aiden",
  title =        "Quantitative Analysis of Culture Using Millions of
                 Digitized Books",
  journal =      j-SCIENCE,
  volume =       "331",
  number =       "6014",
  pages =        "176--182",
  day =          "14",
  month =        jan,
  year =         "2011",
  CODEN =        "SCIEAS",
  DOI =          "https://doi.org/10.1126/science.1199644",
  ISSN =         "0036-8075 (print), 1095-9203 (electronic)",
  ISSN-L =       "0036-8075",
  bibdate =      "Fri Dec 09 11:06:28 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencemag.org/content/331/6014/176.abstract",
  acknowledgement = ack-nhfb,
  fjournal =     "Science",
  journal-URL =  "http://www.sciencemag.org/archive/",
  keywords =     "Zipf's law",
  remark =       "This papers reports results from a large study of
                 cultural phenomena, fame, and word usage from 4\% of
                 all books ever printed. Among the findings is this
                 quote from the first page: ``we estimated the number of
                 words in the English lexicon as 544,000 in 1900,
                 597,000 in 1950, and 1,022,000 in 2000. The lexicon is
                 enjoying a period of enormous growth: The addition of $
                 \approx 8500 $ words/year has increased the size of the
                 language by over 70\% during the past 50 years.'' From
                 page 177: ``Consistent with Zipf's famous law, a large
                 fraction of the words in our lexicon (63\%) were in
                 this lowest-frequency bin. As a result, we estimated
                 that 52\% of the English lexicon --- the majority of
                 the words used in English books --- consists of lexical
                 `dark matter' undocumented in standard references
                 (12).''",
}

@Article{Mir:2011:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "Law of the leading digits and the ideological struggle
                 for numbers",
  journal =      "ArXiv e-prints",
  pages =        "11",
  year =         "2011",
  bibdate =      "Mon Nov 21 07:02:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1104.3948",
  abstract =     "Benford's law states that the occurrence of
                 significant digits in many data sets is not uniform but
                 tends to follow a logarithmic distribution such that
                 the smaller digits appear as first significant digits
                 more frequently than the larger ones. We investigate
                 here numerical data on the country-wise adherent
                 distribution of seven major world religions i.e.,
                 Christianity, Islam, Buddhism, Hinduism, Sikhism,
                 Judaism and Baha'ism to see if the proportion of the
                 leading digits occurring in the distribution conforms
                 to Benford's law. We find that the adherent data of all
                 the religions, except Christianity, excellently does
                 conform to Benford's law. Furthermore, unlike the
                 adherent data on Christianity, the significant digit
                 distribution of the three major Christian denominations
                 i.e. Catholicism, Protestantism and Orthodoxy obeys the
                 law. Thus in spite of their complexity general laws can
                 be established for the evolution of the religious
                 groups.",
  acknowledgement = ack-nhfb,
}

@Article{Muller:2011:HAS,
  author =       "Hans Christian M{\"u}ller",
  title =        "How an arcane statistical law could have prevented the
                 {Greek} disaster",
  journal =      "Economics Intelligence",
  volume =       "??",
  number =       "??",
  pages =        "??",
  day =          "28",
  month =        jul,
  year =         "2011",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sun Nov 20 10:04:08 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://economicsintelligence.com/2011/07/28/how-an-arcane-statistical-law-could-have-prevented-the-greek-disaster/",
  abstract =     "If we had known what we know today, Greece would not
                 have been able to enter the Euro area. The
                 macroeconomic data the country reported to Eurostat in
                 Luxembourg were heavily tweaked. Unfortunately,
                 however, this only became clear years after it was too
                 late.",
  acknowledgement = ack-nhfb,
}

@InCollection{Nigrini:2011:BLA,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: Assessing Conformity",
  crossref =     "Nigrini:2011:FAM",
  pages =        "109--129",
  year =         "2011",
  DOI =          "https://doi.org/10.1002/9781118386798.ch6",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Kolmogorov-Smirnoff tests; mantissa arc
                 test; mean absolute deviation; Z-statistic",
  tableofcontents = "One Digit at a Time: The Z-statistic \\
                 The Chi-square and Kolmogorov--Smirnoff Tests \\
                 The Mean Absolute Deviation (MAD) Test \\
                 Tests Based on the Logarithmic Basis of Benford's Law
                 \\
                 Creating a Perfect Synthetic Benford Set \\
                 The Mantissa Arc Test \\
                 Summary",
}

@InCollection{Nigrini:2011:BLB,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Basics",
  crossref =     "Nigrini:2011:FAM",
  pages =        "85--108",
  year =         "2011",
  DOI =          "https://doi.org/10.1002/9781118386798.ch5",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "An Overview of Benford's Law \\
                 From Theory to Application in 60 Years \\
                 Which Data Sets should Conform to Benford's Law? \\
                 The Effect of Data Set Size \\
                 The Basic Digit Tests \\
                 Running the First-Two Digits Test in Access \\
                 Summary",
}

@InCollection{Nigrini:2011:BLN,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Number Duplication and Last-Two
                 Digits Tests",
  crossref =     "Nigrini:2011:FAM",
  pages =        "153--172",
  year =         "2011",
  DOI =          "https://doi.org/10.1002/9781118386798.ch8",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; COUNTIF formula; digits tests; last-two
                 digits tests; number duplication",
  tableofcontents = "The Number Duplication Test \\
                 Running the Number Duplication Test in Access \\
                 Running the Number Duplication Test in Excel \\
                 The Last-Two Digits Test \\
                 Summary",
}

@InCollection{Nigrini:2011:BLS,
  author =       "Mark J. Nigrini",
  title =        "{Benford's Law}: The Second-Order and Summation
                 Tests",
  crossref =     "Nigrini:2011:FAM",
  pages =        "130--152",
  year =         "2011",
  DOI =          "https://doi.org/10.1002/9781118386798.ch7",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; digits tests; second-order;
                 second-order test; summation test",
  tableofcontents = "A Description of the Second-Order Test \\
                 The Summation Test \\
                 Summary",
}

@Article{Osareh:2011:LLA,
  author =       "Farideh Osareh and Esmaeel Mostafavi",
  title =        "{Lotka's Law} and authorship distribution in Computer
                 Science using {Web of Science (WoS)} during
                 1986--2009",
  journal =      j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
  volume =       "5",
  number =       "2",
  pages =        "171--183",
  year =         "2011",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09737766.2011.10700911",
  ISSN =         "0973-7766 (print), 2168-930X (electronic)",
  ISSN-L =       "0973-7766",
  bibdate =      "Thu Sep 10 17:47:07 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Collnet Journal of Scientometrics and Information
                 Management",
  journal-URL =  "http://www.tandfonline.com/loi/tsim20",
}

@Article{Pericchi:2011:QAD,
  author =       "Luis Pericchi and David Torres",
  title =        "Quick anomaly detection by the {Newcomb--Benford} law,
                 with applications to electoral processes data from the
                 {USA}, {Puerto} {Rico} and {Venezuela}",
  journal =      j-STAT-SCI,
  volume =       "26",
  number =       "4",
  pages =        "502--516",
  year =         "2011",
  CODEN =        "STSCEP",
  DOI =          "https://doi.org/10.1214/09-STS296",
  ISSN =         "0883-4237 (print), 2168-8745 (electronic)",
  ISSN-L =       "0883-4237",
  MRnumber =     "2951385",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://projecteuclid.org/euclid.ss/1330437932",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Science. A Review Journal of the Institute
                 of Mathematical Statistics",
  journal-URL =  "http://projecteuclid.org/all/euclid.ss",
}

@InProceedings{Qadir:2011:IFG,
  author =       "G. Qadir and X. Zhao and A. T. Ho and M. Casey",
  booktitle =    "2011 IEEE International Symposium of Circuits and
                 Systems (ISCAS)",
  title =        "Image forensic of glare feature for improving image
                 retrieval using {Benford's Law}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "2661--2664",
  month =        may,
  year =         "2011",
  DOI =          "https://doi.org/10.1109/ISCAS.2011.5938152",
  ISSN =         "0271-4302",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benfords law; Brightness; computer forensics; discrete
                 wavelet high high sub bands; Discrete wavelet
                 transforms; Equations; Forensics; glare feature;
                 glare-based problems; Histograms; image analysis; image
                 forensic tool; image retrieval; light intensity
                 measurement; Mathematical model; probability;
                 Probability; probability intensity histogram; salient
                 features identification; visual examination",
}

@Article{Rauch:2011:FFE,
  author =       "Bernhard Rauch and Max G{\"o}ttsche and Gernot
                 Br{\"a}hler and Stefan Engel",
  title =        "Fact and Fiction in {EU}-Governmental Economic Data",
  journal =      j-GER-ECON-REV,
  volume =       "12",
  number =       "3",
  pages =        "243--255",
  month =        aug,
  year =         "2011",
  DOI =          "https://doi.org/10.1111/j.1468-0475.2011.00542.x",
  ISSN =         "1465-6485 (print), 1468-0475 (electronic)",
  ISSN-L =       "1465-6485",
  bibdate =      "Sun Nov 20 09:58:25 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1111/j.1468-0475.2011.00542.x/abstract",
  abstract =     "To detect manipulations or fraud in accounting data,
                 auditors have successfully used Benford's law as part
                 of their fraud detection processes. Benford's law
                 proposes a distribution for first digits of numbers in
                 naturally occurring data. Government accounting and
                 statistics are similar in nature to financial
                 accounting. In the European Union (EU), there is
                 pressure to comply with the Stability and Growth Pact
                 criteria. Therefore, like firms, governments might try
                 to make their economic situation seem better. In this
                 paper, we use a Benford test to investigate the quality
                 of macroeconomic data relevant to the deficit criteria
                 reported to Eurostat by the EU member states. We find
                 that the data reported by Greece shows the greatest
                 deviation from Benford's law among all euro states.",
  acknowledgement = ack-nhfb,
  fjournal =     "German Economic Review",
  keywords =     "auditing; Benford's law; fraud detection; government
                 statistics",
  onlinedate =   "28 April 2011",
}

@Article{Ravisankar:2011:DFS,
  author =       "P. Ravisankar and V. Ravi and G. Raghava Rao and I.
                 Bose",
  title =        "Detection of financial statement fraud and feature
                 selection using data mining techniques",
  journal =      j-DEC-SUPP-SYS,
  volume =       "50",
  number =       "2",
  pages =        "491--500",
  month =        jan,
  year =         "2011",
  CODEN =        "DSSYDK",
  DOI =          "https://doi.org/10.1016/j.dss.2010.11.006",
  ISSN =         "0167-9236 (print), 1873-5797 (electronic)",
  ISSN-L =       "0167-9236",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167923610001879",
  abstract =     "Recently, high profile cases of financial statement
                 fraud have been dominating the news. This paper uses
                 data mining techniques such as Multilayer Feed Forward
                 Neural Network (MLFF), Support Vector Machines (SVM),
                 Genetic Programming (GP), Group Method of Data Handling
                 (GMDH), Logistic Regression (LR), and Probabilistic
                 Neural Network (PNN) to identify companies that resort
                 to financial statement fraud. Each of these techniques
                 is tested on a dataset involving 202 Chinese companies
                 and compared with and without feature selection. {PNN}
                 outperformed all the techniques without feature
                 selection, and {GP} and {PNN} outperformed others with
                 feature selection and with marginally equal
                 accuracies.",
  acknowledgement = ack-nhfb,
  fjournal =     "Decision Support Systems",
  keywords =     "Benford's Law; Data mining; Feature selection;
                 Financial fraud detection; Neural networks;
                 t-statistic; {GP}; {SVM}",
}

@Article{Robledo:2011:LZB,
  author =       "Alberto Robledo",
  title =        "Laws of {Zipf} and {Benford}, intermittency, and
                 critical fluctuations",
  journal =      "Chinese Science Bulletin",
  volume =       "56",
  number =       "34",
  publisher =    "SP Science China Press",
  pages =        "3643--3648",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/s11434-011-4827-y",
  ISSN =         "1001-6538 (print), 1861-9541 (electronic)",
  ISSN-L =       "1001-6538",
  bibdate =      "Wed Aug 12 09:46:47 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11434-011-4827-y",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; critical clusters; generalized
                 statistical mechanics; tangent bifurcation; Zipf's
                 law",
}

@Article{Romano:2011:NLR,
  author =       "Paul K. Romano and Harry McLaughlin",
  title =        "On Non-Linear Recursive Sequences and {Benford's
                 Law}",
  journal =      j-FIB-QUART,
  volume =       "49",
  number =       "2",
  pages =        "134--138",
  month =        may,
  year =         "2011",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "11K31 (11B37)",
  MRnumber =     "2801800",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "http://www.fq.math.ca/49-2.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Abstracts/49-2/romano.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Ross:2011:BLG,
  author =       "Kenneth A. Ross",
  title =        "{Benford's Law}, a Growth Industry",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "118",
  number =       "7",
  pages =        "571--583",
  month =        aug # "\slash " # sep,
  year =         "2011",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.118.07.571",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "62A99 (60F99)",
  MRnumber =     "2826449 (2012g:62014)",
  bibdate =      "Mon Jan 30 08:58:20 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/10.4169/amermathmont.118.issue-7;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/10.4169;
                 http://www.jstor.org/stable/pdfplus/10.4169/amer.math.monthly.118.07.571.pdf;
                 http://www.maa.org/history/presidents/ross.html",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
  remark =       "The author was President of the Mathematical
                 Association of America (1995--1996).",
}

@Article{Sambridge:2011:BLF,
  author =       "Malcolm Sambridge and Hrvoje Tkal{\v{c}}i{\'c} and
                 Pierre Arroucau",
  title =        "{Benford}'s law of first digits: from mathematical
                 curiosity to change detector",
  journal =      j-ASIA-PAC-MATH-NEWSL,
  volume =       "1",
  number =       "4",
  pages =        "1--6",
  month =        oct,
  year =         "2011",
  ISSN =         "2010-3484",
  MRclass =      "62A99",
  MRnumber =     "2894867",
  MRreviewer =   "Vladimir S. Anashin",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Asia Pac. Math. Newsl.",
  fjournal =     "Asia Pacific Mathematics Newsletter",
}

@Article{SenDe:2011:BLD,
  author =       "Aditi {Sen De} and Ujjwal Sen",
  title =        "{Benford}'s law detects quantum phase transitions
                 similarly as earthquakes",
  journal =      j-EUROPHYS-LETT,
  volume =       "95",
  number =       "5",
  pages =        "50008",
  month =        sep,
  year =         "2011",
  CODEN =        "EULEEJ",
  DOI =          "https://doi.org/10.1209/0295-5075/95/50008",
  ISSN =         "0295-5075 (print), 1286-4854 (electronic)",
  ISSN-L =       "0295-5075",
  bibdate =      "Mon Nov 14 17:52:09 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1103.5398",
  abstract =     "A century ago, it was predicted that the first
                 significant digit appearing in a data would be
                 nonuniformly distributed, with the number one appearing
                 with the highest frequency. This law goes by the name
                 of Benford's law. It holds for data ranging from
                 infectious disease cases to national greenhouse gas
                 emissions. Quantum phase transitions are cooperative
                 phenomena where qualitative changes occur in many-body
                 systems at zero temperature. We show that the
                 century-old Benford's law can detect quantum phase
                 transitions, much like it detects earthquakes.
                 Therefore, being certainly of very different physical
                 origins, seismic activity and quantum cooperative
                 phenomena may be detected by similar methods. The
                 result has immediate implications in precise
                 measurements in experiments in general, and for
                 realizable quantum computers in particular. It shows
                 that estimation of the first significant digit of
                 measured physical observables is enough to detect the
                 presence of quantum phase transitions in macroscopic
                 systems.",
  acknowledgement = ack-nhfb,
  archiveprefix = "arXiv",
  eprint =       "1103.5398",
  fjournal =     "Europhysics Letters",
  journal-URL =  "http://iopscience.iop.org/0295-5075",
  primaryclass = "quant-ph",
}

@Misc{Shi:2011:ESP,
  author =       "Yun-Quing Shi and DongDong Fu",
  title =        "Apparatus and method for a generalized {Benford's Law}
                 analysis of {DCT} and {JPEG} coefficients",
  howpublished = "US Patent 7940989.",
  day =          "10",
  month =        may,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:49:54 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "US Patent Application 11/772,636 filed 2 July 2007. US
                 Patent issued 10 May 2011.",
  URL =          "http://www.google.com/patents/US7940989",
  acknowledgement = ack-nhfb,
}

@Article{Shikano:2011:WDD,
  author =       "S. Shikano and V. Mack",
  title =        "When does 2nd Digit {Benford's Law}-Test signal an
                 election fraud? {Facts} or misleading test results",
  journal =      "Jahrb{\"u}cher f{\"u}r National{\"o}konomie und
                 Statistik",
  volume =       "231",
  number =       "5--6",
  pages =        "719--732",
  month =        "????",
  year =         "2011",
  DOI =          "????",
  bibdate =      "Mon Feb 18 18:51:04 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://benfordonline.net/fullreference/1015",
  acknowledgement = ack-nhfb,
}

@Article{Tang:2011:ESP,
  author =       "Lian Tang and Da Hui Wang",
  title =        "An explanation of the shift parameter {$ \rho $} in
                 the {Zipf--Mandelbrot} law",
  journal =      "Beijing Shifan Daxue Xuebao",
  volume =       "47",
  number =       "1",
  pages =        "97--100",
  year =         "2011",
  CODEN =        "BSDKDH",
  ISSN =         "0476-0301",
  ISSN-L =       "0476-0301",
  MRclass =      "94A17",
  MRnumber =     "2807603",
  bibdate =      "Sat Nov 12 09:13:23 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Beijing Shifan Daxue Xuebao. Ziran Kexue Ban. Journal
                 of Beijing Normal University (Natural Science)",
}

@Article{Urzua:2011:TZL,
  author =       "Carlos M. Urz{\'u}a",
  title =        "Testing for {Zipf}'s law: a common pitfall",
  journal =      j-ECONOM-LETT,
  volume =       "112",
  number =       "3",
  pages =        "254--255",
  day =          "1",
  month =        sep,
  year =         "2011",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/j.econlet.2011.05.049",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "62F03 (91B82)",
  MRnumber =     "2848721",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165176511002266",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  keywords =     "Zipf's Law",
}

@Article{Vallee:2011:BMF,
  author =       "Robert Vall{\'e}e",
  title =        "{Beno{\^\i}t Mandelbrot} --- further notes",
  journal =      "Kybernetes",
  volume =       "40",
  number =       "9--10",
  pages =        "??--??",
  month =        "????",
  year =         "2011",
  CODEN =        "KBNTA3",
  ISSN =         "0368-492X (print), 1758-7883 (electronic)",
  ISSN-L =       "0368-492X",
  bibdate =      "Fri Nov 25 07:38:10 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.emeraldinsight.com/journals.htm?issn=0368-492X&volume=40&issue=9/10&articleid=17003220",
  acknowledgement = ack-nhfb,
}

@Misc{Wang:2011:BLD,
  author =       "Jialan Wang",
  title =        "{Benford's Law} and the Decreasing Reliability of
                 Accounting Data for {US} Firms. {Studies} in Everyday
                 Life: Investigations and experiments on food, ethics,
                 economics, and the environment",
  howpublished = "Blog posting",
  day =          "9",
  month =        oct,
  year =         "2011",
  bibdate =      "Mon Feb 18 18:54:40 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://econerdfood.blogspot.com/2011/10/benfords-law-and-decreasing-reliability.html",
  acknowledgement = ack-nhfb,
}

@Misc{Wang:2011:BLR,
  author =       "Jialan Wang",
  title =        "{Benford}'s law: a revised analysis",
  howpublished = "Blog posting",
  day =          "24",
  month =        oct,
  year =         "2011",
  bibdate =      "Tue Feb 19 10:33:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://econerdfood.blogspot.com/2011/10/benfords-law-revised-analysis.html",
  acknowledgement = ack-nhfb,
}

@Misc{Weisstein:2011:BL,
  author =       "Eric W. Weisstein",
  title =        "{Benford's Law}",
  howpublished = "MathWorld---A Wolfram Web Resource",
  year =         "2011",
  bibdate =      "Tue Nov 15 08:40:40 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://mathworld.wolfram.com/BenfordsLaw.html",
  acknowledgement = ack-nhfb,
}

@InProceedings{Winter:2011:DFU,
  author =       "Christian Winter and Markus Schneider and York
                 Yannikos",
  editor =       "Gilbert Peterson and Sujeet Shenoi",
  booktitle =    "{Advances in Digital Forensics VII: 7th IFIP WG 11.9
                 International Conference on Digital Forensics, Orlando,
                 FL, USA, January 31-- February 2, 2011, Revised
                 Selected Papers}",
  title =        "Detecting Fraud Using Modified {Benford} Analysis",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xviii + 285",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/978-3-642-24212-0_10",
  ISBN =         "3-642-24211-1 (paperback), 3-642-24212-X (e-book)",
  ISBN-13 =      "978-3-642-24211-3 (paperback), 978-3-642-24212-0
                 (e-book)",
  LCCN =         "HV8079.C65 I357 2011",
  bibdate =      "Wed Aug 12 09:41:22 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  price =        "US\$",
  URL =          "http://link.springer.com/chapter/10.1007/978-3-642-24212-0_10/",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1007/978-3-642-24212-0",
}

@Article{Xu:2011:PCG,
  author =       "B. Xu and J. Wang and G. Liu and Y. Dai",
  title =        "Photorealistic computer graphics forensics based on
                 leading digit law",
  journal =      "Journal of Electronics (China)",
  volume =       "28",
  number =       "1",
  pages =        "95--100",
  month =        "????",
  year =         "2011",
  DOI =          "https://doi.org/10.1007/s11767-011-0474-3",
  bibdate =      "Mon Feb 18 18:55:38 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11767-011-0474-3",
  acknowledgement = ack-nhfb,
}

@Article{Zgela:2011:ATC,
  author =       "Mario {\v{Z}}gela and Jasminka Dob{\v{s}}a",
  title =        "Analysis of Top 500 {Central and East European}
                 Companies Net Income Using {Benford's Law}",
  journal =      j-J-INFO-ORG-SCI,
  volume =       "35",
  number =       "2",
  pages =        "215--228",
  month =        dec,
  year =         "2011",
  ISSN =         "1846-3312 (print), 1846-9418 (electronic)",
  ISSN-L =       "1846-3312",
  bibdate =      "Mon Feb 18 18:57:10 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Prosinac 2011 conference.",
  URL =          "http://hrcak.srce.hr/file/111658;
                 http://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=111658",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informational and Organizational Sciences",
  journal-URL =  "http://jios.foi.hr/index.php/jios/index",
}

@Article{Zhang:2011:ETO,
  author =       "Qunzhi Zhang and Didier Sornette",
  title =        "Empirical test of the origin of {Zipf}'s law in
                 growing social networks",
  journal =      j-PHYSICA-A,
  volume =       "390",
  number =       "23--24",
  pages =        "4124--4130",
  day =          "1",
  month =        nov,
  year =         "2011",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2011.06.063",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437111005103",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Zorzi:2011:BL,
  author =       "Alberto Zorzi",
  title =        "95.22 {Benford}'s law and $ \pi $",
  journal =      j-MATH-GAZ,
  volume =       "95",
  number =       "533",
  pages =        "264--266",
  month =        jul,
  year =         "2011",
  CODEN =        "MAGAAS",
  DOI =          "https://doi.org/10.1017/S0025557200002990",
  ISSN =         "0025-5572 (print), 2056-6328 (electronic)",
  ISSN-L =       "0025-5572",
  bibdate =      "Tue May 5 12:04:16 MDT 2015",
  bibsource =    "http://journals.cambridge.org/action/displayIssue?jid=MAG&volumeId=95&issueId=533;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Gaz.",
  fjournal =     "The Mathematical Gazette",
  journal-URL =  "http://www.m-a.org.uk/jsp/index.jsp?lnk=620",
  remark =       "The journal Web site lacks a search feature, and the
                 archives only cover up to 2007. JSTOR has only issues
                 up to 2007.",
}

@Article{Abrantes-Metz:2012:LM,
  author =       "Rosa M. Abrantes-Metz and Michael Kraten and Albert D.
                 Metz and Gim S. Seow",
  title =        "Libor manipulation?",
  journal =      "Journal of Banking \& Finance",
  volume =       "36",
  number =       "1",
  pages =        "136--150",
  year =         "2012",
  DOI =          "https://doi.org/10.1016/j.jbankfin.2011.06.014",
  ISSN =         "0378-4266 (print), 1872-6372 (electronic)",
  ISSN-L =       "0378-4266",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378426611002032",
  abstract =     "On May 29, 2008 the Wall Street Journal published an
                 article alleging that several global banks were
                 reporting Libor quotes significantly lower than those
                 implied by prevailing credit default swap (CDS)
                 spreads. While acknowledging that the analysis doesn t
                 prove that banks are lying or manipulating Libor, it
                 nevertheless conjectures that these banks may have been
                 low-balling their borrowing rates to avoid looking
                 desperate for cash. In this paper we compare Libor with
                 other short-term borrowing rates, analyze individual
                 bank quotes, and compare these individual quotes to
                 {CDS} spreads and market capitalization data during
                 three periods: 1/1/07 8/8/07 (Period 1), 8/9/07 4/16/08
                 (Period 2), and 4/17/08 5/30/08 (Period 3). We find
                 some anomalous individual quotes, but the evidence is
                 inconsistent with a material manipulation of the {US}
                 dollar 1-month Libor rate.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Bid-rigging; Collusion; Conspiracies;
                 Credit default swap spreads; Libor; Manipulations;
                 Price-fixing",
}

@Article{Anonymous:2012:SB,
  author =       "Anonymous",
  title =        "The scam busters",
  journal =      j-ECONOMIST,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "15",
  month =        dec,
  year =         "2012",
  CODEN =        "EONOEH",
  ISSN =         "0013-0613 (print), 1476-8860 (electronic)",
  ISSN-L =       "0013-0613",
  bibdate =      "Mon Feb 18 19:01:02 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.economist.com/news/finance-and-economics/21568364-how-antitrust-economists-are-getting-better-spotting-cartels-scam-busters",
  acknowledgement = ack-nhfb,
  fjournal =     "The Economist",
  keywords =     "Benford's Law",
}

@TechReport{Balanzario:2012:BLM,
  author =       "E. P. Balanzario",
  title =        "{Benford}'s law for mixtures",
  type =         "Preprint",
  institution =  "????",
  address =      "????",
  month =        "????",
  year =         "2012",
  bibdate =      "Mon Feb 18 19:02:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bharath:2012:BLT,
  author =       "H. M. Bharath",
  title =        "{Benford's Law}: A theoretical explanation for base
                 $2$",
  journal =      "arXiv.org",
  day =          "24",
  month =        nov,
  year =         "2012",
  bibdate =      "Tue Jan 26 09:55:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2012arXiv1211.7008B",
  acknowledgement = ack-nhfb,
  eprint =       "1211.7008",
  keywords =     "Statistics - Other Statistics",
  primaryclass = "stat.OT",
}

@Article{Bharati:2012:CCO,
  author =       "Rakesh Bharati and Susan J. Crain and Vincent
                 Kaminski",
  title =        "Clustering in crude oil prices and the target pricing
                 zone hypothesis",
  journal =      "Energy Economics",
  volume =       "34",
  number =       "4",
  pages =        "1115--1123",
  year =         "2012",
  DOI =          "https://doi.org/10.1016/j.eneco.2011.09.009",
  ISSN =         "0140-9883 (print), 1873-6181 (electronic)",
  ISSN-L =       "0140-9883",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0140988311002258",
  abstract =     "This paper studies the target pricing zone (TPZ)
                 hypothesis for crude oil by examining price clustering
                 in the dollar digit. It is hypothesized that price
                 clustering occurs within an established {TPZ} if {OPEC}
                 is able to defend the upper and lower bounds through
                 output changes. The results show that prices strongly
                 cluster around the dollar digit value of 9 within the
                 {TPZ} sub-periods, but not outside the sub-periods.
                 Furthermore, the degree of clustering declines when
                 production capacity utilization is high and when
                 production significantly exceeds quotas, consistent
                 with OPEC's inability to defend the zone. Nine-centered
                 clustering also results in lower contemporaneous and
                 next-day volatility. These results support the target
                 pricing zone hypothesis of crude oil.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Clustering; Crude oil; Target pricing
                 zone; {OPEC}",
}

@Article{Chen:2012:MRB,
  author =       "Yanguang Chen",
  title =        "The mathematical relationship between {Zipf}'s law and
                 the hierarchical scaling law",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "11",
  pages =        "3285--3299",
  day =          "1",
  month =        jun,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2011.12.031",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437111009678",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLF,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, $ 1 / f $ noise, and fractal hierarchy",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "45",
  number =       "1",
  pages =        "63--73",
  day =          "15",
  month =        jan,
  year =         "2012",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2011.10.001",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0960077911001901",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
  keywords =     "Zipf's Law",
}

@Article{Chen:2012:ZLH,
  author =       "Yanguang Chen",
  title =        "{Zipf}'s law, hierarchical structure, and
                 cards-shuffling model for urban development",
  journal =      j-DISCRETE-DYN-NAT-SOC,
  pages =        "480196",
  year =         "2012",
  CODEN =        "DDNSFA",
  DOI =          "https://doi.org/10.1155/2012/480196",
  ISSN =         "1026-0226 (print), 1607-887X (electronic)",
  ISSN-L =       "1026-0226",
  MRclass =      "91D10",
  MRnumber =     "2914043",
  MRreviewer =   "Sandra L. Arlinghaus",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Discrete Dyn. Nat. Soc.",
  fjournal =     "Discrete Dynamics in Nature and Society. An
                 International Multidisciplinary Research and Review
                 Journal",
  pagecount =    "21",
}

@Article{Clippe:2012:BLT,
  author =       "Paulette Clippe and Marcel Ausloos",
  title =        "{Benford's Law} and {Theil} transform of financial
                 data",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "24",
  pages =        "6556--6567",
  day =          "15",
  month =        dec,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2012.07.063",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437112007546",
  abstract =     "Among econophysics investigations, studies of
                 religious groups have been of interest. On the one
                 hand, the present paper concerns the Antoinist
                 community financial reports a community which appeared
                 at the end of the 19-th century in Belgium. Several
                 growth decay regimes have been previously found over
                 different time spans. However, there is common
                 suspicion about sect finances. In that spirit, the
                 Antoinist community yearly financial reports, income
                 and expenses, are hereby examined through the so-called
                 Benford's Law. The latter is often used as a test about
                 possible accounting wrongdoings. On the other hand,
                 Benford's Law is known to be invariant under scale and
                 base transformation. Therefore, as a further test, of
                 both such data and the use of Benford's Law, the yearly
                 financial reports are nonlinearly remapped through a
                 sort of Theil transformation, i.e. based on a
                 log-transformation. The resulting data is again
                 analyzed along the Benford's Law scheme. Bizarre,
                 puzzling, features are seen. However, it is emphasized
                 that such a non-linear transformation can shift the
                 argument toward a more objective conclusion. In an
                 appendix, some brief discussion is made on why the
                 original Theil mapping should not be used. In a second
                 appendix, an imperfect Benford's Law-like form better
                 suited for anomalous distributions is presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Benford's Laws; Expenses; Income;
                 Religious community; Theil map; Time series",
}

@Article{Cristelli:2012:TMT,
  author =       "Matthieu Cristelli and Michael Batty and Luciano
                 Pietronero",
  title =        "There is More than a Power Law in {Zipf}",
  journal =      j-SCI-REP,
  volume =       "2",
  number =       "??",
  pages =        "1--7",
  month =        nov,
  year =         "2012",
  CODEN =        "SRCEC3",
  DOI =          "https://doi.org/10.1038/srep00812",
  ISSN =         "2045-2322",
  ISSN-L =       "2045-2322",
  bibdate =      "Tue Feb 26 07:32:11 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/srep/2012/121108/srep00812/full/srep00812.html",
  accepted =     "28 August 2012",
  acknowledgement = ack-nhfb,
  articleno =    "812",
  fjournal =     "Scientific Reports",
  journal-URL =  "http://www.nature.com/srep/",
  onlinedate =   "08 November 2012",
  received =     "15 August 2012",
}

@Article{Diekmann:2012:MUB,
  author =       "Andreas Diekmann",
  title =        "Making Use of ``{Benford's Law}'' for the Randomized
                 Response Technique",
  journal =      j-SOC-METH-RES,
  volume =       "41",
  number =       "2",
  pages =        "325--334",
  month =        may,
  year =         "2012",
  DOI =          "https://doi.org/10.1177/0049124112452525",
  ISSN =         "0049-1241 (print), 1552-8294 (electronic)",
  ISSN-L =       "0049-1241",
  MRnumber =     "3190709",
  bibdate =      "Mon Feb 18 19:03:24 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://smr.sagepub.com/content/41/2/325;
                 http://www.socio.ethz.ch/news/Diekmann_Benford_RRT_SMR_2012.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Sociological Methods and Research",
}

@Book{Dorrell:2012:FFB,
  author =       "Darrell D. Dorrell and Gregory A. Gadawski",
  title =        "Financial forensics body of knowledge",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 541",
  year =         "2012",
  DOI =          "https://doi.org/10.1002/9781119200734",
  ISBN =         "0-470-88085-6 (hardcover), 1-118-21897-3 (e-book),
                 1-118-21896-5 (e-book), 1-118-21898-1 (e-book),
                 1-119-20073-3 (e-book)",
  ISBN-13 =      "978-0-470-88085-2 (hardcover), 978-1-118-21897-6
                 (e-book), 978-1-118-21896-9 (e-book), 978-1-118-21898-3
                 (e-book), 978-1-119-20073-4 (e-book)",
  LCCN =         "HV6769 .D675 2012",
  bibdate =      "Thu Oct 13 06:54:34 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley finance",
  URL =          "http://catalogimages.wiley.com/images/db/jimages/9780470880852.jpg;
                 http://site.ebrary.com/id/10534000",
  abstract =     "The definitive, must-have guide for the forensic
                 accounting professionalA comprehensive and practical
                 overview of civil and criminal forensic accounting
                 methodology, Forensic Accounting Body of Knowledge
                 defines the profession of forensic accounting,
                 capturing and codifying methods that define the body of
                 knowledge. Filled with practical forensic accounting
                 tips, tools and techniques, the book contains
                 contributions from US and global professionals spanning
                 all aspects of the financial community, including the
                 law enforcement, investment, investigative, and
                 regulatory arenas. Provides immediately useful tools
                 Includes more than 200 tips and techniques Globally
                 relevant content, with cutting-edge counterterrorism
                 forensic accounting methodology Supported by a
                 continually updated Internet-based software application
                 Offers contributions from twenty financial experts in
                 law enforcement, investigative, and regulatory fields
                 Accompanied by a frequently updated Internet-based
                 software application, Forensic Accounting Body of
                 Knowledge will refine financial information users'
                 approaches, techniques, and methods with useful tools
                 and tips that reflect the continually growing body of
                 forensic accounting knowledge.",
  acknowledgement = ack-nhfb,
  subject =      "Commercial crimes; Forensic accounting; Fraud
                 investigation",
  tableofcontents = "Foundational phase \\
                 Interpersonal phase \\
                 Data collection and analysis phase: part I \\
                 Data collection and analysis phase: part II \\
                 Data collection and analysis phase: part III \\
                 Trial and reports phase \\
                 Counterterrorism: conventional tools for unconventional
                 warfare \\
                 Civil versus criminal law comparison \\
                 Appendix. Forensic inventory: forensic tools,
                 techniques, methods, and methodologies",
}

@Article{Egghe:2012:AGL,
  author =       "Leo Egghe and Raf Guns",
  title =        "Applications of the generalized law of {Benford} to
                 informetric data",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "63",
  number =       "8",
  pages =        "1662--1665",
  month =        aug,
  year =         "2012",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.22690",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Mon Feb 18 19:05:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://onlinelibrary.wiley.com/doi/10.1002/asi.22690/abstract",
  abstract =     "In a previous work (Egghe, 2011), the first author
                 showed that Benford's law (describing the logarithmic
                 distribution of the numbers 1, 2, \ldots{}, 9 as first
                 digits of data in decimal form) is related to the
                 classical law of Zipf with exponent 1. The work of
                 Campanario and Coslado (2011), however, shows that
                 Benford's law does not always fit practical data in a
                 statistical sense. In this article, we use a
                 generalization of Benford's law related to the general
                 law of Zipf with exponent $ \beta > 0 $. Using data
                 from Campanario and Coslado, we apply nonlinear least
                 squares to determine the optimal $ \beta $ and show
                 that this generalized law of Benford fits the data
                 better than the classical law of Benford.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
}

@Article{Egghe:2012:BCA,
  author =       "Leo Egghe and Raf Guns",
  title =        "Brief Communication: Applications of the generalized
                 law of {Benford} to informetric data",
  journal =      j-J-AM-SOC-INF-SCI-TECHNOL,
  volume =       "63",
  number =       "8",
  pages =        "1662--1665",
  month =        aug,
  year =         "2012",
  CODEN =        "JASIEF",
  DOI =          "https://doi.org/10.1002/asi.22690",
  ISSN =         "1532-2882 (print), 1532-2890 (electronic)",
  ISSN-L =       "1532-2882",
  bibdate =      "Fri Sep 11 10:43:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jasist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Society for Information
                 Science and Technology: JASIST",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1532-2890",
  onlinedate =   "26 Jun 2012",
}

@Article{Egghe:2012:TPS,
  author =       "Leo Egghe and Ronald Rousseau",
  title =        "Theory and practice of the shifted {Lotka} function",
  journal =      j-SCIENTOMETRICS,
  volume =       "91",
  number =       "1",
  pages =        "295--301",
  month =        apr,
  year =         "2012",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-011-0539-y",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Thu Sep 3 07:35:27 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-011-0539-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Eliahou:2012:MDP,
  author =       "Shalom Eliahou and Bruno Mass{\'e} and Dominique
                 Schneider",
  title =        "On the mantissa distribution of powers of natural and
                 prime numbers",
  journal =      "Acta Mathematica Hungarica",
  volume =       "139",
  number =       "1--2",
  pages =        "1--5",
  month =        apr,
  year =         "2013",
  DOI =          "https://doi.org/10.1007/s10474-012-0244-1",
  ISSN =         "0001-5954, 0236-5294, 1588-2632",
  ISSN-L =       "0001-5954",
  bibdate =      "Mon Feb 18 19:06:54 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s10474-012-0244-1",
  acknowledgement = ack-nhfb,
}

@Article{Eliazar:2012:PLC,
  author =       "Iddo I. Eliazar and Morrel H. Cohen",
  title =        "Power-law connections: From {Zipf} to {Heaps} and
                 beyond",
  journal =      j-INFO-PROC-MAN,
  volume =       "23",
  number =       "3",
  pages =        "56--74",
  day =          "1",
  month =        may,
  year =         "2012",
  CODEN =        "IPMADK",
  DOI =          "https://doi.org/10.1016/j.aop.2013.01.013",
  ISSN =         "0306-4573 (print), 1873-5371 (electronic)",
  ISSN-L =       "0306-4573",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0003491613000171",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing and Management",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03064573",
  keywords =     "Zipf's Law",
}

@Article{Friar:2012:GSB,
  author =       "James L. Friar and Terrance Goldman and Juan
                 P{\'e}rez-Mercader",
  title =        "Genome Sizes and the {Benford} Distribution",
  journal =      j-PLOS-ONE,
  volume =       "7",
  number =       "5",
  pages =        "e36624:1--e36624:9",
  month =        may,
  year =         "2012",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0036624",
  ISSN =         "1932-6203",
  ISSN-L =       "1932-6203",
  bibdate =      "Mon Feb 18 19:08:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0036624",
  abstract =     "Data on the number of Open Reading Frames (ORFs) coded
                 by genomes from the 3 domains of Life show the presence
                 of some notable general features. These include
                 essential differences between the Prokaryotes and
                 Eukaryotes, with the number of ORFs growing linearly
                 with total genome size for the former, but only
                 logarithmically for the latter.",
  accepted =     "11 April 2012",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
  onlinedate =   "18 May 2012",
  received =     "7 April 2011",
}

@Article{Gambini:2012:PDD,
  author =       "Alessandro Gambini and Giovanni Mingari Scarpello and
                 Daniele Ritelli",
  title =        "Probability of digits by dividing random numbers: A $
                 \psi $ and $ \zeta $ functions approach",
  journal =      j-EXPO-MATH,
  volume =       "30",
  number =       "3",
  pages =        "223--238",
  month =        "????",
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.exmath.2012.03.001",
  ISSN =         "0723-0869 (print), 1878-0792 (electronic)",
  ISSN-L =       "0723-0869",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0723086912000230",
  abstract =     "This paper begins with the statistics of the decimal
                 digits of $ n / d $ with $ (n, d) \in N^2 $ randomly
                 chosen. Starting with a statement by Ces{\`a}ro on
                 probabilistic number theory, see Ces{\`a}ro (1885)
                 [3,4], we evaluate, through the Euler function, an
                 integral appearing there. Furthermore the probabilistic
                 statement itself is proved, using a different approach:
                 in any case the probability of a given digit $r$ to be
                 the first decimal digit after dividing a couple of
                 random integers is $ p_r = 1 / 20 + 1 / 2 \{ \psi (r /
                 10 + 11 / 10) - \psi (r / 10 10 + 1) \} $. The theorem
                 is then generalized to real numbers (Theorem 1, holding
                 a proof of both $ n / d$ results) and to the $ \alpha $
                 th power of the ratio of integers (Theorem 2), via an
                 elementary approach involving the function and the
                 Hurwitz function. The article provides historic
                 remarks, numerical examples, and original theoretical
                 contributions: also it complements the recent renewed
                 interest in {Benford's Law} among number theorists.",
  acknowledgement = ack-nhfb,
  ajournal =     "Expo. Math.",
  fjournal =     "Expositiones Mathematicae",
  hoc-program-1 = "func p(r) return(1/20 + (1/2)*(psi((r + 11)/10) -
                 psi(r/10 + 1)))",
  hoc-program-2 = "for (r = 0; r < 10; ++r) printf({"}%2d: %.5f {"}, r,
                 p(r)); println {""}",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07230869",
  keywords =     "Benford's Law; Elementary probability; Euler $\psi$
                 function; Euler function; Hurwitz $\zeta$ function;
                 Hurwitz function",
  remark =       "This paper proves formulas for the probability of
                 first-digit occurrences in the ratios of random
                 integers, and compares the predictions with the
                 somewhat different ones from Benford's Law. Their work
                 simplifies a result of Ces{\`a}ro (1885), and predicts
                 that the probability of the first quotient digit being
                 $r$ is given by $ p(r) = 1 / 20 + (1 / 2)*(\psi ((r +
                 11) / 10) - \psi (r / 10 + 1)) $. That predicts these
                 pairs of $ (r, p(r)) $: $ (0, 0.12673) $, $ (1,
                 0.11736) $, $ (2, 0.10992) $, $ (3, 0.10390) $, $ (4,
                 0.09894) $, $ (5, 0.09478) $, $ (6, 0.09125) $, $ (7,
                 0.08822) $, $ (8, 0.08560) $, $ (9, 0.08330) $. Those
                 values may be compared with the Benford's Law
                 prediction for the second digit (possibly zero) of $
                 (0, 0.120) $, $ (1, 0.114) $, $ (2, 0.109) $, $ (3,
                 0.104) $, $ (4, 0.100) $, $ (5, 0.097) $, $ (6, 0.093)
                 $, $ (7, 0.090) $, $ (8, 0.088) $, and $ (9, 0.085)
                 $.",
}

@Article{Geyer:2012:ABL,
  author =       "A. Geyer and J. Mart{\'\i}",
  title =        "Applying {Benford}'s law to volcanology",
  journal =      "Geology",
  volume =       "40",
  number =       "4",
  pages =        "327--330",
  month =        apr,
  year =         "2012",
  DOI =          "https://doi.org/10.1130/G32787.1",
  bibdate =      "Mon Feb 18 19:11:36 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://geology.gsapubs.org/content/40/4/327",
  acknowledgement = ack-nhfb,
}

@InCollection{Gorroochurn:2012:BPB,
  author =       "Prakash Gorroochurn",
  title =        "{Benford} and the Peculiar Behavior of the First
                 Significant Digit (1938)",
  crossref =     "Gorroochurn:2012:CPP",
  chapter =      "27",
  pages =        "233--239",
  year =         "2012",
  DOI =          "https://doi.org/10.1002/9781118314340.ch27",
  bibdate =      "Sat Feb 23 17:26:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "(Benford) distribution; a distribution of
                 distributions; and Benford's law; Benford and the
                 peculiar behavior of the first significant digit
                 (1938); First 100 Fibonacci Numbers; first-digit law or
                 Benford's law; scale invariance; the leading digit and
                 its behavior",
}

@InProceedings{Guettler:2012:BGQ,
  author =       "S. Guettler and F. Thiemann and R. A. E. Mueller",
  editor =       "M. Clasen and G. Fr{\"o}hlich and H. Bernhardt and K.
                 Hildebrand and B. Theuvsen",
  booktitle =    "{Informationstechnologie f{\"u}r eine nachhaltige
                 Landbewirtschaftung. Fokus Forstwirtschaft. Referate
                 der 32. GIL-Jahrestagung, 29. Februar--1. M{\"a}rz
                 2012, Freising}. ({German}) [Information technology for
                 sustainable land management. Focus on forestry. Papers
                 of the 32nd GIL Annual Conference 29, February--1 March
                 2012, Freising]",
  title =        "{Benfords Gesetz: Ein Qualit{\"a}tstest f{\"u}r
                 statistische Reihen angewendet auf Handelsdaten f{\"u}r
                 Agrarprodukte}. ({German}) [{Benford's Law}: a quality
                 test applied for statistical series on trade data for
                 agricultural products]",
  volume =       "194",
  publisher =    "Gesellschaft f{\"u}r Informatik.",
  address =      "Bonn, Germany",
  bookpages =    "334 (est.)",
  pages =        "111--114",
  year =         "2012",
  ISBN =         "3-88579-288-5",
  ISBN-13 =      "978-3-88579-288-8",
  ISSN =         "1617-5468",
  LCCN =         "????",
  bibdate =      "Tue Feb 19 05:44:08 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Informatics",
  URL =          "http://www.gil-net.de/Publikationen/24_111.pdf",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Hein:2012:SFF,
  author =       "J. Hein and R. Zobrist and C. Konrad and G.
                 Schuepfer",
  title =        "Scientific fraud in 20 falsified anesthesia papers",
  journal =      "{Der Anaesthesist}",
  volume =       "61",
  number =       "6",
  pages =        "543--549",
  month =        jun,
  year =         "2012",
  CODEN =        "ANATAE",
  DOI =          "https://doi.org/10.1007/s00101-012-2029-x",
  ISSN =         "0003-2417 (print), 1432-055X (electronic)",
  ISSN-L =       "0003-2417",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s00101-012-2029-x",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/101",
  keywords =     "Benford's Law",
}

@Article{Henselmann:2012:ABL,
  author =       "Klaus Henselmann and Elisabeth Scherr and Dominik
                 Ditter",
  title =        "Applying {Benford's Law} to individual financial
                 reports: An empirical investigation on the basis of
                 {SEC XBRL} filings",
  journal =      "Working Papers in Accounting Valuation Auditing",
  volume =       "2012-1",
  pages =        "1--23",
  year =         "2012",
  bibdate =      "Thu Oct 13 07:14:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://hdl.handle.net/10419/88418;
                 http://www.econstor.eu/bitstream/10419/88418/1/773918388.pdf",
  acknowledgement = ack-nhfb,
}

@MastersThesis{Iudica:2012:BLM,
  author =       "Federico Iudica",
  title =        "{Benford's Law}: Mathematical Properties and Forensic
                 Accounting Applications",
  type =         "{Master}'s Thesis",
  school =       "Facolt{\`a} di Impresa e Management, Cattedra di
                 Matematica, Luiss Guido Carli University",
  address =      "Rome, Italy",
  pages =        "iv + 56",
  year =         "2012",
  bibdate =      "Tue Feb 19 05:54:59 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://tesi.eprints.luiss.it/8189/1/iudica-tesi-2012.pdf",
  acknowledgement = ack-nhfb,
  advisor =      "Marco Dall'Aglio",
}

@Article{Janvresse:2012:AAU,
  author =       "{\'E}lise Janvresse and Thierry {De La Rue}",
  title =        "Averaging along Uniform Random Integers",
  journal =      "Uniform Distribution Theory",
  volume =       "7",
  number =       "2",
  pages =        "35--60",
  month =        "????",
  year =         "2012",
  DOI =          "????",
  ISSN =         "1336-913X",
  ISSN-L =       "1336-913X",
  bibdate =      "Tue Feb 19 05:56:13 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.boku.ac.at/MATH/udt/vol07/no2/03JanRue16-11.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.boku.ac.at/MATH/udt/",
  keywords =     "Benford's Law",
}

@PhdThesis{Janvresse:2012:QCP,
  author =       "{\'E}lise Janvresse",
  title =        "Quelques contributions aux probabilit{\'e}s et {\`a}
                 la th{\'e}orie ergodique. ({French}) [Some
                 contributions to probability theory and ergodic
                 theory]",
  type =         "Document de synth{\`e}se pr{\'e}sent{\'e} pour
                 l'{Habilitation {\`a} Diriger des Recherches}",
  school =       "l'Universit{\'e} de Rouen",
  address =      "Rouen, France",
  pages =        "67",
  day =          "17",
  month =        feb,
  year =         "2012",
  bibdate =      "Tue Feb 19 05:57:33 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.univ-rouen.fr/LMRS/Persopage/Janvresse/hdr_Janvresse.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  language =     "French",
}

@InProceedings{Khosravani:2012:TIB,
  author =       "A. Khosravani and C. Rasinariu",
  title =        "Transformation invariance of {Benford} variables and
                 their numerical modeling",
  crossref =     "Niola:2012:RRA",
  pages =        "57--61",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:01:26 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.wseas.us/e-library/conferences/2012/SaintMalo/ACMIN/ACMIN-06.pdf",
  acknowledgement = ack-nhfb,
}

@Article{Kim:2012:BLN,
  author =       "Sangrak Kim",
  title =        "{Benford's Law} in non-equilibrium processes: Droplet
                 collisions case",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "20",
  pages =        "4970--4975",
  day =          "15",
  month =        oct,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2012.05.043",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437112004141",
  abstract =     "Benford's Law is investigated for the simulation
                 results generated from non-equilibrium molecular
                 dynamics. A statistic to measure how closely a set of
                 the numbers follows Benford's Law is defined. The
                 simulation data are from the collisions of two nano
                 droplets with different impact velocities. When a
                 non-equilibrium system returns to its equilibrium
                 state, some physical quantities relevant to the
                 non-equilibrium settings follow Benford's Law more
                 closely. The initial settings for the non-equilibrium
                 state can be interpreted as a data fabrication of its
                 corresponding equilibrium state. A connection with the
                 Shannon entropy for the first digit distribution is
                 also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Molecular dynamics; Non-equilibrium
                 process",
}

@Article{Kossovsky:2012:SNR,
  author =       "Alex Ely Kossovsky",
  title =        "Statistician's New Role as a Detective --- Testing
                 Data for Fraud",
  journal =      "Ciencias Econ{\'o}mica",
  volume =       "30",
  number =       "2",
  pages =        "179--200",
  month =        "????",
  year =         "2012",
  ISSN =         "0252-9521 (print), 2215-3489 (electronic)",
  ISSN-L =       "0252-9521",
  bibdate =      "Thu Oct 13 07:24:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://revistas.ucr.ac.cr/index.php/economicas/article/view/8015/7634",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://revistas.ucr.ac.cr/index.php/economicas/index",
  keywords =     "Benford's Law",
}

@Article{Li:2012:DTR,
  author =       "Xiang Hua Li and Yu Qian Zhao and Miao Liao and Frank
                 Y. Shih and Yun Q. Shi",
  title =        "Detection of tampered region for {JPEG} images by
                 using mode-based first digit features",
  journal =      j-EURASIP-J-ADV-SIGNAL-PROCESS,
  volume =       "2012",
  number =       "1",
  pages =        "190:1--190:??",
  month =        aug,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1186/1687-6180-2012-190",
  ISSN =         "1687-6172 (print), 1687-6180 (electronic)",
  ISSN-L =       "1687-6172",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1186/1687-6180-2012-190",
  acknowledgement = ack-nhfb,
  fjournal =     "EURASIP Journal on Advances in Signal Processing",
  journal-URL =  "http://www.asp.eurasipjournals.com/;
                 http://asp.eurasipjournals.springeropen.com/",
  keywords =     "Benford's Law",
}

@Article{LimKaiJie:2012:CES,
  author =       "Shawn {Lim Kai Jie} and Mohandas Kalaichelvan",
  title =        "A Critical Evaluation of the Significance of Round
                 Numbers in {European} Equity Markets in Light of the
                 Predictions from {Benford's Law}",
  journal =      "International Research Journal of Finance and
                 Economics",
  volume =       "95",
  number =       "??",
  pages =        "196--210",
  day =          "28",
  month =        aug,
  year =         "2012",
  DOI =          "????",
  ISSN =         "1450-2887",
  bibdate =      "Tue Feb 19 06:04:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://mpra.ub.uni-muenchen.de/40960/;
                 http://mpra.ub.uni-muenchen.de/40960/1/IRJFE_95_15.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Marcus:2012:UFA,
  author =       "Adam Marcus",
  title =        "Update on {Fujii}: Anesthesia journal finds
                 overwhelming statistical evidence of data fabrication",
  howpublished = "Web site article.",
  day =          "8",
  month =        mar,
  year =         "2012",
  bibdate =      "Wed Jun 20 14:33:00 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://retractionwatch.com/2012/03/08/update-on-fujii-anesthesia-journal-finds-overwhelming-statistical-evidence-of-data-fabrication/",
  acknowledgement = ack-nhfb,
}

@Article{Masse:2012:RNS,
  author =       "Bruno Mass{\'e} and Dominique Schneider",
  title =        "Random number sequences and the first digit
                 phenomenon",
  journal =      j-ELECTRON-J-PROBAB,
  volume =       "17",
  pages =        "86:1--86:17",
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1214/EJP.v17-1900",
  ISSN =         "1083-6489",
  ISSN-L =       "1083-6489",
  MRclass =      "60B10 (11A63 11B05)",
  MRnumber =     "2988401",
  MRreviewer =   "Rita Giuliano Antonini",
  bibdate =      "Mon Sep 1 19:06:47 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ejp.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://ejp.ejpecp.org/article/view/1900",
  abstract =     "The sequences of mantissa of positive integers and of
                 prime numbers are known not to be distributed as
                 Benford's law in the sense of the natural density. We
                 show that we can correct this defect by selecting the
                 integers or the primes by means of an adequate random
                 process and we investigate the rate of convergence. Our
                 main tools are uniform bounds for deterministic and
                 random trigonometric polynomials. We then adapt the
                 random process to prove the same result for logarithms
                 and iterated logarithms of integers. Finally we show
                 that, in many cases, the mantissa law of the $n$ th
                 randomly selected term converges weakly to the
                 Benford's law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Probability",
  journal-URL =  "http://ejp.ejpecp.org/",
  keywords =     "Benford's law; density; mantissa; weak convergence",
}

@InProceedings{Mebane:2012:SDT,
  author =       "Walter R. {Mebane, Jr.}",
  editor =       "????",
  booktitle =    "{Proceedings of the 2012 Annual Meeting of the Midwest
                 Political Science Association, Chicago, IL, April
                 11--14, 2012}",
  title =        "Second-Digit Tests for Voters' Election Strategies and
                 Election Fraud",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2012",
  DOI =          "",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "",
  bibdate =      "Sat Sep 10 14:22:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Mir:2012:LDD,
  author =       "T. A. Mir",
  title =        "The leading digit distribution of the worldwide
                 illicit financial flows",
  journal =      "ArXiv e-prints",
  year =         "2012",
  bibdate =      "Tue Feb 19 06:07:33 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1201.3432",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Mir:2012:LLD,
  author =       "Tariq Ahmad Mir",
  title =        "The law of the leading digits and the world
                 religions",
  journal =      j-PHYSICA-A,
  volume =       "391",
  number =       "3",
  pages =        "792--798",
  day =          "1",
  month =        feb,
  year =         "2012",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2011.09.001",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 http://www.sciencedirect.com/",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437111007175",
  abstract =     "Benford's Law states that the occurrence of
                 significant digits in many data sets is not uniform but
                 tends to follow a logarithmic distribution such that
                 the smaller digits appear as first significant digits
                 more frequently than the larger ones. We investigate
                 here numerical data on the country-wise adherent
                 distribution of seven major world religions i.e.
                 Christianity, Islam, Buddhism, Hinduism, Sikhism,
                 Judaism and Baha'ism to see if the proportion of the
                 leading digits occurring in the distribution conforms
                 to Benford's Law. We find that the adherent data of all
                 the religions, except Christianity, excellently does
                 conform to Benford's Law. Furthermore, unlike the
                 adherent data on Christianity, the significant digit
                 distribution of the three major Christian denominations
                 i.e., Catholicism, Protestantism and Orthodoxy obeys
                 the law. Thus in spite of their complexity, general
                 laws can be established for the evolution of religious
                 groups.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Adherents; Benford's Law; Religion",
}

@Article{Nebel:2012:DHG,
  author =       "J.-C. Nebel and S. Pezzulli",
  title =        "Distribution of Human Genes Observes {Zipf's Law}",
  journal =      "Kingston University Research \& Innovation Reports
                 (KURIR)",
  volume =       "8",
  number =       "??",
  pages =        "1--9",
  month =        "????",
  year =         "2012",
  DOI =          "????",
  ISSN =         "1749-5652",
  ISSN-L =       "1749-5652",
  bibdate =      "Tue Feb 19 06:09:05 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://staffnet.kingston.ac.uk/~ku33185/Papers/PDFformat/Kurir12.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://kurir.kingston.ac.uk/",
  remark =       "Kingston University, London, UK. Year 2012 volume is
                 not yet online on 19 February 2013.",
}

@Book{Nigrini:2012:BLA,
  author =       "Mark J. (Mark John) Nigrini",
  title =        "{Benford's Law}: Applications for Forensic Accounting,
                 Auditing, and Fraud Detection",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 330",
  year =         "2012",
  ISBN =         "1-118-15285-9 (hardcover), 1-118-28226-4,
                 1-118-28284-1, 1-118-28686-3",
  ISBN-13 =      "978-1-118-15285-0 (hardcover), 978-1-118-28226-7,
                 978-1-118-28284-7, 978-1-118-28686-9",
  LCCN =         "HV6691 .N54 2012",
  bibdate =      "Sun Feb 17 10:03:10 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.scribd.com/doc/86733139/Benford-s-Law-Applications-for-Forensic-Accounting-Auditing-and-Fraud-Detection",
  acknowledgement = ack-nhfb,
  tableofcontents = "Foreword / xi \\
                 Preface / xiii \\
                 About the Author / xix \\
                 Chapter 1: Introduction and Mathematical Foundations /
                 1 \\
                 Benford's Expected Digit Frequencies / 5 \\
                 Defining the First and First-Two Digits / 6 \\
                 Digit Patterns of U.S. Census Data / 8 \\
                 Logging on to Benford's Law / 10 \\
                 General Significant Digit Law / 13 \\
                 Log and Behold, the Census Data / 13 \\
                 Love at First Sight / 15 \\
                 Mantissa Test and Census Data / 19 \\
                 Number of Records and Benford's Law Tests / 20 \\
                 When Should Data Conform to Benford's Law? / 21 \\
                 Conclusions / 23 \\
                 Chapter 2: Theorems, Truisms, and a Little Trivia / 25
                 \\
                 Digits of Corporate Payments Data / 26 \\
                 Digits of Lake Data / 28 \\
                 Scale Invariance Theorem / 31 \\
                 Mean Absolute Deviation / 34 \\
                 Scale Invariance and Census Data / 34 \\
                 Scale Invariance and Corporate Payments / 35 \\
                 Scale Invariance and Lake Data / 36 \\
                 A Level Playing Field Becomes Benford / 38 \\
                 Multiplication by $1 / x$ / 42 \\
                 All Distributions Lead to Benford / 43 \\
                 Getting a Gripf on Benford and Zipf / 46 \\
                 Conclusions / 50 \\
                 Chapter 3: More Formulas and Facts, and a Little
                 Fibonacci / 51 \\
                 Fibonacci Numbers / 51 \\
                 Lucas Numbers / 53 \\
                 Back to Square One / 55 \\
                 $3 n + 1$ Problem / 58 \\
                 Ultimate Uniform Distribution / 60 \\
                 Benford Embraces Other Bases / 62 \\
                 Nigrini's Second Last Theorem / 65 \\
                 Conclusions / 69 \\
                 Chapter 4: Primary Benford's Law Tests / 71 \\
                 Corporate Payments Data / 72 \\
                 Data Profile / 72 \\
                 First Come, First Served / 74 \\
                 Playing Second Fiddle / 75 \\
                 First-Two Digits Test / 78 \\
                 Running the Digit Tests in Excel / 80 \\
                 Running the Digit Tests in Access / 83 \\
                 Conclusions / 87 \\
                 Chapter 5: Advanced Benford's Law Tests / 89 \\
                 Summation Test / 90 \\
                 Running the Summation Test in Excel / 94 \\
                 Running the Summation Test in Access / 95 \\
                 Second-Order Test / 97 \\
                 An Analysis of Payments Data / 102 \\
                 An Analysis of Journal Entry Data / 104 \\
                 An Analysis of Census Data / 107 \\
                 Running the Second-Order Test in Excel / 108 \\
                 Excel, Thanks a Million(s) / 110 \\
                 Scale Invariance and the Second-Order Test / 113 \\
                 Conclusions / 114 \\
                 Chapter 6: Associated Benford's Law Tests / 117 \\
                 Number Duplication Test / 117 \\
                 An Analysis of Payments Data / 119 \\
                 An Analysis of Census Data / 121 \\
                 Running the Number Duplication Test in Excel / 122 \\
                 Running the Number Duplication Test in Access / 126 \\
                 Last-Two Digits Test / 129 \\
                 An Analysis of Payments Data / 130 \\
                 An Analysis of Census Data / 131 \\
                 An Analysis of Election Results / 132 \\
                 Running the Last-Two Digits Test in Excel / 135 \\
                 Running the Last-Two Digits Test in Access / 136 \\
                 Distortion Factor Model / 138 \\
                 Distortion and the Census Data / 145 \\
                 Conclusions / 146 \\
                 Chapter 7: Assessing Conformity to Benford's Law / 149
                 \\
                 $Z$-Statistic / 150 \\
                 Chi-Square Test / 153 \\
                 Kolmogorov--Smirnoff Test / 157 \\
                 Mean Absolute Deviation Test / 158 \\
                 The Logarithmic Basis of Benford's Law / 160 \\
                 Creating a Perfect Synthetic Benford Set / 163 \\
                 Mantissa Arc Test / 165 \\
                 Conclusions / 169 \\
                 Chapter 8: Examples of Fraudulent Data / 171 \\
                 The Inside Story / 172 \\
                 The Vendor Who Never Was / 174 \\
                 Not Paying Attention / 175 \\
                 Funny Money / 177 \\
                 The Heart of the Matter / 181 \\
                 Going the Extra Mile / 182 \\
                 Laugh All the Way to the Bank / 184 \\
                 Culture Shock / 187 \\
                 Having a Bad Hair Day / 189 \\
                 An Unclean Bill of Health / 191 \\
                 Turning the Table on Tax Evasion / 193 \\
                 Conclusions / 196 \\
                 Chapter 9: Fraudulent Financial Statements, Part I /
                 199 \\
                 Number Crunching / 200 \\
                 Wrong Numbers / 205 \\
                 A Look at Enron's and AIG's Numbers / 207 \\
                 Figuring Out the Controllers / 210 \\
                 Conclusions / 213 \\
                 Chapter 10: Fraudulent Financial Statements, Part II /
                 215 \\
                 Digital Yoga by Absaroka / 216 \\
                 Can't See the Forest for the Trees / 218 \\
                 Digit a Little Deeper into Papua New Guinea / 221 \\
                 The Good, the Bad, and the Ugly / 227 \\
                 Dig a Little Deeper / 233 \\
                 There Are More Questions than Answers / 237 \\
                 Conclusions / 244 \\
                 Chapter 11: Madoff and Other Ponzi Schemes / 247 \\
                 The Madoff Claims / 248 \\
                 Don't Bank on Kaupthing / 249 \\
                 The Whole Ball of Waxenberg / 252 \\
                 General Motors Demoted to Private / 253 \\
                 Chrysler Unable to Dodge Bankruptcy / 255 \\
                 Discussion of the Claims Results / 258 \\
                 A Review of the Madoff Returns / 259 \\
                 Apple, Dell, Berkshire, and Benford / 262 \\
                 Discussion of the Returns Results / 265 \\
                 Chapter 12: Earth Science and Income Tax Applications /
                 267 \\
                 Still Waters Run Deep / 268 \\
                 The Lay of the Lake / 274 \\
                 For a Few Dollars Less / 281 \\
                 A Clean Bill of Clinton / 286 \\
                 Conclusions / 290 \\
                 Chapter 13: Future Directions and Conclusions / 293 \\
                 My Law / 295 \\
                 Insights into Number Invention / 300 \\
                 Lehman's Charitable Gifts / 306 \\
                 The Bottom Line / 310 \\
                 Glossary of Selected Terms / 315 \\
                 References / 323 \\
                 Index / 327",
}

@InCollection{Odueke:2012:TFA,
  author =       "Adeola Odueke and George R. S. Weir",
  editor =       "George R. S. Weir and A. Al-Nemrat",
  booktitle =    "Issues in Cybercrime, Security and Digtal Forensics",
  title =        "Triage in Forensic Accounting using {Zipf's Law}",
  publisher =    "University of Strathclyde Publishing",
  address =      "Glasgow, UK",
  bookpages =    "????",
  pages =        "33--43",
  year =         "2012",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Feb 19 06:11:19 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.cis.strath.ac.uk/cis/research/publications/papers/strath_cis_publication_2590.pdf",
  acknowledgement = ack-nhfb,
}

@Misc{Regan:2012:BLB,
  author =       "K. W. Regan",
  title =        "{Benford's Law} and Baseball",
  howpublished = "Web document",
  day =          "29",
  month =        jul,
  year =         "2012",
  bibdate =      "Sat Feb 16 12:48:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://rjlipton.wordpress.com/2012/07/29/benfords-law-and-baseball/",
  acknowledgement = ack-nhfb,
}

@Article{Ross:2012:FDS,
  author =       "Kenneth A. Ross",
  title =        "First Digits of Squares and Cubes",
  journal =      j-MATH-MAG,
  volume =       "85",
  number =       "1",
  pages =        "37--43",
  month =        feb,
  year =         "2012",
  CODEN =        "MAMGA8",
  ISSN =         "0025-570X",
  ISSN-L =       "0025-570X",
  bibdate =      "Tue Feb 19 06:14:55 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.maa.org/history/presidents/ross.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics Magazine",
  journal-URL =  "http://www.maa.org/pubs/mathmag.html",
  keywords =     "Benford's Law",
  remark =       "The author was President of the Mathematical
                 Association of America (1995--1996).",
}

@Article{Schupfer:2012:FWG,
  author =       "G. Sch{\"u}pfer and J. Hein and M. Casutt and L.
                 Steiner and C. Konrad",
  title =        "{Vom Finanz- zum Wissenschaftsbetrug: Methode, den
                 Irrungen in der medizinischen Literatur beizukommen}.
                 ({German}) [{From} financial to scientific fraud:
                 Method to overcome errors in the medical literature]",
  journal =      "Der Anaesthesist",
  volume =       "61",
  number =       "6",
  pages =        "537--542",
  month =        jun,
  year =         "2012",
  DOI =          "https://doi.org/10.1007/s00101-012-2028-y",
  ISSN =         "0003-2417 (print), 1432-055X (electronic)",
  ISSN-L =       "0003-2417",
  bibdate =      "Wed Jun 20 14:26:36 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://link.springer.com/journal/101",
  keywords =     "Benford's law; distribution; Medicine; scientific
                 fraud; statistics",
  language =     "German",
}

@Article{Shelburne:2012:ED,
  author =       "Brian Shelburne",
  title =        "The {ENIAC}'s 1949 Determination of $ \pi $",
  journal =      j-IEEE-ANN-HIST-COMPUT,
  volume =       "99",
  number =       "PrePrints",
  year =         "2012",
  CODEN =        "IAHCEX",
  DOI =          "https://doi.org/10.1109/MAHC.2011.61",
  ISSN =         "1058-6180 (print), 1934-1547 (electronic)",
  ISSN-L =       "1058-6180",
  bibdate =      "Fri Feb 3 15:38:23 2012",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  abstract =     "In January 1950, George W. Reitwiesner published ``An
                 ENIAC Determination of $ \pi $ and $e$ to more than
                 2000 Decimal Places'' in Mathematical Tables and Other
                 Aides to Computation \cite{Reitwiesner:1950:EDM} which
                 described the first use of a computer, the ENIAC, to
                 calculate the decimal expansion of $ \pi $. Since the
                 history of $ \pi $ stretches back over thousands of
                 years, the use of the ENIAC to determine $ \pi $ is an
                 important historical and technological milestone. It is
                 especially interesting since the ENIAC was not designed
                 to perform this type of calculation as it could only
                 store 200 decimal digits while the determination of e
                 and $ \pi $ required manipulating numbers 2000+ digits
                 long. Starting with Reitwiesner's description of the
                 calculation, the known architecture of the ENIAC, how
                 it was programmed, and the mathematics used, we examine
                 why the calculation was undertaken, how the calculation
                 had to be done, and what was subsequently learned.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE annals of the history of computing",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=85",
  pdfdate =      "8 August 2011",
  remark =       "This paper contains an interesting survey of work on
                 the calculation of $ \pi $ up to the early 1950s, with
                 a detailed reconstruction of its determination on the
                 ENIAC. From page 1 of the paper: ``Early in June, 1949,
                 Professor John von Neumann expressed an interest in the
                 possibility that the ENIAC might sometime be employed
                 to determine the value of $ \pi $ and $e$ to many
                 decimal places with a view toward obtaining a
                 statistical measure of the randomness of the
                 distribution of the digits.'' From page 2: ``\ldots{}
                 Augustus De Morgan (1806--1871) who noticed the smaller
                 number of appearances of the digit 7 in Shank's 607
                 digit determination of $ \pi $. It was later determined
                 that Shank's determination had an error beginning at
                 the 528th digit.'' From page 11: ``A preliminary
                 investigation has indicated that the digits of $e$
                 deviate significantly from randomness (in the sense of
                 staying closer to their expected values than a random
                 sequence of this length normally would) while for $ \pi
                 $ no significant deviations have so far been
                 detected.'' See \cite{Metropolis:1950:STV} for that
                 analysis.",
}

@Article{Song:2012:QEM,
  author =       "Jongwoo Song and Seongjoo Song",
  title =        "A quantile estimation for massive data with
                 generalized {Pareto} distribution",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "56",
  number =       "1",
  pages =        "143--150",
  day =          "1",
  month =        jan,
  year =         "2012",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:18 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947311002477",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@InCollection{Sorell:2012:ZLV,
  author =       "C. Joseph Sorell",
  editor =       "Carol A. Chapelle",
  booktitle =    "The Encyclopedia of Applied Linguistics",
  title =        "{Zipf's Law} and Vocabulary",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  year =         "2012",
  DOI =          "https://doi.org/10.1002/9781405198431.wbeal1302",
  ISBN =         "1-4051-9843-5",
  ISBN-13 =      "978-1-4051-9843-1",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1002/9781405198431",
  keywords =     "child language; computational linguistics; corpus;
                 pragmatics; second language acquisition; vocabulary",
}

@Article{Sottili:2012:BLT,
  author =       "Gianluca Sottili and Danilo M. Palladino and Biagio
                 Giaccio and Paolo Messina",
  title =        "{Benford's Law} in Time Series Analysis of Seismic
                 Clusters",
  journal =      j-MATH-GEOSCI,
  volume =       "44",
  number =       "5",
  pages =        "619--634",
  month =        jul,
  year =         "2012",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11004-012-9398-1",
  ISSN =         "1874-8953 (print), 1874-8961 (electronic)",
  ISSN-L =       "1874-8953",
  bibdate =      "Tue Feb 19 06:15:52 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11004-012-9398-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Geosciences",
  journal-URL =  "http://link.springer.com/journal/11004",
}

@MastersThesis{Stanton:2012:DFU,
  author =       "Gabriella Stanton",
  title =        "Detecting Fraud: Utilizing New Technology to Advance
                 the Audit Profession",
  type =         "Honors thesis",
  school =       "University of New Hampshire",
  address =      "Durham, NH 03824, USA",
  pages =        "26",
  month =        "Spring",
  year =         "2012",
  bibdate =      "Thu Oct 13 09:10:26 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://scholars.unh.edu/cgi/viewcontent.cgi?article=1017&context=honors",
  acknowledgement = ack-nhfb,
  advisor =      "Jake Rose",
  keywords =     "Benford's Law; Zipf's Law",
}

@Article{Strauch:2012:UP,
  author =       "O. Strauch",
  title =        "Unsolved Problems",
  journal =      "Uniform Distribution Theory",
  volume =       "??",
  number =       "??",
  publisher =    "Mathematical Institute of the Slovak Academy of
                 Sciences and BOKU --- University of Natural Resources
                 and Life Sciences",
  address =      "Bratislava, Slovakia and Vienna, Austria",
  pages =        "1--98",
  month =        "????",
  year =         "2012",
  DOI =          "????",
  ISSN =         "1336-913X",
  ISSN-L =       "1336-913X",
  bibdate =      "Tue Feb 19 06:17:17 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Unsolved Problems Section on the home page of
                 \booktitle{Uniform Distribution Theory}.",
  URL =          "http://www.boku.ac.at/MATH/udt/unsolvedproblems.pdf",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.boku.ac.at/MATH/udt/",
}

@InProceedings{Taimori:2012:PTS,
  author =       "A. Taimori and F. Razzazi and A. Behrad and A. Ahmadi
                 and M. Babaie-Zadeh",
  booktitle =    "2012 IEEE International Symposium on Signal Processing
                 and Information Technology (ISSPIT)",
  title =        "A proper transform for satisfying {Benford's Law} and
                 its application to double {JPEG} image forensics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "000240--000244",
  month =        dec,
  year =         "2012",
  DOI =          "https://doi.org/10.1109/ISSPIT.2012.6621294",
  ISSN =         "2162-7843",
  ISSN-L =       "2162-7843",
  bibdate =      "Sat Sep 10 11:40:17 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ieeexplore.ieee.org/document/6621294/",
  acknowledgement = ack-nhfb,
  keywords =     "2D discrete cosine transform; Benford law; Benford's
                 Law; data compression; discrete cosine transform;
                 discrete cosine transforms; Discrete wavelet
                 transforms; double JPEG; double JPEG image forensics;
                 filtering theory; image coding; image forensics; image
                 manipulation; Kullback-Leibler divergence; Lighting;
                 Matched filters; natural image data; normalized cross
                 correlation; Pearson chi-square test statistic;
                 significant digits statistics; single compressed
                 images; statistical analysis; statistical fitness
                 criteria; transform domain; variance filter; variance
                 filtering",
}

@Article{Tavangar:2012:SUC,
  author =       "Mahdi Tavangar and Majid Asadi",
  title =        "Some unified characterization results on the
                 generalized {Pareto} distributions based on generalized
                 order statistics",
  journal =      j-METRIKA,
  volume =       "75",
  number =       "7",
  pages =        "997--1007",
  month =        oct,
  year =         "2012",
  CODEN =        "MTRKA8",
  DOI =          "https://doi.org/10.1007/s00184-011-0364-6",
  ISSN =         "0026-1335 (print), 1435-926X (electronic)",
  ISSN-L =       "0026-1335",
  bibdate =      "Mon Feb 2 16:28:42 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/metrika.bib",
  URL =          "http://link.springer.com/article/10.1007/s00184-011-0364-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Metrika",
  journal-URL =  "http://link.springer.com/journal/184",
}

@Article{Valadier:2012:BPR,
  author =       "Michel Valadier",
  title =        "The {Benford} phenomenon for random variables.
                 {Discussion} of {Feller}'s way",
  journal =      "ArXiv e-prints",
  pages =        "23",
  day =          "9",
  month =        mar,
  year =         "2012",
  bibdate =      "Tue Feb 19 06:20:32 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1203.2518",
  acknowledgement = ack-nhfb,
}

@Article{Wang:2012:LPW,
  author =       "Dongbo Wang and Danhao Zhu and Xinning Su",
  title =        "{Lotka} phenomenon in the words' syntactic
                 distribution complexity",
  journal =      j-SCIENTOMETRICS,
  volume =       "90",
  number =       "2",
  pages =        "483--498",
  month =        feb,
  year =         "2012",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-011-0546-z",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:38 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-011-0546-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Book{Wapner:2012:UEC,
  author =       "Leonard M. Wapner",
  title =        "Unexpected expectations: the curiosities of a
                 mathematical crystal ball",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "xvi + 204",
  year =         "2012",
  ISBN =         "1-56881-721-5 (hardback)",
  ISBN-13 =      "978-1-56881-721-7 (hardback)",
  LCCN =         "QA95 .W34 2012",
  bibdate =      "Tue May 5 16:15:08 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathgaz2010.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "Mathematical expectation or expected value represents
                 the long-term average numerical outcome to an
                 experiment performed a large number of times. Routinely
                 used in the physical sciences, business, and economics,
                 mathematical expectation has also been used to
                 calculate strategies in games of chance and even to
                 justify the belief in God. How can this expression,
                 which is trivial to calculate, have such broad
                 applications and at the same time yield unexpected
                 irresolvable paradoxes? In an easily accessible
                 presentation, this book explores these puzzling and
                 entertaining mysteries.",
  acknowledgement = ack-nhfb,
  author-dates = "1948--",
  subject =      "Mathematical recreations",
  tableofcontents = "Dedication \\
                 Table of Contents \\
                 Acknowledgments \\
                 The Crystal Ball \\
                 1. Looking Back \\
                 2. The ABCs of E \\
                 3. Doing the Right Thing \\
                 4. Aversion Perversion \\
                 5. And the Envelope Please! \\
                 6. Parrondo's Paradox: You Can Win for Losing \\
                 7. Imperfect Recall \\
                 8. Non-zero-sum Games: The Inadequacy of Individual
                 Rationality \\
                 9. Newcomb's Paradox \\
                 10. Benford's Law \\
                 Let the Mystery Be! \\
                 Bibliography",
}

@Article{Zea:2012:BEP,
  author =       "Luz Milena Zea and Rodrigo B. Silva and Marcelo
                 Bourguignon and Andrea M. Santos and Gauss M.
                 Cordeiro",
  title =        "The Beta Exponentiated {Pareto} Distribution with
                 Application to Bladder Cancer Susceptibility",
  journal =      j-INT-J-STAT-PROBAB,
  volume =       "1",
  number =       "2",
  pages =        "8--??",
  month =        "????",
  year =         "2012",
  CODEN =        "????",
  ISSN =         "1927-7032 (print), 1927-7040 (electronic)",
  ISSN-L =       "1927-7032",
  bibdate =      "Tue Jun 9 14:40:16 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/intjstatprobab.bib",
  URL =          "http://www.ccsenet.org/journal/index.php/ijsp/article/view/16301",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Statistics and Probability",
  journal-URL =  "http://www.ccsenet.org/journal/index.php/ijsp/issue/archive",
}

@Article{Zeng:2012:TMB,
  author =       "Jianping Zeng and Jiangjiao Duan and Wenjun Cao and
                 Chengrong Wu",
  title =        "Topics modeling based on selective {Zipf}
                 distribution",
  journal =      j-EXPERT-SYST-APPL,
  volume =       "39",
  number =       "7",
  pages =        "6541--6546",
  day =          "1",
  month =        jun,
  year =         "2012",
  CODEN =        "ESAPEH",
  DOI =          "https://doi.org/10.1016/j.eswa.2011.12.051",
  ISSN =         "0957-4174 (print), 1873-6793 (electronic)",
  ISSN-L =       "0957-4174",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0957417411017222",
  acknowledgement = ack-nhfb,
  fjournal =     "Expert Systems with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09574174",
  keywords =     "Zipf's Law",
}

@Article{Abu-Dayyeh:2013:ESS,
  author =       "Walid Abu-Dayyeh and Aissa Assrhani and Kamarulzaman
                 Ibrahim",
  title =        "Estimation of the shape and scale parameters of
                 {Pareto} distribution using ranked set sampling",
  journal =      j-STAT-PAPERS,
  volume =       "54",
  number =       "1",
  pages =        "207--225",
  month =        feb,
  year =         "2013",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-011-0420-3",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:38 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-011-0420-3",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{Alali:2013:BLA,
  author =       "Fatima A. Alali and Silvia Romero",
  title =        "{Benford's Law}: Analyzing a Decade of Financial
                 Data",
  journal =      "Journal of Emerging Technologies in Accounting",
  volume =       "10",
  number =       "1",
  pages =        "1--39",
  month =        dec,
  year =         "2013",
  DOI =          "https://doi.org/10.2308/jeta-50749",
  ISSN =         "1554-1908 (print), 1558-7940 (electronic)",
  ISSN-L =       "1554-1908",
  bibdate =      "Thu Oct 13 08:07:00 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaajournals.org/doi/pdf/10.2308/jeta-50749",
  acknowledgement = ack-nhfb,
}

@Article{Andriotis:2013:JSD,
  author =       "Panagiotis Andriotis and George Oikonomou and Theo
                 Tryfonas",
  title =        "{JPEG} steganography detection with {Benford's Law}",
  journal =      "Digital Investigation",
  volume =       "9",
  number =       "3--4",
  pages =        "246--257",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/j.diin.2013.01.005",
  ISSN =         "1742-2876 (print), 1873-202X (electronic)",
  ISSN-L =       "1742-2876",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/datacompression.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1742287613000066",
  abstract =     "In this paper we present a novel approach to the
                 problem of steganography detection in {JPEG} images by
                 applying a statistical attack. The method is based on
                 the empirical Benford's Law and, more specifically, on
                 its generalized form. We prove and extend the validity
                 of the logarithmic rule in colour images and introduce
                 a blind steganographic method which can flag a file as
                 a suspicious stego-carrier. The proposed method
                 achieves very high accuracy and speed and is based on
                 the distributions of the first digits of the quantized
                 Discrete Cosine Transform coefficients present in
                 JPEGs. In order to validate and evaluate our algorithm,
                 we developed steganographic tools which are able to
                 analyse image files and we subsequently applied them on
                 the popular Uncompressed Colour Image Database.
                 Furthermore, we demonstrate that not only can our
                 method detect steganography but, if certain criteria
                 are met, it can also reveal which steganographic
                 algorithm was used to embed data in a {JPEG} file.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Data hiding; Generalized Benford's Law;
                 Quantized DCT coefficients; Quantized {DCT}
                 coefficients; Steganalysis; Steganography detection",
}

@Misc{Anonymous:2013:NBL,
  author =       "Anonymous",
  title =        "Number 1 and {Benford's Law} --- Numberphile",
  howpublished = "Web video lecture.",
  day =          "20",
  month =        jan,
  year =         "2013",
  bibdate =      "Fri Oct 09 06:28:24 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.youtube.com/watch?v=XXjlR2OK1kM",
  acknowledgement = ack-nhfb,
}

@Article{Aron:2013:CFM,
  author =       "Jacob Aron",
  title =        "Crime-fighting maths law confirms planetary riches",
  journal =      j-NEW-SCIENTIST,
  volume =       "220",
  number =       "2945",
  pages =        "12-",
  year =         "2013",
  CODEN =        "NWSCAL",
  DOI =          "https://doi.org/10.1016/S0262-4079(13)62775-X",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S026240791362775X",
  abstract =     "The statistical tool called Benford's law has been
                 shown to work for our catalogue of exoplanets, backing
                 up predictions that the galaxy is brimming with alien
                 worlds.",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law",
}

@Article{Banks:2013:BLM,
  author =       "David G. Banks",
  title =        "{Benford's Law} Made Easy: Common Software Eases use
                 of Fraud Search Theorem",
  journal =      "Fraud Magazine",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        jan # "\slash " # feb,
  year =         "2013",
  ISSN =         "1553-6645",
  ISSN-L =       "1553-6645",
  bibdate =      "Sun Feb 17 08:11:01 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.fraud-magazine.com/article.aspx?id=4294968485",
  acknowledgement = ack-nhfb,
  fjournal =     "Fraud Magazine. {A} Publication of the Association of
                 Certified Fraud Examiners",
}

@Article{Birajdar:2013:DIF,
  author =       "Gajanan K. Birajdar and Vijay H. Mankar",
  title =        "Digital image forgery detection using passive
                 techniques: A survey",
  journal =      "Digital Investigation",
  volume =       "10",
  number =       "3",
  pages =        "226--245",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/j.diin.2013.04.007",
  ISSN =         "1742-2876 (print), 1873-202X (electronic)",
  ISSN-L =       "1742-2876",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1742287613000364",
  abstract =     "Today manipulation of digital images has become easy
                 due to powerful computers, advanced photo-editing
                 software packages and high resolution capturing
                 devices. Verifying the integrity of images and
                 detecting traces of tampering without requiring extra
                 prior knowledge of the image content or any embedded
                 watermarks is an important research field. An attempt
                 is made to survey the recent developments in the field
                 of digital image forgery detection and complete
                 bibliography is presented on blind methods for forgery
                 detection. Blind or passive methods do not need any
                 explicit priori information about the image. First,
                 various image forgery detection techniques are
                 classified and then its generalized structure is
                 developed. An overview of passive image authentication
                 is presented and the existing blind forgery detection
                 techniques are reviewed. The present status of image
                 forgery detection technique is discussed along with a
                 recommendation for future research.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Image authentication; Image forensic;
                 Image manipulation detection; Image tampering
                 detection; Passive/blind image forgery detection",
}

@InCollection{Cali:2013:FA,
  author =       "J. Cali",
  editor =       "Jay A. Siegel and Pekka J. Saukko and Max M. Houck",
  booktitle =    "Encyclopedia of Forensic Sciences",
  title =        "Forensic Accounting",
  publisher =    "Academic Press",
  address =      "Waltham",
  pages =        "423--431",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/B978-0-12-382165-2.00218-X",
  ISBN =         "0-12-382166-5",
  ISBN-13 =      "978-0-12-382166-9",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B978012382165200218X",
  abstract =     "Forensic accounting is defined as the action of
                 identifying, recording, settling, extracting, sorting,
                 reporting, and verifying past financial data or other
                 accounting activities for settling current or
                 prospective legal disputes or using such past financial
                 data for projecting future financial data to settle
                 legal disputes. Forensic accountants practice a special
                 area of accountancy that requires them to have
                 knowledge of the courtroom, rules of evidence, and
                 investigative techniques in addition to generally
                 accepted accounting principles and generally accepted
                 auditing standards. The practice of forensic accounting
                 is used in criminal investigations to prosecute fraud,
                 embezzlement, ponzi, and terrorist-financing schemes.
                 While in civil litigation disputes, forensic accounting
                 methods are employed to determine the value of economic
                 damages related to insurance claims, lost profits,
                 bankruptcy, qui-tam actions, and divorce. The ultimate
                 role of the forensic accountant is to use their
                 forensic accounting skills to prepare a written report
                 and to provide expert testimony based on the findings
                 in the written report that will help the judge and the
                 members of the jury to better understand complex
                 financial transactions.",
  acknowledgement = ack-nhfb,
  keywords =     "Arson for profit; Bank Secrecy Act; Benford's Law;
                 Business interruption claims; Civil litigation
                 disputes; Currency transaction reports; Divorce;
                 Economic damages; Financial motive; FinCEN; Forensic
                 accounting; Forensic auditing; Fraud; Fraud
                 examination; Fraud investigation; Fraud schemes; Hidden
                 assets; Income from unknown sources; Income
                 reconstruction; Insurance fraud; Life care plans; Lost
                 profit computations; Money laundering; Mortgage fraud;
                 Offshore accounts; Patriot Act; Ponzi scheme; Qui-tam
                 actions; Securities fraud; Specified unlawful acts;
                 Suspicious activity reports",
}

@Article{Deligny:2013:RRL,
  author =       "Hugues Deligny and Paul Jolissaint",
  title =        "Relations de r{\'e}currence lin{\'e}aires,
                 primitivit{\'e} et loi de {Benford}. ({French})
                 [{Linear} recurrence relations, primitivity, and
                 {Benford}'s law]",
  journal =      j-ELEM-MATH,
  volume =       "68",
  number =       "1",
  pages =        "9--21",
  year =         "2013",
  DOI =          "https://doi.org/10.4171/EM/213",
  ISSN =         "0013-6018 (print), 1420-8962 (electronic)",
  ISSN-L =       "0013-6018",
  MRclass =      "11K36",
  MRnumber =     "3016461",
  MRreviewer =   "Simon Kristensen",
  bibdate =      "Thu Feb 14 07:02:03 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Elemente der Mathematik",
  language =     "French",
}

@Article{deVries:2013:CLN,
  author =       "Pepijn de Vries and Albertinka J. Murk",
  title =        "Compliance of {LC50} and {NOEC} data with {Benford's
                 Law}: An indication of reliability?",
  journal =      "Ecotoxicology and Environmental Safety",
  volume =       "98",
  number =       "0",
  pages =        "171--178",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/j.ecoenv.2013.09.002",
  ISSN =         "0147-6513 (print), 1090-2414 (electronic)",
  ISSN-L =       "0147-6513",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0147651313003692",
  abstract =     "Reliability of research data is essential, especially
                 when potentially far-reaching conclusions will be based
                 on them. This is also, amongst others, the case for
                 ecotoxicological data used in risk assessment.
                 Currently, several approaches are available to classify
                 the reliability of ecotoxicological data. The process
                 of classification, such as using the Klimisch score, is
                 time-consuming and focuses on the application of
                 standardised protocols and the documentation of the
                 study. The presence of irregularities and the integrity
                 of the performed work, however, are not addressed. The
                 present study shows that Benford's Law, based on the
                 occurrence of first digits following a logarithmic
                 scale, can be applied to ecotoxicity test data for
                 identifying irregularities. This approach is already
                 successfully applied in accounting. Benford's Law can
                 be used as reliability indicator, in addition to
                 existing reliability classifications. The law can be
                 used to efficiently trace irregularities in large data
                 sets of interpolated (no) effect concentrations such as
                 LC50s (possibly the result of data manipulation),
                 without having to evaluate the source of each
                 individual record. Application of the law to systems in
                 which large amounts of toxicity data are registered
                 (e.g., European Commission Regulation concerning the
                 Registration, Evaluation, Authorisation and Restriction
                 of Chemicals) can therefore be valuable.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Data evaluation; LC50; NOEC; Quality
                 assessment; Reliability; {LC50}; {NOEC}",
}

@Article{diGiovanni:2013:FET,
  author =       "Julian di Giovanni and Andrei A. Levchenko",
  title =        "Firm entry, trade, and welfare in {Zipf}'s world",
  journal =      j-J-INT-ECON,
  volume =       "89",
  number =       "2",
  pages =        "283--296",
  day =          "15",
  month =        mar,
  year =         "2013",
  CODEN =        "JIECBE",
  DOI =          "https://doi.org/10.1016/j.jinteco.2012.08.002",
  ISSN =         "0022-1996 (print), 1873-0353 (electronic)",
  ISSN-L =       "0022-1996",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022199612001365",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of International Economics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/09247963",
  keywords =     "Zipf's Law",
}

@Article{Egghe:2013:FRB,
  author =       "L. Egghe",
  title =        "The functional relation between the impact factor and
                 the uncitedness factor revisited",
  journal =      j-J-INFORMETRICS,
  volume =       "7",
  number =       "1",
  pages =        "183--189",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/j.joi.2012.10.007",
  ISSN =         "1751-1577 (print), 1875-5879 (electronic)",
  ISSN-L =       "1751-1577",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1751157712000909",
  abstract =     "We give a heuristic proof of the relation between the
                 impact factor (IF) and the uncitedness factor (U), the
                 fraction of the papers that are uncited: $ U = 1 / (1 +
                 I F) $. This generalizes the proof of Hsu and Huang
                 [Physica A 391, 2129 2134, 2012] who obtain the same
                 result but based on the assumption of the validity of
                 the Matthew-effect. This new informetric function opens
                 the discussion on universal informetric laws,
                 distribution dependent laws and parameter dependent
                 laws of which examples from the informetrics literature
                 are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informetrics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/17511577",
  keywords =     "Benford's Law; Distribution dependent law; Impact
                 factor; Parameter dependent law; Uncitedness factor;
                 Universal informetric law",
}

@Article{Eliazar:2013:BLP,
  author =       "Iddo I. Eliazar",
  title =        "{Benford's Law}: A {Poisson} perspective",
  journal =      j-PHYSICA-A,
  volume =       "392",
  number =       "16",
  pages =        "3360--3373",
  year =         "2013",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2013.03.057",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "62E10 (60G55 82C05)",
  MRnumber =     "3069159",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437113002902",
  abstract =     "Benford's Law is a counterintuitive statistical law
                 asserting that the distribution of leading digits,
                 taken from a large ensemble of positive numerical
                 values that range over many orders of scale, is
                 logarithmic rather than uniform (as intuition
                 suggests). In this paper we explore Benford's Law from
                 a Poisson perspective, considering ensembles of
                 positive numerical values governed by Poisson-process
                 statistics. We show that this Poisson setting naturally
                 accommodates Benford's Law and: (i) establish a Poisson
                 characterization and a Poisson multidigit-extension of
                 Benford's Law; (ii) study a system-invariant
                 leading-digit distribution which generalizes Benford's
                 Law, and establish a Poisson characterization and a
                 Poisson multidigit-extension of this distribution;
                 (iii) explore the universal emergence of the
                 system-invariant leading-digit distribution, couple
                 this universal emergence to the universal emergence of
                 the Weibull and Fr{\'e}chet extreme-value
                 distributions, and distinguish the special role of
                 Benford's Law in this universal emergence; (iv) study
                 the continued-fractions counterpart of the
                 system-invariant leading-digit distribution, and
                 establish a Poisson characterization of this
                 distribution; and (v) unveil the elemental connection
                 between the system-invariant leading-digit distribution
                 and its continued-fractions counterpart. This paper
                 presents a panoramic Poisson approach to Benford's Law,
                 to its system-invariant generalization, and to its
                 continued-fractions counterpart.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Continued fractions; Extreme-value
                 statistics; Invariance; Poisson limit theorems;
                 Power-laws; Universality",
}

@Article{Fernandez:2013:SPC,
  author =       "Arturo J. Fern{\'a}ndez",
  title =        "Smallest {Pareto} confidence regions and
                 applications",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "62",
  number =       "??",
  pages =        "11--25",
  month =        jun,
  year =         "2013",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:41 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947312004501",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@InCollection{Gangopadhyay:2013:EZL,
  author =       "Kausik Gangopadhyay and Banasri Basu",
  title =        "Evolution of {Zipf}'s law for {Indian} urban
                 agglomerations via-{\`a}-vis {Chinese} urban
                 agglomerations",
  crossref =     "Abergel:2013:ESR",
  pages =        "119--129",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-88-470-2553-0_8",
  MRclass =      "91B80",
  MRnumber =     "2963609",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "New Econ. Windows",
  acknowledgement = ack-nhfb,
}

@Article{GomesdaSilva:2013:SAS,
  author =       "Carlos {Gomes da Silva} and Pedro M. R. Carreira",
  title =        "Selecting Audit Samples Using {Benford's Law}",
  journal =      j-AUDITING,
  volume =       "32",
  number =       "2",
  pages =        "53--65",
  month =        may,
  year =         "2013",
  DOI =          "https://doi.org/10.2308/ajpt-50340",
  ISSN =         "0278-0380 (print), 1558-7991 (electronic)",
  ISSN-L =       "0278-0380",
  bibdate =      "Thu Oct 13 08:05:18 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://aaajournals.org/doi/pdf/10.2308/ajpt-50340",
  acknowledgement = ack-nhfb,
  fjournal =     "Auditing: A Journal of Practice \& Theory",
}

@TechReport{Grammatikos:2013:UBL,
  author =       "T. Grammatikos and N. I. Papanikolaou",
  title =        "Using {Benford's Law} to Detect Fraudulent Practices
                 in Banking",
  type =         "SSRN Scholarly Paper",
  number =       "2352775",
  institution =  "Social Science Research Network",
  address =      "Rochester, NY, USA",
  year =         "2013",
  bibdate =      "Sat Sep 10 11:54:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InProceedings{Haferkorn:2013:HVA,
  author =       "Martin Haferkorn",
  editor =       "Fethi Rabhi and Peter Gomber",
  booktitle =    "{Enterprise applications and services in the finance
                 industry: 6th International Workshop, FinanceCom 2012,
                 Barcelona, Spain, June 10, 2012. Revised papers}",
  title =        "Humans vs. Algorithms --- Who Follows
                 {Newcomb--Benford's Law} Better with Their Order
                 Volume?",
  chapter =      "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "61--70",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-3-642-36219-4_4",
  ISBN =         "3-642-36219-2",
  ISBN-13 =      "978-3-642-36219-4",
  LCCN =         "HG173 .I58 2012",
  bibdate =      "Wed Feb 13 19:15:28 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4_4",
  acknowledgement = ack-nhfb,
  book-URL =     "http://link.springer.com/content/pdf/10.1007/978-3-642-36219-4",
  remark =       "This may be the first publication to reference this
                 bibliography. It examines trading patterns of several
                 days on the German Stock Exchange (Deutsche B{\"o}rse),
                 with a total volume of almost 10 million trades, split
                 almost equally between human and algorithmic traders.
                 It finds that the algorithmic trades follow Benford's
                 Law closely, but the human trades do not. It points out
                 that algorithmic trading could be manipulated to make
                 it look more like human trades, so as not to alert
                 competitors to its actions.",
  subject =      "Financial services industry; Information technology;
                 Congresses; Data processing",
}

@Article{Hofmarcher:2013:FSD,
  author =       "P. Hofmarcher and K. Hornik",
  title =        "First Significant Digits and the Credit Derivative
                 Market During the Financial Crisis",
  journal =      "Contemporary Economics",
  volume =       "7",
  number =       "2",
  pages =        "21--29",
  month =        "????",
  year =         "2013",
  DOI =          "https://doi.org/10.5709/ce.1897-9254.80",
  bibdate =      "Sat Sep 10 12:11:42 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2286063",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Hubert:2013:DID,
  author =       "Mia Hubert and Goedele Dierckx and Dina Vanpaemel",
  title =        "Detecting influential data points for the {Hill}
                 estimator in {Pareto}-type distributions",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "65",
  number =       "??",
  pages =        "13--28",
  month =        sep,
  year =         "2013",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:43 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S016794731200285X",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Khosravani:2013:DBD,
  author =       "Azar Khosravani and Constantin Rasinariu",
  title =        "$n$-digit {Benford} distributed random variables",
  journal =      j-ADV-APPL-STAT,
  volume =       "36",
  number =       "2",
  pages =        "119--130",
  month =        oct,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "0972-3617",
  ISSN-L =       "0972-3617",
  MRclass =      "60E05 (11K45)",
  MRnumber =     "3134635",
  bibdate =      "Wed Aug 16 09:06:43 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advapplstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.pphmj.com/abstract/7887.htm",
  acknowledgement = ack-nhfb,
  fjournal =     "Advances and Applications in Statistics",
  journal-URL =  "http://www.pphmj.com/journals/contents/adas.htm",
}

@Article{Kossovsky:2013:RQO,
  author =       "A. Ely Kossovsky",
  title =        "On the Relative Quantities Occurring within Physical
                 Data Sets",
  journal =      "arxiv.org",
  month =        may,
  year =         "2013",
  bibdate =      "Thu Oct 13 07:31:45 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://adsabs.harvard.edu/abs/2013arXiv1305.1893E",
  acknowledgement = ack-nhfb,
  keywords =     "Mathematics - Statistics Theory",
  primaryclass = "math.ST",
}

@Article{Lu:2013:DZH,
  author =       "Linyuan L{\"u} and Zi-Ke Zhang and Tao Zhou",
  title =        "Deviation of {Zipf}'s and {Heaps' Laws} in Human
                 Languages with Limited Dictionary Sizes",
  journal =      j-SCI-REP,
  volume =       "3",
  number =       "??",
  pages =        "1--7",
  month =        "????",
  year =         "2013",
  CODEN =        "SRCEC3",
  DOI =          "https://doi.org/10.1038/srep01082",
  ISSN =         "2045-2322",
  bibdate =      "Tue Feb 26 07:39:15 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.nature.com/srep/2013/130130/srep01082/full/srep01082.html",
  accepted =     "21 December 2012",
  acknowledgement = ack-nhfb,
  articleno =    "1082",
  fjournal =     "Scientific Reports",
  journal-URL =  "http://www.nature.com/srep/",
  onlinedate =   "30 January 2013",
  received =     "11 June 2012",
}

@InProceedings{Mebane:2013:SDI,
  author =       "Walter R. {Mebane, Jr.} and T. Kent",
  editor =       "????",
  booktitle =    "{Proceedings of the 2013 Annual Meeting of the Midwest
                 Political Science Association, Chicago, IL, April
                 11--14, 2013}",
  title =        "Second Digit Implications of Voters' Strategies and
                 Mobilizations in the {United States} during the 2000s",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "2013",
  bibdate =      "Sat Sep 10 14:33:23 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Michalski:2013:DCF,
  author =       "T. Michalski and G. Stoltz",
  title =        "Do Countries Falsify Economic Data Strategically?
                 {Some} Evidence That They Might",
  journal =      j-REV-ECON-STAT,
  volume =       "95",
  number =       "2",
  pages =        "591--616",
  month =        may,
  year =         "2013",
  CODEN =        "RECSA9",
  DOI =          "https://doi.org/10.1162/REST_a_00274",
  ISSN =         "0034-6535 (print), 1530-9142 (electronic)",
  ISSN-L =       "0034-6535",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.mitpressjournals.org/doi/abs/10.1162/REST_a_00274",
  acknowledgement = ack-nhfb,
  fjournal =     "Review of Economics and Statistics",
  journal-URL =  "http://www.jstor.org/journal/revieconstat;
                 http://www.mitpressjournals.org/loi/rest",
  keywords =     "Benford's Law",
}

@InProceedings{Milani:2013:AAB,
  author =       "S. Milani and M. Tagliasacchi and S. Tubaro",
  booktitle =    "2013 IEEE International Conference on Acoustics,
                 Speech and Signal Processing",
  title =        "Antiforensics attacks to {Benford's Law} for the
                 detection of double compressed images",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "3053--3057",
  month =        may,
  year =         "2013",
  DOI =          "https://doi.org/10.1109/ICASSP.2013.6638219",
  ISSN =         "1520-6149",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "antiforensics attack strategy; Benford's law; data
                 compression; Detectors; digit statistics; digital
                 forensics; double image compression detectors; first
                 digit law; Forensics; fraud detection methods; image
                 coding; Image coding; Image reconstruction; object
                 detection; PSNR; Quantization (signal); statistical
                 analysis; Transform coding",
}

@Book{Newbold:2013:SBE,
  author =       "Paul Newbold and William L. (William Lee) Carlson and
                 Betty Thorne",
  title =        "Statistics for Business and Economics",
  publisher =    "Pearson Education",
  address =      "Harlow, Essex, UK",
  edition =      "Eighth",
  pages =        "792",
  year =         "2013",
  ISBN =         "0-273-76706-2",
  ISBN-13 =      "978-0-273-76706-0",
  LCCN =         "HF1017 .N48 2013",
  bibdate =      "Fri Mar 22 09:03:53 MDT 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-mjn # "\slash " # ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Commercial statistics; Economics; Statistical methods;
                 Statistics",
}

@Article{Norris:2013:NRA,
  author =       "Pippa Norris",
  title =        "The new research agenda studying electoral integrity",
  journal =      j-ELECT-STUDIES,
  volume =       "32",
  number =       "4",
  pages =        "563--575",
  year =         "2013",
  DOI =          "https://doi.org/10.1016/j.electstud.2013.07.015",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Special Symposium: The new research agenda on
                 electoral integrity",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379413001157",
  abstract =     "A rapidly-growing research agenda shared by scholars
                 and applied policy analysts is beginning to explore
                 three questions: when do elections meet standards of
                 electoral integrity? When do they fail to do so? And
                 what can be done to mitigate these problems? To address
                 these issues, Part 1 in this paper outlines the concept
                 of electoral integrity, proposing a comprehensive and
                 broad definition founded upon global norms and
                 international conventions. Part 2 argues that several
                 sub-fields contribute towards the study of electoral
                 integrity, although commonly fragmented at present,
                 including (i) public sector management; (ii) political
                 culture; (iii) comparative institutions; and (iv)
                 security studies. The emerging research agenda focused
                 on electoral integrity, cutting across these
                 conventional disciplinary boundaries, is characterized
                 by its problem-oriented focus and global comparative
                 framework, as well as by its use of pluralistic methods
                 and analytical techniques. Part 3 outlines the
                 contribution of papers in this symposium. The
                 conclusion summarizes the key features of this new
                 research agenda studying electoral integrity.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Benford's Law; Corruption; Democracy and
                 democratization; Elections; Electoral integrity; Fraud;
                 Voting",
}

@Article{Ozer:2013:BLD,
  author =       "G. Ozer and B. Babacan",
  title =        "{Benford's Law} and Digital Analysis: Application on
                 {Turkish} Banking Sector",
  journal =      "Business and Economics Research Journal",
  volume =       "4",
  number =       "1",
  pages =        "29--41",
  month =        "",
  year =         "2013",
  DOI =          "",
  ISSN =         "1309-2448",
  bibdate =      "Sat Sep 10 15:29:55 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.berjournal.com/",
  keywords =     "Benford's Law",
}

@Article{Pain:2013:RSA,
  author =       "Jean-Christophe Pain",
  title =        "Regularities and symmetries in atomic structure and
                 spectra",
  journal =      "High Energy Density Physics",
  volume =       "9",
  number =       "3",
  pages =        "392--401",
  month =        sep,
  year =         "2013",
  CODEN =        "HEDPBW",
  DOI =          "https://doi.org/10.1016/j.hedp.2013.04.007",
  ISSN =         "1574-1818 (print), 1878-0563 (electronic)",
  ISSN-L =       "1574-1818",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1574181813000475",
  abstract =     "The use of statistical methods for the description of
                 complex quantum systems was primarily motivated by the
                 failure of a line-by-line interpretation of atomic
                 spectra. Such methods reveal regularities and trends in
                 the distributions of levels and lines. In the past,
                 much attention was paid to the distribution of energy
                 levels (Wigner surmise, random-matrix model). However,
                 information about the distribution of the lines (energy
                 and strength) is lacking. Thirty years ago, Learner
                 found empirically an unexpected law: the logarithm of
                 the number of lines whose intensities lie between
                 $^{2k}I_0$ and $^{2k + 1}I_0$, $ I_0$ being a reference
                 intensity and $k$ an integer, is a decreasing linear
                 function of $k$. In the present work, the fractal
                 nature of such an intriguing regularity is outlined and
                 a calculation of its fractal dimension is proposed.
                 Other peculiarities are also presented, such as the
                 fact that the distribution of line strengths follows
                 Benford's law of anomalous numbers, the existence of
                 additional selection rules (PH coupling), the symmetry
                 with respect to a quarter of the subshell in the
                 spin-adapted space (LL coupling) and the odd even
                 staggering in the distribution of quantum numbers,
                 pointed out by Bauche and Coss{\'e}.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.sciencedirect.com/science/journal/15741818",
  keywords =     "Atomic physics; Benford's Law; Fractals; Group theory;
                 High-energy-density matter; Hot plasmas; Symmetries",
}

@Article{Phatarfod:2013:SAB,
  author =       "Ravi Phatarfod",
  title =        "Some aspects of the {Benford} law of leading
                 significant digits",
  journal =      "The Mathematical Scientist",
  volume =       "38",
  number =       "2",
  pages =        "73--85",
  year =         "2013",
  ISSN =         "0312-3685 (print), 1475-6080 (electronic)",
  ISSN-L =       "0312-3685",
  MRclass =      "62P99 (11A63)",
  MRnumber =     "3184679",
  bibdate =      "Tue Jan 26 11:01:15 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://appliedprobability.org/content.aspx?Group=tms&Page=tmsabstracts38_2#one",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Sci.",
  fjournal =     "The Mathematical Scientist",
  journal-URL =  "http://www.appliedprobability.org/content.aspx?Group=tms&Page=tms",
}

@Article{Piva:2013:OIF,
  author =       "Alessandro Piva",
  title =        "An Overview on Image Forensics",
  journal =      "ISRN Signal Processing",
  volume =       "2013",
  number =       "??",
  pages =        "496701",
  month =        "????",
  year =         "2013",
  DOI =          "https://doi.org/10.1155/2013/496701",
  ISSN =         "2090-5041 (print), 2090-505X (electronic)",
  ISSN-L =       "2090-5041",
  bibdate =      "Tue Feb 19 06:21:47 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.isrn.com/journals/sp/2013/496701/",
  accepted =     "26 November 2012",
  acknowledgement = ack-nhfb,
  fjournal =     "International Scholarly Research Network Signal
                 Processing",
  journal-URL =  "http://www.isrn.com/journals/sp/",
  keywords =     "Benford's Law",
  pagecount =    "22",
  received =     "6 November 2012",
}

@Article{Rauch:2013:LME,
  author =       "Bernhard Rauch and M. G{\"o}ttsche and Florian {El
                 Mouaaouy}",
  title =        "{LIBOR} Manipulation --- Empirical Analysis of
                 Financial Market Benchmarks Using {Benford's Law}",
  journal =      "Social Sciences Research Network",
  volume =       "??",
  number =       "??",
  pages =        "26",
  day =          "5",
  month =        dec,
  year =         "2013",
  DOI =          "https://doi.org/10.2139/ssrn.2363895",
  bibdate =      "Sat Sep 10 15:58:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2363895",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; collusion; financial institutions;
                 inter-bank offered rates; manipulation; price-fixing",
}

@Article{Scollnik:2013:CTP,
  author =       "David P. M. Scollnik",
  title =        "Comments on two papers concerning estimation of the
                 parameters of the {Pareto} distribution in the presence
                 of outliers",
  journal =      j-STAT-METHODOL,
  volume =       "13",
  number =       "??",
  pages =        "1--11",
  month =        jul,
  year =         "2013",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:55 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312712000822",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Article{Slepkov:2013:BLT,
  author =       "Aaron D. Slepkov and Kevin B. Ironside and David
                 DiBattista",
  title =        "{Benford's Law}: Textbook Exercises and
                 Multiple-Choice Testbanks",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??",
  day =          "19",
  month =        nov,
  year =         "2013",
  bibdate =      "Tue Jan 26 09:56:51 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1311.4787v1",
  abstract =     "Benford's Law describes the finding that the
                 distribution of leading (or leftmost) digits of
                 innumerable datasets follows a well-defined logarithmic
                 trend, rather than an intuitive uniformity. In practice
                 this means that the most common leading digit is 1,
                 with an expected frequency of 30.1\%, and the least
                 common is 9, with an expected frequency of 4.6\%. The
                 history and development of Benford's Law is inexorably
                 linked to physics, yet there has been a dearth of
                 physics-related Benford datasets reported in the
                 literature. Currently, the most common application of
                 Benford's Law is in detecting number invention and
                 tampering such as found in accounting-, tax-, and
                 voter-fraud. We demonstrate that answers to
                 end-of-chapter exercises in physics and chemistry
                 textbooks conform to Benford's Law. Subsequently, we
                 investigate whether this fact can be used to gain
                 advantage over random guessing in multiple-choice
                 tests, and find that while testbank answers in
                 introductory physics closely conform to Benford's Law,
                 the testbank is nonetheless secure against such a
                 Benford's attack for banal reasons.",
  acknowledgement = ack-nhfb,
}

@Article{Smith:2013:BNS,
  author =       "Aaron Carl Smith",
  title =        "{Benford--Newcomb} Subsequences for Fraud Detection",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??",
  day =          "22",
  month =        jan,
  year =         "2013",
  bibdate =      "Tue Jan 26 10:01:46 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1301.6086v1",
  abstract =     "Benford's law is frequently used to evaluate the
                 likihood that data is misrepresentative. Typically
                 statistical tests measure the likihood. Another method
                 of employing Benford's law is to compare the frequency
                 of leading digits to the probabilities of leading
                 digits over a subset of the natural numbers. This paper
                 proposes using the probabilities of leading digits from
                 uniform, natural numbers to establish interval criteria
                 for when to look more closely into the possibility of
                 misrepresentative data.",
  acknowledgement = ack-nhfb,
}

@Article{Soo:2013:ZGG,
  author =       "Kwok Tong Soo",
  title =        "{Zipf}, {Gibrat} and geography: Evidence from {China},
                 {India} and {Brazil}",
  journal =      j-PAP-REG-SCI,
  pages =        "??--??",
  year =         "2013",
  DOI =          "https://doi.org/10.1111/j.1435-5957.2012.00477.x",
  ISSN =         "1056-8190 (print), 1435-5957 (electronic)",
  ISSN-L =       "1056-8190",
  bibdate =      "Mon Feb 25 06:13:56 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Papers in Regional Science",
  keywords =     "dynamic panel data models; Gibrat's Law; state
                 populations; Zipf's Law",
  xxnote =       "Online, but not yet in print with assigned page
                 numbers, on 25 February 2013.",
}

@Article{Srivastava:2013:FD,
  author =       "Tanya Kaushal Srivastava",
  title =        "The First Digit $1$",
  journal =      j-RESONANCE,
  volume =       "18",
  number =       "12",
  pages =        "1073--1085",
  month =        dec,
  year =         "2013",
  CODEN =        "RESOFE",
  DOI =          "https://doi.org/10.1007/s12045-013-0135-y",
  ISSN =         "0971-8044 (print), 0973-712X (electronic)",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s12045-013-0135-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Resonance",
  journal-URL =  "http://link.springer.com/journal/12045",
  keywords =     "Benford's Law",
}

@Article{Tavangar:2013:CGP,
  author =       "Mahdi Tavangar and Marzieh Hashemi",
  title =        "On characterizations of the generalized {Pareto}
                 distributions based on progressively censored order
                 statistics",
  journal =      j-STAT-PAPERS,
  volume =       "54",
  number =       "2",
  pages =        "381--390",
  month =        may,
  year =         "2013",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-012-0434-5",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Sun Feb 1 10:12:38 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-012-0434-5",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{vanZyl:2013:GPD,
  author =       "J. Martin van Zyl",
  title =        "The generalized {Pareto} distribution fitted to
                 research outputs of countries",
  journal =      j-SCIENTOMETRICS,
  volume =       "94",
  number =       "3",
  pages =        "1099--1109",
  month =        mar,
  year =         "2013",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-012-0798-2",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:49 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-012-0798-2",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Wainer:2013:VRS,
  author =       "Howard Wainer and Polina Harik and John Neter",
  title =        "Visual Revelations: {Stigler}'s {Law of Eponymy} and
                 {Marey}'s Train Schedule: Did {Serjev} Do It Before
                 {Ibry}, and What About {Jules Petiet}?",
  journal =      j-CHANCE,
  volume =       "26",
  number =       "1",
  pages =        "53--56",
  year =         "2013",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.2013.772394",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Tue Feb 3 09:42:07 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/chance.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
}

@Article{Wjcik:2013:HFI,
  author =       "Micha{\l} Ryszard W{\'o}jcik",
  title =        "How fast increasing powers of a continuous random
                 variable converge to {Benford's Law}",
  journal =      j-STAT-PROB-LETT,
  volume =       "83",
  number =       "12",
  pages =        "2688--2692",
  year =         "2013",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2013.09.003",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715213002927",
  abstract =     "It is known that increasing powers of a continuous
                 random variable converge in distribution to Benford's
                 Law as the exponent approaches infinity. The rate of
                 convergence has been estimated using Fourier analysis,
                 but we present an elementary method, which is easier to
                 apply and provides a better estimation in the widely
                 studied case of a uniformly distributed random
                 variable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Fourier coefficients; Mantissa
                 distribution; Significand distribution; Uniform
                 distribution modulo 1",
}

@Article{Wojcik:2013:HFI,
  author =       "Michal Ryszard W{\'o}jcik",
  title =        "How fast increasing powers of a continuous random
                 variable converge to {Benford's Law}",
  journal =      j-STAT-PROB-LETT,
  volume =       "83",
  number =       "12",
  pages =        "2688--2692",
  month =        dec,
  year =         "2013",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2013.09.003",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60F15 (60E05)",
  MRnumber =     "3118213",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715213002927",
  abstract =     "It is known that increasing powers of a continuous
                 random variable converge in distribution to {Benford's
                 Law} as the exponent approaches infinity. The rate of
                 convergence has been estimated using Fourier analysis,
                 but we present an elementary method, which is easier to
                 apply and provides a better estimation in the widely
                 studied case of a uniformly distributed random
                 variable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
  keywords =     "Benford's Law; Fourier coefficients; Mantissa
                 distribution; Significand distribution; Uniform
                 distribution modulo 1",
}

@Article{Yan:2013:CNE,
  author =       "Su Yan and W. Scott Spangler and Ying Chen",
  title =        "Chemical Name Extraction Based on Automatic Training
                 Data Generation and Rich Feature Set",
  journal =      j-TCBB,
  volume =       "10",
  number =       "5",
  pages =        "1218--1233",
  month =        sep,
  year =         "2013",
  CODEN =        "ITCBCY",
  DOI =          "https://doi.org/10.1109/TCBB.2013.101",
  ISSN =         "1545-5963 (print), 1557-9964 (electronic)",
  ISSN-L =       "1545-5963",
  bibdate =      "Thu Jan 9 15:34:03 MST 2014",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tcbb.bib",
  abstract =     "The automation of extracting chemical names from text
                 has significant value to biomedical and life science
                 research. A major barrier in this task is the
                 difficulty of getting a sizable and good quality data
                 to train a reliable entity extraction model. Another
                 difficulty is the selection of informative features of
                 chemical names, since comprehensive domain knowledge on
                 chemistry nomenclature is required. Leveraging random
                 text generation techniques, we explore the idea of
                 automatically creating training sets for the task of
                 chemical name extraction. Assuming the availability of
                 an incomplete list of chemical names, called a
                 dictionary, we are able to generate well-controlled,
                 random, yet realistic chemical-like training documents.
                 We statistically analyze the construction of chemical
                 names based on the incomplete dictionary, and propose a
                 series of new features, without relying on any domain
                 knowledge. Compared to state-of-the-art models learned
                 from manually labeled data and domain knowledge, our
                 solution shows better or comparable results in
                 annotating real-world data with less human effort.
                 Moreover, we report an interesting observation about
                 the language for chemical names. That is, both the
                 structural and semantic components of chemical names
                 follow a Zipfian distribution, which resembles many
                 natural languages.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE/ACM Transactions on Computational Biology and
                 Bioinformatics",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J954",
}

@Article{Young:2013:ATL,
  author =       "D. S. Young",
  title =        "Approximate tolerance limits for {Zipf--Mandelbrot}
                 distributions",
  journal =      j-PHYSICA-A,
  volume =       "392",
  number =       "7",
  pages =        "1702--1711",
  day =          "1",
  month =        apr,
  year =         "2013",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2012.11.056",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Feb 27 07:32:55 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437112010497",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Zipf's Law",
}

@Article{Alexopoulos:2014:BLA,
  author =       "Theodoros Alexopoulos and Stefanos Leontsinis",
  title =        "{Benford}'s Law in Astronomy",
  journal =      j-J-ASTROPHYS-ASTRON,
  volume =       "35",
  number =       "4",
  pages =        "639--648",
  year =         "2014",
  CODEN =        "JASRD7",
  DOI =          "https://doi.org/10.1007/s12036-014-9303-z",
  ISSN =         "0250-6335 (print), 0973-7758 (electronic)",
  ISSN-L =       "0250-6335",
  bibdate =      "Wed Aug 12 10:02:04 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See follow-up \cite{Hill:2016:HLI}.",
  URL =          "http://link.springer.com/article/10.1007/s12036-014-9303-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Astrophysics and Astronomy",
  journal-URL =  "http://www.springerlink.com/content/0250-6335",
  keywords =     "Benford's law; galaxies; significant digit.; stars;
                 Universe",
}

@Article{Alexopoulos:2014:BLU,
  author =       "Theodoros Alexopoulos and Stefanos Leontsinis",
  title =        "{Benford's Law} and the {Universe}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "6",
  day =          "23",
  month =        jan,
  year =         "2014",
  bibdate =      "Tue Jan 26 10:06:48 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1401.5794v2",
  abstract =     "Benford's law predicts the occurrence of the nth digit
                 of numbers in datasets originating from various sources
                 of the world, ranging from financial data to atomic
                 spectra. It is intriguing that although many features
                 of Benford's law have been proven and analysed, it is
                 still not fully mathematically understood. In this
                 paper we investigate the distances of galaxies and
                 stars by comparing the first, second and third
                 significant digit probabilities with Benford's
                 predictions. It is found that the distances of galaxies
                 follow reasonably well the first digit law and the star
                 distances agree very well with the first, second and
                 third significant digit.",
  acknowledgement = ack-nhfb,
}

@Article{Alves:2014:BLA,
  author =       "Alexandre Donizeti Alves and Horacio Hideki Yanasse
                 and Nei Yoshihiro Soma",
  title =        "{Benford's Law} and articles of scientific journals:
                 comparison of {JCR\reg} and {Scopus} data",
  journal =      j-SCIENTOMETRICS,
  volume =       "98",
  number =       "1",
  pages =        "173--184",
  month =        jan,
  year =         "2014",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-013-1030-8",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:05:57 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s11192-013-1030-8.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
  keywords =     "Articles; Benford's Law; JCR; Scopus",
}

@Article{Aron:2014:LLN,
  author =       "Jacob Aron",
  title =        "Looking for life in numbers",
  journal =      j-NEW-SCIENTIST,
  volume =       "222",
  number =       "2968",
  pages =        "46--47",
  year =         "2014",
  CODEN =        "NWSCAL",
  DOI =          "https://doi.org/10.1016/S0262-4079(14)60925-8",
  ISSN =         "0262-4079 (print), 1364-8500 (electronic)",
  ISSN-L =       "0262-4079",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0262407914609258",
  acknowledgement = ack-nhfb,
  fjournal =     "New Scientist",
  journal-URL =  "http://www.sciencedirect.com/science/journal/02624079",
  keywords =     "Benford's Law",
}

@Article{Arshadi:2014:BLB,
  author =       "Laleh Arshadi and Amir Hossein Jahangir",
  title =        "{Benford's Law} behavior of {Internet} traffic",
  journal =      j-J-NETW-COMPUT-APPL,
  volume =       "40",
  number =       "0",
  pages =        "194--205",
  year =         "2014",
  CODEN =        "JNCAF3",
  DOI =          "https://doi.org/10.1016/j.jnca.2013.09.007",
  ISSN =         "1084-8045 (print), 1095-8592 (electronic)",
  ISSN-L =       "1084-8045",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1084804513001951",
  abstract =     "In this paper, we analyze the Internet traffic from a
                 different point of view based on Benford's law, an
                 empirical law that describes the distribution of
                 leading digits in a collection of numbers met in
                 naturally occurring phenomena. We claim that Benford's
                 law holds for the inter-arrival times of TCP flows in
                 case of normal traffic. Consequently, any type of
                 anomalies affecting TCP flows, including intentional
                 intrusions or unintended faults and network failures in
                 general, can be detected by investigating the
                 first-digit distributions of the inter-arrival times of
                 TCP SYN packets. In this paper we apply our findings to
                 the detection of intentional attacks, and leave other
                 types of anomalies for future works. We support our
                 claim with related researches that indicate the TCP
                 flow inter-arrival times can be modeled by Weibull
                 distribution with shape parameter less than 1, and show
                 the relation between Weibull distributed data and
                 Benford's law. Finally, we validate our findings on
                 real traffic and achieve encouraging results.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. netw. comput. appl.",
  fjournal =     "Journal of Network and Computer Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10848045",
  keywords =     "Anomaly detection; Benford's law; Benford's Law;
                 Benford's law; Benford's Law; Computer network traffic
                 analysis; Weibull distribution",
}

@Article{Ausloos:2014:BBL,
  author =       "M. Ausloos and C. Herteliu and B. Ileanu",
  title =        "Breakdown of {Benford's Law} for birth data",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "17",
  day =          "6",
  month =        oct,
  year =         "2014",
  bibdate =      "Tue Jan 26 09:59:08 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1410.1755v1",
  abstract =     "Long birth time series for Romania are investigated
                 from Benford's law point of view, distinguishing
                 between families with a religious (Orthodox and
                 Non-Orthodox) affiliation. The data extend from Jan.
                 01, 1905 till Dec. 31, 2001, i.e. over 97 years or
                 35\,429 days. The results point to a drastic breakdown
                 of Benford's law. Some interpretation is proposed,
                 based on the statistical aspects due to population
                 sizes, rather than on human thought constraints when
                 the law breakdown is usually expected. Benford's law
                 breakdown clearly points to natural causes.",
  acknowledgement = ack-nhfb,
}

@Article{Ausloos:2014:ZMP,
  author =       "Marcel Ausloos",
  title =        "{Zipf--Mandelbrot--Pareto} model for co-authorship
                 popularity",
  journal =      j-SCIENTOMETRICS,
  volume =       "101",
  number =       "3",
  pages =        "1565--1586",
  month =        dec,
  year =         "2014",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-014-1302-y",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:06:06 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-014-1302-y",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Beckett:2014:TPA,
  author =       "Phil Beckett",
  title =        "Taking a preventative approach towards the {Bribery
                 Act}",
  journal =      "Computer Fraud \& Security",
  volume =       "2014",
  number =       "6",
  pages =        "16--18",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/S1361-3723(14)70502-0",
  ISSN =         "1361-3723 (print), 1873-7056 (electronic)",
  ISSN-L =       "1361-3723",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1361372314705020",
  abstract =     "The UK's Serious Fraud Office (SFO) recently tried to
                 reinvigorate activity around the Bribery Act.1 It
                 warned companies and banks that if they fail to prevent
                 financial crime by their staff, they could face great
                 fines and official blacklisting from European
                 contracts. This proposed amendment put forward by the
                 {SFO} would give the {UK} powers to take direct action
                 against corporates, enabling it to levy US-style fines
                 and brand them with assisted bribery. And so
                 organisations need to ensure that awareness of and
                 compliance with the Bribery Act is part of their risk
                 analysis and mitigation activities and they should
                 start by looking at their data.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@InCollection{Berger:2014:BSL,
  author =       "Arno Berger and Gideon Eshun",
  editor =       "Ziyad AlSharawi and Jim M. Cushing and Saber Elaydi",
  booktitle =    "{Theory and Applications of Difference Equations and
                 Discrete Dynamical Systems: ICDEA, Muscat, Oman, May
                 26--30, 2013}",
  title =        "{Benford} Solutions of Linear Difference Equations",
  volume =       "102",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  bookpages =    "xvi + 222",
  pages =        "23--60",
  year =         "2014",
  DOI =          "https://doi.org/10.1007/978-3-662-44140-4_2",
  ISBN =         "3-662-44139-X, 3-662-44140-3 (e-book)",
  ISBN-13 =      "978-3-662-44139-8, 978-3-662-44140-4 (e-book)",
  LCCN =         "QA218 .T446 2014",
  MRclass =      "60-02 (11A63 11K06 60C05 60F05)",
  MRnumber =     "3280199",
  bibdate =      "Wed Aug 12 09:51:04 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Springer Proceedings in Mathematics \& Statistics",
  acknowledgement = ack-nhfb,
}

@Article{Berger:2014:CBL,
  author =       "Arno Berger and Gideon Eshun",
  title =        "A Characterization of {Benford's Law} in Discrete-Time
                 Linear Systems",
  journal =      j-J-DYN-DIFFER-EQU,
  volume =       "??",
  number =       "??",
  pages =        "1--39",
  month =        "????",
  year =         "2014",
  CODEN =        "JDDEEH",
  DOI =          "https://doi.org/10.1007/s10884-014-9393-y",
  ISSN =         "1040-7294 (print), 1572-9222 (electronic)",
  ISSN-L =       "1040-7294",
  MRclass =      "37A05, 37A45, 11J71, 62E20",
  bibdate =      "Wed Aug 12 10:09:25 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of dynamics and differential equations",
  keywords =     "$$\mathbb {Q}$$ Q -independence; 11J71; 37A05; 37A45;
                 62E20; Benford's sequence; Nonresonant set; Uniform
                 distribution mod 1",
}

@Article{Best:2014:BBZ,
  author =       "Andrew Best and Patrick Dynes and Xixi Edelsbrunner
                 and Brian McDonald and Steven J. Miller and Kimsy Tor
                 and Caroline Turnage-Butterbaugh and Madeleine
                 Weinstein",
  title =        "{Benford} Behavior of {Zeckendorf} Decompositions",
  journal =      j-FIB-QUART,
  volume =       "52",
  number =       "5",
  pages =        "35--??",
  month =        dec,
  year =         "2014",
  CODEN =        "FIBQAU",
  ISSN =         "0015-0517",
  ISSN-L =       "0015-0517",
  MRclass =      "11B39 (11B05)",
  MRnumber =     "3479486",
  MRreviewer =   "Martin Johann Stein",
  bibdate =      "Mon Nov 25 10:05:44 MST 2019",
  bibsource =    "http://www.fq.math.ca/52-5.html;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "http://www.fq.math.ca/Papers1/52-5/Best-Benford.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Fib. Quart",
  fjournal =     "The Fibonacci Quarterly. Official Organ of the
                 Fibonacci Association",
  journal-URL =  "http://www.fq.math.ca/",
}

@Article{Bhole:2014:BDN,
  author =       "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh",
  title =        "{Benford} distributions in {NMR}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "6",
  day =          "27",
  month =        jun,
  year =         "2014",
  bibdate =      "Tue Jan 26 10:03:00 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1406.7077v1",
  abstract =     "Benford's Law is an empirical law which predicts the
                 frequency of significant digits in databases
                 corresponding to various phenomena, natural or
                 artificial. Although counter intuitive at the first
                 sight, it predicts a higher occurrence of digit $1$,
                 and decreasing occurrences to other larger digits. Here
                 we report the Benford analysis of various NMR databases
                 and draw several interesting inferences. We observe
                 that, in general, NMR signals follow Benford
                 distribution in time-domain as well as in frequency
                 domain. Our survey included NMR signals of various
                 nuclear species in a wide variety of molecules in
                 different phases, namely liquid, liquid-crystalline,
                 and solid. We also studied the dependence of Benford
                 distribution on NMR parameters such as signal to noise
                 ratio, number of scans, pulse angles, and apodization.
                 In this process we also find that, under certain
                 circumstances, the Benford analysis can distinguish a
                 genuine spectrum from a visually identical simulated
                 spectrum. Further we find that chemical-shift databases
                 and amplitudes of certain radio frequency pulses
                 generated using optimal control techniques also satisfy
                 Benford's law to a good extent.",
  acknowledgement = ack-nhfb,
}

@Article{Cournane:2014:NAB,
  author =       "S. Cournane and N. Sheehy and J. Cooke",
  title =        "The novel application of {Benford}'s second order
                 analysis for monitoring radiation output in
                 interventional radiology",
  journal =      "Physica Medica",
  volume =       "30",
  number =       "4",
  pages =        "413--418",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.ejmp.2013.11.004",
  ISSN =         "1120-1797 (print), 1724-191X (electronic)",
  ISSN-L =       "1120-1797",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1120179713004328",
  abstract =     "Benford's law is an empirical observation which
                 predicts the expected frequency of digits in naturally
                 occurring datasets spanning multiple orders of
                 magnitude, with the law having been most successfully
                 applied as an audit tool in accountancy. This study
                 investigated the sensitivity of the technique in
                 identifying system output changes using simulated
                 changes in interventional radiology Dose-Area-Product
                 (DAP) data, with any deviations from Benford's
                 distribution identified using z-statistics. The
                 radiation output for interventional radiology X-ray
                 equipment is monitored annually during quality control
                 testing; however, for a considerable portion of the
                 year an increased output of the system, potentially
                 caused by engineering adjustments or spontaneous system
                 faults may go unnoticed, leading to a potential
                 increase in the radiation dose to patients. In normal
                 operation recorded examination radiation outputs vary
                 over multiple orders of magnitude rendering the
                 application of normal statistics ineffective for
                 detecting systematic changes in the output. In this
                 work, the annual DAP datasets complied with Benford's
                 first order law for first, second and combinations of
                 the first and second digits. Further, a continuous
                 rolling second order technique was devised for trending
                 simulated changes over shorter timescales. This
                 distribution analysis, the first employment of the
                 method for radiation output trending, detected
                 significant changes simulated on the original data,
                 proving the technique useful in this case. The
                 potential is demonstrated for implementation of this
                 novel analysis for monitoring and identifying change in
                 suitable datasets for the purpose of system process
                 control.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Interventional radiology; Radiation
                 dose",
}

@Article{Dunstan:2014:GSD,
  author =       "D. J. Dunstan and A. J. Bushby",
  title =        "Grain size dependence of the strength of metals: The
                 {Hall--Petch} effect does not scale as the inverse
                 square root of grain size",
  journal =      j-INT-J-PLAST,
  volume =       "53",
  number =       "0",
  pages =        "56--65",
  year =         "2014",
  CODEN =        "IJPLER",
  DOI =          "https://doi.org/10.1016/j.ijplas.2013.07.004",
  ISSN =         "0749-6419 (print), 1879-2154 (electronic)",
  ISSN-L =       "0749-6419",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S074964191300140X",
  abstract =     "The classic data in the literature for the grain size
                 dependence of the strength in many metals are reviewed.
                 The exponent $x$ relating strength to grain size $
                 d^{-x}$ is not often the eponymous inverse square-root
                 relationship (known as the Hall--Petch effect), but is
                 widely scattered from values as low as $ x = 0.2$ to
                 values as high as $ x = 1$. These exponents for
                 individual datasets are shown to be largely
                 meaningless. For an ensemble of n selected datasets,
                 the fit to the functional form $ \ln [d] / d + {\rm
                 const}$ with $ n + 1$ free fitting parameters is found
                 to be almost as good as the fit to $ 1 / \sqrt [d] +
                 {\rm const}$ with $ 2 n$ fitting parameters (the
                 Hall--Petch fit). The probability that the former is
                 the preferable fit is high. Some data sets do not agree
                 with the $ \ln [d] / d$ fit, but their deviation is
                 readily explained on simple physical grounds. Moreover,
                 even when they are included in the fit, statistical
                 tests still show that the $ \ln [d] / d$ form is
                 preferable by a wide margin. The conclusion is that the
                 Hall--Petch effect is not another size effect sui
                 generis but is the same size effect as that observed in
                 epitaxial thin film growth and in micromechanical
                 testing of small specimens. Consequently we propose
                 that grain size strengthening of metals is driven by
                 constraints on stress and dislocation curvature
                 according to the space available.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Plasticity",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07496419",
  keywords =     "Benford's Law; Dislocations; Grain boundaries;
                 Metallic material; Polycrystalline material; Yield
                 condition",
}

@TechReport{Edelsbrunner:2014:BLC,
  author =       "X. Edelsbrunner and K. Huan and B. Mackall and S. J.
                 Miller and J. Powell and C. Turnage-Butterbaugh and M.
                 Weinstein",
  title =        "{Benford's Law}, the {Cauchy} Distribution and
                 Financial Data",
  type =         "Report",
  institution =  "????",
  address =      "????",
  year =         "2014",
  bibdate =      "Sat Sep 10 11:09:53 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InProceedings{Ferariu:2014:PGP,
  author =       "L. Ferariu and C. Cimpanu",
  booktitle =    "{2014 18th International Conference System Theory,
                 Control and Computing (ICSTCC)}",
  title =        "{Pareto} genetic path planning hybridized with
                 multi-objective {Dijkstra}'s algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "341--346",
  year =         "2014",
  DOI =          "https://doi.org/10.1109/ICSTCC.2014.6982439",
  bibdate =      "Wed Mar 18 11:11:53 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dijkstra-edsger-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6982439",
  acknowledgement = ack-nhfb,
}

@Article{Gonzalez-Alvarez:2014:POH,
  author =       "David L. Gonz{\'a}lez-{\'A}lvarez and Miguel A.
                 Vega-Rodr{\'\i}guez and {\'A}lvaro Rubio-Largo",
  title =        "Parallelizing and optimizing a hybrid differential
                 evolution with {Pareto} tournaments for discovering
                 motifs in {DNA} sequences",
  journal =      j-J-SUPERCOMPUTING,
  volume =       "70",
  number =       "2",
  pages =        "880--905",
  month =        nov,
  year =         "2014",
  CODEN =        "JOSUED",
  DOI =          "https://doi.org/10.1007/s11227-014-1266-y",
  ISSN =         "0920-8542 (print), 1573-0484 (electronic)",
  ISSN-L =       "0920-8542",
  bibdate =      "Fri Feb 13 12:13:17 MST 2015",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0920-8542&volume=70&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jsuper.bib",
  URL =          "http://link.springer.com/article/10.1007/s11227-014-1266-y",
  acknowledgement = ack-nhfb,
  fjournal =     "The Journal of Supercomputing",
  journal-URL =  "http://link.springer.com/journal/11227",
}

@Article{Gray:2014:TGR,
  author =       "Glen L. Gray and Roger S. Debreceny",
  title =        "A taxonomy to guide research on the application of
                 data mining to fraud detection in financial statement
                 audits",
  journal =      j-INT-J-ACCOUNT-INFO-SYS,
  volume =       "15",
  number =       "4",
  pages =        "357--380",
  year =         "2014",
  CODEN =        "IJAIA7",
  DOI =          "https://doi.org/10.1016/j.accinf.2014.05.006",
  ISSN =         "1467-0895 (print), 1873-4723 (electronic)",
  ISSN-L =       "1467-0895",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "2013 Research Symposium on Information Integrity \&
                 Information Systems Assurance",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1467089514000323",
  abstract =     "This paper explores the application of data mining
                 techniques to fraud detection in the audit of financial
                 statements and proposes a taxonomy to support and guide
                 future research. Currently, the application of data
                 mining to auditing is at an early stage of development
                 and researchers take a scatter-shot approach,
                 investigating patterns in financial statement
                 disclosures, text in annual reports and MD\&As, and the
                 nature of journal entries without appropriate guidance
                 being drawn from lessons in known fraud patterns. To
                 develop structure to research in data mining, we create
                 a taxonomy that combines research on patterns of
                 observed fraud schemes with an appreciation of areas
                 that benefit from productive application of data
                 mining. We encapsulate traditional views of data mining
                 that operates primarily on quantitative data, such as
                 financial statement and journal entry data. In
                 addition, we draw on other forms of data mining,
                 notably text and email mining.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Accounting Information
                 Systems",
  keywords =     "Auditing; Benford's Law; Data mining; Fraud",
}

@Article{Hackl:2014:CPP,
  author =       "Franz Hackl and Michael E. Kummer and Rudolf
                 Winter-Ebmer",
  title =        "99 Cent: Price points in e-commerce",
  journal =      "Information Economics and Policy",
  volume =       "26",
  number =       "0",
  pages =        "12--27",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.infoecopol.2013.10.001",
  ISSN =         "0167-6245 (print), 1873-5975 (electronic)",
  ISSN-L =       "0167-6245",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167624513000450",
  abstract =     "Setting prices ending in nines is a common feature of
                 many markets for consumer products. This prevalence has
                 been explained either by a specific image of such price
                 points or by the exploitation of rational inattention
                 on the part of the consumers who want to economize on
                 the cost of information processing. We use data from an
                 Austrian price comparison site and find a remarkable
                 prevalence of such price setting. Prices ending with
                 nine are also sticky: price-setters change them with a
                 significantly lower probability; rivals underbid these
                 prices more seldom if they represent the cheapest price
                 on the market, and we observe higher price jumps by
                 price leaders for these price points. Finally, we
                 explore the impact of these price points on the
                 consumers demand.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; E-commerce; Focal prices; Price
                 stability; Pricing behavior",
}

@Article{He:2014:EPD,
  author =       "Hui He and Na Zhou and Ruiming Zhang",
  title =        "On estimation for the {Pareto} distribution",
  journal =      j-STAT-METHODOL,
  volume =       "21",
  number =       "??",
  pages =        "49--58",
  month =        nov,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:46:01 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312714000288",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Article{Holz:2014:QCG,
  author =       "Carsten A. Holz",
  title =        "The quality of {China}'s {GDP} statistics",
  journal =      "China Economic Review",
  volume =       "30",
  number =       "0",
  pages =        "309--338",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.chieco.2014.06.009",
  ISSN =         "1043-951X (print), 1873-7781 (electronic)",
  ISSN-L =       "1043-951X",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1043951X14000753",
  abstract =     "Since the 1998 wind of falsification and
                 embellishment, Chinese official statistics on gross
                 domestic product (GDP) have repeatedly come under
                 scrutiny. This paper evaluates the quality of China's
                 GDP statistics in four stages. First, it reviews past
                 and ongoing suspicions of the quality of GDP data and
                 examines the evidence. Second, it documents the
                 institutional framework for data compilation and
                 concludes on the implications for data quality. Third,
                 it asks how the Chinese National Bureau of Statistics
                 could possibly go about credibly falsifying GDP data
                 without being found out. Fourth, it examines if the
                 first- and second-digit distributions of official GDP
                 data conform to established data regularities
                 (Benford's Law). The findings are that the supposed
                 evidence for GDP data falsification is not compelling,
                 that the National Bureau of Statistics has much
                 institutional scope for falsifying GDP data, and that
                 certain manipulations of nominal and real data would be
                 virtually undetectable. Official GDP data, however,
                 exhibit few statistical anomalies (conform to Benford's
                 Law) and the National Bureau of Statistics thus either
                 makes no significant use of its scope to falsify data,
                 or is aware of statistical data regularities when it
                 falsifies data.",
  acknowledgement = ack-nhfb,
  keywords =     "Accuracy of national statistics; Benford's Law;
                 Compilation of {GDP} and sectoral value-added; National
                 income accounting; National statistical system",
}

@Article{Hou:2014:PFD,
  author =       "I-Hong Hou and Piyush Gupta",
  title =        "Proportionally fair distributed resource allocation in
                 multiband wireless systems",
  journal =      j-IEEE-TRANS-NETWORKING,
  volume =       "22",
  number =       "6",
  pages =        "1819--1830",
  month =        dec,
  year =         "2014",
  CODEN =        "IEANEP",
  DOI =          "https://doi.org/10.1109/TNET.2013.2284494",
  ISSN =         "1063-6692 (print), 1558-2566 (electronic)",
  ISSN-L =       "1063-6692",
  bibdate =      "Thu Feb 12 18:29:37 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransnetworking.bib",
  abstract =     "A challenging problem in multiband multicell
                 self-organized wireless systems, such as
                 femtocells/picocells in cellular networks, multichannel
                 Wi-Fi networks, and more recent wireless networks over
                 TV white spaces, is of distributed resource allocation.
                 This in general involves four components: channel
                 selection, client association, channel access, and
                 client scheduling. In this paper, we present a unified
                 framework for jointly addressing the four components
                 with the global system objective of maximizing the
                 clients throughput in a proportionally fair manner. Our
                 formulation allows a natural dissociation of the
                 problem into two subparts. We show that the first part,
                 involving channel access and client scheduling, is
                 convex and derive a distributed adaptation procedure
                 for achieving a Pareto-optimal solution. For the second
                 part, involving channel selection and client
                 association, we develop a Gibbs-sampler-based approach
                 for local adaptation to achieve the global objective,
                 as well as derive fast greedy algorithms from it that
                 achieve good solutions often.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE\slash ACM Transactions on Networking",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J771",
}

@Article{Huang:2014:GSP,
  author =       "Mu-Hsuan Huang and Wei-Tzu Huang and Cheng-Ching Chang
                 and Dar-Zen Chen and Chang-Pin Lin",
  title =        "The greater scattering phenomenon beyond {Bradford}'s
                 law in patent citation",
  journal =      j-J-ASSOC-INF-SCI-TECHNOL,
  volume =       "65",
  number =       "9",
  pages =        "1917--1928",
  month =        sep,
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1002/asi.23092",
  ISSN =         "2330-1643 (print), 2330-1643 (electronic)",
  ISSN-L =       "2330-1643",
  bibdate =      "Fri Sep 11 12:15:14 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jaist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Information Science and
                 Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "8 Apr 2014",
}

@Article{Huettenberger:2014:DSM,
  author =       "Lars Huettenberger and Christian Heine and Christoph
                 Garth",
  title =        "Decomposition and Simplification of Multivariate Data
                 using {Pareto} Sets",
  journal =      j-IEEE-TRANS-VIS-COMPUT-GRAPH,
  volume =       "20",
  number =       "12",
  pages =        "2684--2693",
  month =        dec,
  year =         "2014",
  CODEN =        "ITVGEA",
  DOI =          "https://doi.org/10.1109/TVCG.2014.2346447",
  ISSN =         "1077-2626 (print), 1941-0506 (electronic), 2160-9306",
  ISSN-L =       "1077-2626",
  bibdate =      "Thu Feb 12 16:40:54 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetransviscomputgraph.bib",
  URL =          "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html",
  abstract-URL = "http://csdl.computer.org/csdl/trans/tg/2014/12/06875963-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Visualization and Computer
                 Graphics",
  journal-URL =  "http://www.computer.org/csdl/trans/tg/index.html",
}

@InProceedings{Iorliam:2014:DBI,
  author =       "A. Iorliam and A. T. S. Ho and N. Poh and Y. Q. Shi",
  booktitle =    "2014 International Workshop on Biometrics and
                 Forensics (IWBF)",
  title =        "Do biometric images follow {Benford's Law}?",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--6",
  month =        mar,
  year =         "2014",
  DOI =          "https://doi.org/10.1109/IWBF.2014.6914261",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "backend attack; Benford law; Benford's law; Biomedical
                 imaging; biometric image manipulation; biometric
                 images; biometric sample tampering; biometrics (access
                 control); data compression; digital forensics; Discrete
                 cosine transforms; double compressed face image; double
                 compressed fingerprint image; EER; equal error rate;
                 Face; Fingerprint recognition; forensic biometrics;
                 forensics; image coding; Image coding; Image matching;
                 malicious tampering detection; natural image tampering
                 detection; security concern; sensor level tampering;
                 single compressed face image; single compressed
                 fingerprint image; spoofing; template contamination;
                 Transform coding",
}

@Article{Jameson:2014:BLC,
  author =       "Marie Jameson and Jesse Thomer and Lynelle Ye",
  title =        "{Benford's Law} for Coefficients of Newforms",
  journal =      "arxiv.org",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "7",
  month =        jul,
  year =         "2014",
  bibdate =      "Sat Sep 10 12:26:03 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1407.1577",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

@Article{Kraus:2014:DWD,
  author =       "Cornelia Kraus and Raul Valverde",
  title =        "A Data Warehouse Design for the Detection of Fraud in
                 the Supply Chain by Using the {Benford's Law}",
  journal =      j-AM-J-APPL-SCI,
  volume =       "11",
  number =       "9",
  pages =        "1507--1518",
  month =        sep,
  year =         "2014",
  CODEN =        "AJASCJ",
  DOI =          "https://doi.org/10.3844/ajassp.2014.1507.1518",
  ISSN =         "1546-9239 (print), 1554-3641 (electronic)",
  ISSN-L =       "1546-9239",
  bibdate =      "Mon Jun 1 13:40:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Am. J. Appl. Sci.",
  fjournal =     "American Journal of Applied Sciences",
  journal-URL =  "https://thescipub.com/journals/ajas/archive",
}

@Article{Leemann:2014:SAS,
  author =       "Lucas Leemann and Daniel Bochsler",
  title =        "A systematic approach to study electoral fraud",
  journal =      j-ELECT-STUDIES,
  volume =       "35",
  number =       "0",
  pages =        "33--47",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.electstud.2014.03.005",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379414000390",
  abstract =     "Integrity of elections relies on fair procedures at
                 different stages of the election process, and fraud can
                 occur in many instances and different forms. This paper
                 provides a general approach for the detection of fraud.
                 While most existing contributions focus on a single
                 instance and form of fraud, we propose a more
                 encompassing approach, testing for several empirical
                 implications of different possible forms of fraud. To
                 illustrate this approach we rely on a case of electoral
                 irregularities in one of the oldest democracies: In a
                 Swiss referendum in 2011, one in twelve municipalities
                 irregularly destroyed the ballots, rendering a recount
                 impossible. We do not know whether this happened due to
                 sloppiness, or to cover possible fraudulent actions.
                 However, one of our statistical tests leads to results,
                 which point to irregularities in some of the
                 municipalities, which lost their ballots: they reported
                 significantly fewer empty ballots than the other
                 municipalities. Relying on several tests leads to the
                 well known multiple comparisons problem. We show two
                 strategies and illustrate strengths and weaknesses of
                 each potential way to deal with multiple tests.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Benford's Law; Electoral forensics; Electoral fraud;
                 Referendums; Switzerland",
}

@Article{Lin:2014:CCE,
  author =       "Fengyi Lin and Sheng-Fu Wu",
  title =        "Comparison of cosmetic earnings management for the
                 developed markets and emerging markets: Some empirical
                 evidence from the {United States} and {Taiwan}",
  journal =      "Economic Modelling",
  volume =       "36",
  number =       "0",
  pages =        "466--473",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.econmod.2013.10.002",
  ISSN =         "0264-9993 (print), 1873-6122 (electronic)",
  ISSN-L =       "0264-9993",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0264999313004288",
  abstract =     "This study examines the effect of the implementation
                 of corporate governance regulations on cosmetic
                 earnings management in developed and emerging markets
                 respectively. Using Benford's Law, the analysis employs
                 84,870 positive earnings observations for all publicly
                 listed US and Taiwan companies from 1990 to 2011. The
                 empirical results show that, regardless of developed
                 markets and emerging markets, the phenomenon of
                 cosmetic earnings management exists. In contrast to
                 developed markets, corporate managers of emerging
                 markets have stronger incentives to manipulate
                 earnings. More importantly, it was found that the
                 degree of earnings management is significantly less
                 after implementing corporate governance regulations
                 both in developed and emerging markets. This result
                 suggests that the implementation of corporate
                 governance regulations plays an important role in
                 reducing the earnings manipulative behavior. The
                 findings of the study add more evidence to the ongoing
                 debate about the effectiveness of corporate governance
                 regulations in preventing earnings management.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Corporate governance; Cosmetic earnings
                 management",
}

@Article{Lin:2014:RAA,
  author =       "Fengyi Lin and Chung-Min Wu and Tzu-Yi Fang and
                 Jheng-Ci Wun",
  title =        "The relations among accounting conservatism,
                 institutional investors and earnings manipulation",
  journal =      "Economic Modelling",
  volume =       "37",
  number =       "0",
  pages =        "164--174",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.econmod.2013.10.020",
  ISSN =         "0264-9993 (print), 1873-6122 (electronic)",
  ISSN-L =       "0264-9993",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0264999313004471",
  abstract =     "Most scholars have indicated corporations using
                 accounting conservatism to reduce earnings
                 manipulation, although certain scholars believe that
                 firms have more incentive to increase earnings
                 manipulation. Institutional investors play an important
                 external monitoring role, and affect firm's earnings
                 manipulation. Previous studies adopted accruals as an
                 earnings manipulation proxy to detect the relationship
                 among accounting conservatism, institutional investor
                 shareholdings, and earnings manipulation. We further
                 investigate the relationship among accounting
                 conservatism, institutional investor shareholdings, and
                 earnings manipulation by using Benford's law. Our
                 results indicate that firms with more conservative
                 financial reporting have less probability of engaging
                 in earnings-manipulative activities. We also find the
                 negative association between earnings management and
                 institutional investor shareholdings. However, if
                 corporate financial statements tend toward
                 conservatism, institutional investor shareholdings
                 could increase managers' incentive to manage earnings.
                 Our findings have important implications for investors
                 to make investment decisions.",
  acknowledgement = ack-nhfb,
  keywords =     "Accounting conservatism; Benford's law; Benford's Law;
                 Benford's law; Benford's Law; Earnings management;
                 Institutional investor shareholdings",
}

@Article{Lu:2014:ODE,
  author =       "Lu Lu and Christine M. Anderson-Cook and Dennis K. J.
                 Lin",
  title =        "Optimal designed experiments using a {Pareto} front
                 search for focused preference of multiple objectives",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "71",
  number =       "??",
  pages =        "1178--1192",
  month =        mar,
  year =         "2014",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:43:50 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947313001382",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Luca:2014:FDF,
  author =       "Florian Luca and Pantelimon St{\u{a}}nic{\u{a}}",
  title =        "On the first digits of the {Fibonacci} numbers and
                 their {Euler} function",
  journal =      "Uniform Distribution Theory",
  volume =       "9",
  number =       "1",
  pages =        "21--25",
  year =         "2014",
  ISSN =         "1336-913X (print), 2309-5377 (electronic)",
  ISSN-L =       "1336-913X",
  MRclass =      "11B39 (11K36)",
  MRnumber =     "3237073",
  MRreviewer =   "Huaning Liu",
  bibdate =      "Tue Jan 26 11:12:44 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib",
  URL =          "https://math.boku.ac.at/udt/vol09/no1/03LucaStanica.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Unif. Distrib. Theory",
  fjournal =     "Uniform Distribution Theory",
  journal-URL =  "https://doaj.org/toc/1336-913X",
}

@Article{MacDougall:2014:AIC,
  author =       "Margaret MacDougall",
  title =        "Assessing the Integrity of Clinical Data: When is
                 Statistical Evidence Too Good to be True?",
  journal =      "Topoi: An International Review of Philosophy",
  volume =       "33",
  number =       "2",
  pages =        "323--337",
  month =        oct,
  year =         "2014",
  DOI =          "https://doi.org/10.1007/s11245-013-9216-5",
  ISSN =         "0167-7411 (print), 1572-8749 (electronic)",
  ISSN-L =       "0167-7411",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11245-013-9216-5",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/11245",
  keywords =     "Benford's Law",
}

@Article{Marden:2014:APO,
  author =       "Jason R. Marden and H. Peyton Young and Lucy Y. Pao",
  title =        "Achieving {Pareto} Optimality Through Distributed
                 Learning",
  journal =      j-SIAM-J-CONTROL-OPTIM,
  volume =       "52",
  number =       "5",
  pages =        "2753--2770",
  month =        "????",
  year =         "2014",
  CODEN =        "SJCODC",
  DOI =          "https://doi.org/10.1137/110850694",
  ISSN =         "0363-0129 (print), 1095-7138 (electronic)",
  ISSN-L =       "0363-0129",
  bibdate =      "Thu Feb 12 07:28:17 MST 2015",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toclist/SICON/52/5;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjcontroloptim.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Control and Optimization",
  journal-URL =  "http://epubs.siam.org/sicon",
  onlinedate =   "January 2014",
}

@Book{Miller:2014:JFM,
  author =       "Irwin Miller and Marylees Miller",
  title =        "{John E. Freund}'s mathematical statistics with
                 applications",
  publisher =    "Pearson",
  address =      "Boston, MA, USA",
  edition =      "Eighth",
  pages =        "xi + 529",
  year =         "2014",
  ISBN =         "0-321-80709-X (hardcover)",
  ISBN-13 =      "978-0-321-80709-0 (hardcover)",
  LCCN =         "QA276 .M4726 2014",
  bibdate =      "Thu Oct 13 07:03:41 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  author-dates = "1928--",
  remark =       "Revised edition of \cite{Miller:2004:JFM}.",
  subject =      "Mathematical statistics",
}

@Article{Mir:2014:BLB,
  author =       "T. A. Mir",
  title =        "The {Benford Law} behavior of the religious activity
                 data",
  journal =      j-PHYSICA-A,
  volume =       "408",
  number =       "0",
  pages =        "1--9",
  year =         "2014",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2014.03.074",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437114002854",
  abstract =     "An important aspect of religious association is that
                 adherents, as part of their religious duty, carry out
                 various activities. One religious group known for
                 keeping the elaborate records of day-to-day activities
                 of its members is the Jehovah's Witnesses (JWs) a
                 worldwide Christian religious group. We analyse the
                 historical records of the country-wide data associated
                 with twelve different religious activities of {JWs} to
                 see if there are any patterns in the distribution of
                 the first digits as predicted by Benford's Law. This
                 law states that the first digits of numbers in data
                 sets are not uniformly distributed but often, not
                 always, follow a logarithmic distribution such that the
                 numbers beginning with smaller digits appear more
                 frequently than those with larger ones. We find that
                 the data on religious activities like peak publishers,
                 pioneer publishers, baptizations, public meetings,
                 congregations, bible studies, time spent in
                 door-to-door contacts, attendances at the memorial
                 services, total literature and individual magazines
                 distributed, new subscriptions and back-calls received
                 excellently conforms to Benford's Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Jehovah's Witnesses; Religious
                 activities",
}

@Article{Mir:2014:BLP,
  author =       "Tariq Ahmad Mir and Marcel Ausloos and Roy Cerqueti",
  title =        "{Benford}'s law predicted digit distribution of
                 aggregated income taxes: the surprising conformity of
                 {Italian} cities and regions",
  journal =      j-EUR-PHYS-J-B,
  volume =       "87",
  number =       "11",
  year =         "2014",
  CODEN =        "EPJBFY",
  DOI =          "https://doi.org/10.1140/epjb/e2014-50525-2",
  ISSN =         "1434-6028 (print), 1434-6036 (electronic)",
  ISSN-L =       "1434-6028",
  bibdate =      "Wed Aug 12 10:00:00 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  eid =          "261",
  fjournal =     "European Physical Journal B: Condensed Matter and
                 Complex Systems",
  journal-URL =  "http://link.springer.com/journal/10051",
  keywords =     "Statistical and Nonlinear Physics",
}

@Article{Mitov:2014:EAP,
  author =       "Kosto V. Mitov and Saralees Nadarajah",
  title =        "Extremal and additive processes generated by {Pareto}
                 distributed random vectors",
  journal =      j-ESAIM-PROBAB-STATIST,
  volume =       "18",
  number =       "??",
  pages =        "667--??",
  month =        "????",
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1051/ps/2014001",
  ISSN =         "1292-8100 (print), 1262-3318 (electronic)",
  ISSN-L =       "1262-3318",
  bibdate =      "Mon Feb 9 06:54:48 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/esaim-probab-stat.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ESAIM: Probability and Statistics",
  journal-URL =  "http://www.edpsciences.org/ps/",
}

@Book{Oleksy:2014:DMB,
  author =       "Marius Oleksy",
  title =        "{Data Mining und Benford's Law als
                 Controllinginstrumente}. ({German}) [{Data} mining and
                 {Benford's Law} as controlling instruments]",
  volume =       "45",
  publisher =    "EHV Academicpress",
  address =      "Bremen, Germany",
  pages =        "220",
  year =         "2014",
  ISBN =         "3-86741-923-X (paperback), 3-86741-928-0",
  ISBN-13 =      "978-3-86741-923-9 (paperback), 978-3-86741-928-4",
  LCCN =         "????",
  bibdate =      "Sat Jan 23 08:09:16 MST 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wismarer Schriften zu Management und Recht",
  URL =          "http://deposit.d-nb.de/cgi-bin/dokserv?id=4627278\%26prov=M\%26dok\_var=1\%26dok\_ext=htm",
  acknowledgement = ack-nhfb,
  language =     "German",
  tableofcontents = "1 Ziel und Abgrenzung der Arbeit / 16 \\
                 1.1 Ziel / 18 \\
                 1.2 Abgrenzung und die Hypothese / 18 \\
                 2 Die Menge von Benford, die Benford Verteilung / 19
                 \\
                 2.1 Untersuchungen der Benford-Verteilung / 20 \\
                 2.2 Anwendungen des Benford-Gesetzes im Finanzbereich /
                 24 \\
                 3 Datenursprung und Datenschutz / 25 \\
                 3.1 Gesch{\"a}ftsmodell der DekaBank Luxembourg S.A. /
                 26 \\
                 3.2 Systemarchitektur und die Datenquelle / 27 \\
                 3.3 Datenschutz / 28 \\
                 4 Orthodoxe Beweise der Verteilungskonformit{\"a}t / 30
                 \\
                 4.1 Anpassungstests / 30 \\
                 4.1.1 Nullhypothese und Fehlentscheidungen in der
                 Statistik / 31 \\
                 4.1.2 Normalverteilung / 33 \\
                 4.1.3 Signifikanztests / 40 \\
                 4.2 Auswahl der Anpassungstest / 50 \\
                 5 Konzept des Frameworks f{\"u}r das Data Mining / 51
                 \\
                 5.1 Einf{\"u}hrung in Data Mining / 51 \\
                 5.2 Data Mining Phasen und Prozesse / 53 \\
                 5.3 Biologische Grundlagen eines k{\"u}nstlichen
                 Neurons / 61 \\
                 5.4 K{\"u}nstliches Neuron / 62 \\
                 5.5 Architektur des K{\"u}nstlichen Neuronalen Netzes /
                 84 \\
                 5.6 Auswahl der Musterregeln / 94 \\
                 5.7 Entwicklung eines Testszenarios / 102 \\
                 5.8 Kriterien f{\"u}r Wissensextraktion / 104 \\
                 5.9 Kriterien f{\"u}r den Testbetrieb / 107 \\
                 6 Auswahl der Finanztransaktionen / 109 \\
                 6.1 Finanztransaktionen / 109 \\
                 6.2 Auswahl der Daten f{\"u}r die Untersuchung / 111
                 \\
                 7 Modellentwurf der Datentransformation / 114 \\
                 7.1 Import Datenmodell / 120 \\
                 7.2 Target Datenmodell / 123 \\
                 8 Datenstrukturen, Datenselection und Unwandlung / 128
                 \\
                 8.1 Datenstrukturen des Initialen Datenmodells / 130
                 \\
                 8.2 Datenstrukturen des Import Datenmodells / 133 \\
                 8.3 Datenstrukturen des Target Datenmodells / 136 \\
                 9. Data Mining / 140 \\
                 9.1 Bewertung der Transaktionen / 141 \\
                 9.2 Die Tests / 152 \\
                 9.3 Interpretation der Ergebnisse / 155 \\
                 9.4 Anwendung in der Praxis / 158 \\
                 Glossar / 166 \\
                 Literaturverzeichnis / 179 \\
                 Anh{\"a}nge / 181",
}

@Article{Olver:2014:MIM,
  author =       "F. W. J. Olver",
  title =        "Mathematics that has intrigued me",
  journal =      "Analysis and Applications (Singapore)",
  volume =       "12",
  number =       "4",
  pages =        "341--354",
  year =         "2014",
  DOI =          "https://doi.org/10.1142/S0219530514500262",
  ISSN =         "0219-5305 (print), 1793-6861 (electronic)",
  ISSN-L =       "0219-5305",
  MRclass =      "33-03 (01A70 39A06 65-03)",
  MRnumber =     "3218916",
  bibdate =      "Sun Nov 5 09:03:34 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Lecture delivered at Asymptotics and Applied Analysis,
                 Conference in Honor of Frank W. J. Olver's 75th
                 Birthday, January 10--14, 2000, San Diego State
                 University, San Diego, California.",
  acknowledgement = ack-nhfb,
  ajournal =     "Anal. Appl. (Singap.)",
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  fjournal =     "Analysis and Applications",
  journal-URL =  "https://www.worldscientific.com/worldscinet/aa",
  remark =       "This paper was completed after Frank Olver's death by
                 his son, Peter J. Olver, from handwritten notes. It
                 also contains a summary of Frank Olver's education and
                 career. In the paper, Frank Olver discusses the
                 application of Benford's Law to test data selection.",
}

@Article{Rane:2014:BLG,
  author =       "Ameya Deepak Rane and Utkarsh Mishra and Anindya
                 Biswas and Aditi Sen(De) and Ujjwal Sen",
  title =        "{Benford's Law} gives better scaling exponents in
                 phase transitions of quantum {$ X Y $} models",
  journal =      j-PHYS-REV-E,
  volume =       "90",
  number =       "2",
  pages =        "022144:1--022144:8",
  day =          "29",
  month =        aug,
  year =         "2014",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.90.022144",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibdate =      "Tue Jan 26 10:14:12 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.90.022144",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  numpages =     "8",
}

@Article{Rauch:2014:DPM,
  author =       "Bernhard Rauch and Max G{\"o}ttsche and Stephan
                 Langenegger",
  title =        "Detecting Problems in Military Expenditure Data Using
                 Digital Analysis",
  journal =      "Defence and Peace Economics",
  volume =       "25",
  number =       "2",
  pages =        "97--111",
  month =        "????",
  year =         "2014",
  DOI =          "https://doi.org/10.1080/10242694.2013.763438",
  bibdate =      "Sat Sep 10 15:55:05 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/10242694.2013.763438",
  accepted =     "07 Dec 2012",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://www.tandfonline.com/toc/gdpe20",
  keywords =     "Benford's Law; digital analysis; forensic accounting,;
                 military expenditure data",
  received =     "24 May 2012",
}

@Article{Rauch:2014:DVS,
  author =       "Bernhard Rauch and Max G{\"o}ttsche and Gernot
                 Br{\"a}hler and Thomas Kronfeld",
  title =        "Deficit versus Social Statistics: Empirical Evidence
                 for the Effectiveness of {Benford's Law}",
  journal =      j-APPL-ECON-LETT,
  volume =       "21",
  number =       "3",
  pages =        "147--151",
  month =        "????",
  year =         "2014",
  DOI =          "https://doi.org/10.1080/13504851.2013.844319",
  ISSN =         "1350-4851 (print), 1466-4291 (electronic)",
  ISSN-L =       "1350-4851",
  bibdate =      "Sat Sep 10 15:51:42 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/13504851.2013.844319",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Economics Letters",
  journal-URL =  "http://www.tandfonline.com/toc/RAEL20",
  keywords =     "Benford's Law",
}

@Article{Roukema:2014:FDA,
  author =       "Boudewijn F. Roukema",
  title =        "A first-digit anomaly in the {2009 Iranian
                 Presidential} election",
  journal =      j-J-APPL-STAT,
  volume =       "41",
  number =       "1",
  pages =        "164--199",
  year =         "2014",
  DOI =          "https://doi.org/10.1080/02664763.2013.838664",
  ISSN =         "0266-4763 (print), 1360-0532 (electronic)",
  ISSN-L =       "0266-4763",
  MRclass =      "Database Expansion Item",
  MRnumber =     "3291207",
  bibdate =      "Wed Mar 5 08:09:17 MST 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/japplstat.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Applied Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/cjas20",
}

@Article{Savanur:2014:LLA,
  author =       "Kiran Savanur and S. Gayathri Devi and P. V. Konnur",
  title =        "{Lotka's Law} and Authorship Distribution in the
                 Journal of `{{\booktitle{Columbia Law Review}}}'",
  journal =      j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
  volume =       "8",
  number =       "1",
  pages =        "193--208",
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09737766.2014.947840",
  ISSN =         "0973-7766 (print), 2168-930X (electronic)",
  ISSN-L =       "0973-7766",
  bibdate =      "Thu Sep 10 17:47:12 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Collnet Journal of Scientometrics and Information
                 Management",
  journal-URL =  "http://www.tandfonline.com/loi/tsim20",
}

@Article{Sjoberg:2014:AAS,
  author =       "Fredrik M. Sjoberg",
  title =        "Autocratic adaptation: The strategic use of
                 transparency and the persistence of election fraud",
  journal =      j-ELECT-STUDIES,
  volume =       "33",
  number =       "0",
  pages =        "233--245",
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.electstud.2013.08.004",
  ISSN =         "0261-3794 (print), 1873-6890 (electronic)",
  ISSN-L =       "0261-3794",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0261379413001273",
  abstract =     "Why would an autocrat want, or at least make it appear
                 to want, to reduce election fraud? In recent years,
                 non-democratic rulers have surprisingly begun to
                 embrace fraud-reducing technologies, like web cameras
                 or transparent ballot boxes. The reason for this is
                 found in the relative ease by which one type of fraud
                 can be replaced with another. With the help of new
                 fraud identification techniques, I argue that the
                 installation of web cameras in polling stations changes
                 how fraud is conducted. Web cameras do not reduce
                 fraud, but rather make certain blatant forms of fraud,
                 like ballot box stuffing, more costly. Autocrats then
                 substitute for other types of fraud, such as
                 fabricating the vote count out of view of the
                 cameras.",
  acknowledgement = ack-nhfb,
  fjournal =     "Electoral Studies",
  keywords =     "Autocracy; Benford's Law; Election fraud; Election
                 monitoring; Fraud forensics; Web cameras; {ICT}",
}

@Article{Tripathi:2014:IEP,
  author =       "Yogesh Mani Tripathi and Somesh Kumar and C.
                 Petropoulos",
  title =        "Improved estimators for parameters of a {Pareto}
                 distribution with a restricted scale",
  journal =      j-STAT-METHODOL,
  volume =       "18",
  number =       "??",
  pages =        "1--13",
  month =        may,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Fri Feb 6 07:45:59 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312713000749",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
}

@Article{Wojcik:2014:CBL,
  author =       "Micha{\l} Ryszard W{\'o}jcik",
  title =        "A characterization of {Benford's Law} through
                 generalized scale-invariance",
  journal =      j-MATH-SOC-SCI,
  volume =       "71",
  number =       "??",
  pages =        "1--5",
  month =        sep,
  year =         "2014",
  DOI =          "https://doi.org/10.1016/j.mathsocsci.2014.03.006",
  ISSN =         "0165-4896 (print), 1879-3118 (electronic)",
  ISSN-L =       "0165-4896",
  MRclass =      "60E05 (62E10)",
  MRnumber =     "3249768",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0165489614000262",
  abstract =     "If $X$ is uniformly distributed modulo $1$ and $Y$ is
                 independent of $X$ then $ Y + X$ is also uniformly
                 distributed modulo $1$. We prove a converse for any
                 continuous random variable $Y$ (or a reasonable
                 approximation to a continuous random variable) so that
                 if $X$ and $ Y + X$ are equally distributed modulo $1$
                 and $Y$ is independent of $X$ then $X$ is uniformly
                 distributed modulo $1$ (or approximates the uniform
                 distribution equally reasonably). This translates into
                 a characterization of Benford's Law through a
                 generalization of scale-invariance: from multiplication
                 by a constant to multiplication by an independent
                 random variable.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematical Social Sciences",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01654896",
  keywords =     "Benford's Law",
}

@Article{Xie:2014:GTK,
  author =       "Min Xie and Laks V. S. Lakshmanan and Peter T. Wood",
  title =        "Generating top-$k$ packages via preference
                 elicitation",
  journal =      j-PROC-VLDB-ENDOWMENT,
  volume =       "7",
  number =       "14",
  pages =        "1941--1952",
  month =        oct,
  year =         "2014",
  CODEN =        "????",
  ISSN =         "2150-8097",
  ISSN-L =       "2150-8097",
  bibdate =      "Wed Feb 4 17:20:43 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/vldbe.bib",
  abstract =     "There are several applications, such as play lists of
                 songs or movies, and shopping carts, where users are
                 interested in finding top-$k$ packages, consisting of
                 sets of items. In response to this need, there has been
                 a recent flurry of activity around extending classical
                 recommender systems (RS), which are effective at
                 recommending individual items, to recommend packages,
                 or sets of items. The few recent proposals for package
                 RS suffer from one of the following drawbacks: they
                 either rely on hard constraints which may be difficult
                 to be specified exactly by the user or on returning
                 Pareto-optimal packages which are too numerous for the
                 user to sift through. To overcome these limitations, we
                 propose an alternative approach for finding
                 personalized top-$k$ packages for users, by capturing
                 users' preferences over packages using a linear utility
                 function which the system learns. Instead of asking a
                 user to specify this function explicitly, which is
                 unrealistic, we explicitly model the uncertainty in the
                 utility function and propose a preference
                 elicitation-based framework for learning the utility
                 function through feedback provided by the user. We
                 propose several sampling-based methods which, given
                 user feedback, can capture the updated utility
                 function. We develop an efficient algorithm for
                 generating top-$k$ packages using the learned utility
                 function, where the rank ordering respects any of a
                 variety of ranking semantics proposed in the
                 literature. Through extensive experiments on both real
                 and synthetic datasets, we demonstrate the efficiency
                 and effectiveness of the proposed system for finding
                 top-$k$ packages.",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the VLDB Endowment",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J1174",
}

@Article{Yang:2014:RAE,
  author =       "Z. K. Yang and D. M. Lin and M. Z. Xu",
  title =        "The Re-applicability Explore of {Lotka's Law} in
                 Patent Documents",
  journal =      j-COLLNET-J-SCIENTOMETRICS-INF-MANAGE,
  volume =       "8",
  number =       "1",
  pages =        "183--191",
  year =         "2014",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/09737766.2014.916875",
  ISSN =         "0973-7766 (print), 2168-930X (electronic)",
  ISSN-L =       "0973-7766",
  bibdate =      "Thu Sep 10 17:47:12 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/collnet-j-scientometrics-info-manage.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Collnet Journal of Scientometrics and Information
                 Management",
  journal-URL =  "http://www.tandfonline.com/loi/tsim20",
}

@Article{Zahran:2014:EAS,
  author =       "Sammy Zahran and Terrence Iverson and Stephan Weiler
                 and Anthony Underwood",
  title =        "Evidence that the accuracy of self-reported lead
                 emissions data improved: A puzzle and discussion",
  journal =      j-J-RISK-UNCERT,
  volume =       "49",
  number =       "3",
  pages =        "235--257",
  year =         "2014",
  CODEN =        "JRUNEN",
  DOI =          "https://doi.org/10.1007/s11166-014-9204-1",
  ISSN =         "0895-5646 (print), 1573-0476 (electronic)",
  ISSN-L =       "0895-5646",
  bibdate =      "Sat Sep 10 14:35:50 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Risk and Uncertainty",
  journal-URL =  "http://link.springer.com/journal/11166",
  keywords =     "Benford's Law",
}

@Article{Zomaya:2014:POC,
  author =       "Albert Y. Zomaya",
  title =        "{Pareto}-Optimal Cloud Bursting",
  journal =      j-IEEE-TRANS-PAR-DIST-SYS,
  volume =       "25",
  number =       "10",
  pages =        "2670--2682",
  month =        oct,
  year =         "2014",
  CODEN =        "ITDSEO",
  ISSN =         "1045-9219 (print), 1558-2183 (electronic)",
  ISSN-L =       "1045-9219",
  bibdate =      "Thu Feb 12 13:58:32 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranspardistsys.bib",
  URL =          "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html",
  abstract-URL = "http://www.computer.org/csdl/trans/td/2014/10/06587242-abs.html",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Parallel and Distributed
                 Systems",
  journal-URL =  "http://www.computer.org/tpds/archives.htm",
}

@Article{Abushal:2015:EPP,
  author =       "Tahani A. Abushal and Ahmed A. Soliman",
  title =        "Estimating the {Pareto} parameters under progressive
                 censoring data for constant-partially accelerated life
                 tests",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "85",
  number =       "5",
  pages =        "917--934",
  year =         "2015",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2013.853768",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Wed Feb 11 16:24:25 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Ausloos:2015:BBL,
  author =       "M. Ausloos and C. Herteliu and B. Ileanu",
  title =        "Breakdown of {Benford's Law} for birth data",
  journal =      j-PHYSICA-A,
  volume =       "419",
  number =       "0",
  pages =        "736--745",
  year =         "2015",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2014.10.041",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437114008796",
  abstract =     "Long birth time series for Romania are investigated
                 from Benford's Law point of view, distinguishing
                 between families with a religious (Orthodox and
                 Non-Orthodox) affiliation. The data extend from Jan.
                 01, 1905 till Dec. 31, 2001, i.e. over 97 years or
                 35\,429 days. The results point to a drastic breakdown
                 of Benford's Law. Some interpretation is proposed,
                 based on the statistical aspects due to population
                 sizes, rather than on human thought constraints when
                 the law breakdown is usually expected. Benford's Law
                 breakdown clearly points to natural causes.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Benford's Laws; Births; Non-Orthodoxes;
                 Orthodoxes; Religious community; Time series",
}

@Book{Bahmann:2015:AMM,
  author =       "Paul Bahmann",
  title =        "{Eine Analyse von monet{\"a}ren, makro{\"o}konomischen
                 Daten der BRD und DDR: Ziffernanalyse auf Grundlage des
                 Benford's Law}. ({German}) [{An} analysis of monetary,
                 macroeconomic data of the {FRG} and the {GDR}: numeric
                 analysis on the basis of {Benford's Law}]",
  publisher =    "AV Akademikerverlag",
  address =      "Saarbr{\"u}cken, Germany",
  pages =        "76",
  year =         "2015",
  ISBN =         "3-639-80882-7",
  ISBN-13 =      "978-3-639-80882-7",
  LCCN =         "????",
  bibdate =      "Sat Jan 23 07:58:34 MST 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Balanzario:2015:BLM,
  author =       "Eugenio P. Balanzario",
  title =        "{Benford's Law} for mixtures",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "44",
  number =       "4",
  pages =        "698--709",
  year =         "2015",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610926.2012.752849",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  MRclass =      "60E05 (60G57)",
  MRnumber =     "3315782",
  bibdate =      "Tue Jan 26 11:02:38 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics. Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}

@Article{Beck:2015:PPI,
  author =       "M{\'e}lanie Beck and Martin J. Gander",
  title =        "On the positivity of {Poisson} integrators for the
                 {Lotka--Volterra} equations",
  journal =      j-BIT-NUM-MATH,
  volume =       "55",
  number =       "2",
  pages =        "319--340",
  month =        jun,
  year =         "2015",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/s10543-014-0505-1",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Sat Aug 8 13:47:11 MDT 2015",
  bibsource =    "http://link.springer.com/journal/10543/55/2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib",
  URL =          "http://link.springer.com/article/10.1007/s10543-014-0505-1",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT Numerical Mathematics",
  journal-URL =  "http://link.springer.com/journal/10543",
}

@Book{Berger:2015:IBL,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "An introduction to {Benford's Law}",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "viii + 248",
  year =         "2015",
  DOI =          "https://doi.org/10.1515/9781400866588",
  ISBN =         "0-691-16306-5, 1-4008-6658-8 (e-book)",
  ISBN-13 =      "978-0-691-16306-2, 978-1-4008-6658-8 (e-book)",
  LCCN =         "QA273.6 .B474 2015",
  bibdate =      "Fri Jan 22 12:19:25 MST 2016",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  URL =          "http://site.ebrary.com/id/11040167;
                 http://www.degruyter.com/viewbooktoc/product/465875",
  acknowledgement = ack-nhfb,
  subject =      "Distribution; Probability measures",
  tableofcontents = "Preface / vii 1 Introduction / 1 \\
                 1.1 History / 3 \\
                 1.2 Empirical evidence / 4 \\
                 1.3 Early explanations / 6 \\
                 1.4 Mathematical framework / 7 \\
                 2 Significant Digits and the Significand / 11 \\
                 2.1 Significant digits / 11 \\
                 2.2 The significand / 12 \\
                 2.3 The significand s-algebra / 14 \\
                 3 The Benford Property / 22 \\
                 3.1 Benford sequences / 23 \\
                 3.2 Benford functions / 28 \\
                 3.3 Benford distributions and random variables / 29 \\
                 4 The Uniform Distribution and Benford's Law / 43 \\
                 4.1 Uniform distribution characterization of Benford's
                 law / 43 \\
                 4.2 Uniform distribution of sequences and functions /
                 46 \\
                 4.3 Uniform distribution of random variables / 54 \\
                 5 Scale-, Base-, and Sum-Invariance / 63 \\
                 5.1 The scale-invariance property / 63 \\
                 5.2 The base-invariance property / 74 \\
                 5.3 The sum-invariance property / 80 \\
                 6 Real-valued Deterministic Processes / 90 \\
                 6.1 Iteration of functions / 90 \\
                 6.2 Sequences with polynomial growth / 93 \\
                 6.3 Sequences with exponential growth / 97 \\
                 6.4 Sequences with super-exponential growth / 101 \\
                 6.5 An application to Newton's method / 111 \\
                 6.6 Time-varying systems / 116 \\
                 6.7 Chaotic systems: Two examples / 124 \\
                 6.8 Differential equations / 127 \\
                 7 Multi-dimensional Linear Processes / 135 \\
                 7.1 Linear processes, observables, and difference
                 equations / 135 \\
                 7.2 Nonnegative matrices / 139 \\
                 7.3 General matrices / 145 \\
                 7.4 An application to Markov chains / 162 \\
                 7.5 Linear difference equations / 165 \\
                 7.6 Linear differential equations / 170 \\
                 8 Real-valued Random Processes / 180 \\
                 8.1 Convergence of random variables to Benford's law /
                 180 \\
                 8.2 Powers, products, and sums of random variables /
                 182 \\
                 8.3 Mixtures of distributions / 202 \\
                 8.4 Random maps / 213 \\
                 9 Finitely Additive Probability and Benford's Law / 216
                 \\
                 9.1 Finitely additive probabilities / 217 \\
                 9.2 Finitely additive Benford probabilities / 219 \\
                 10 Applications of Benford's Law / 223 \\
                 10.1 Fraud detection / 224 \\
                 10.2 Detection of natural phenomena / 225 \\
                 10.3 Diagnostics and design / 226 \\
                 10.4 Computations and Computer Science / 228 \\
                 10.5 Pedagogical tool / 230 \\
                 List of Symbols / 231 \\
                 Bibliography / 234 \\
                 Index / 245",
}

@Article{Berger:2015:MLF,
  author =       "Arno Berger",
  title =        "Most linear flows on {$ R^d $} are {Benford}",
  journal =      j-J-DIFFER-EQU,
  volume =       "259",
  number =       "5",
  pages =        "1933--1957",
  year =         "2015",
  CODEN =        "JDEQAK",
  DOI =          "https://doi.org/10.1016/j.jde.2015.03.016",
  ISSN =         "0022-0396 (print), 1090-2732 (electronic)",
  ISSN-L =       "0022-0396",
  MRclass =      "60F99 (11J71 11K41 37A05 37A45 62E20)",
  MRnumber =     "3349424",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022039615001527",
  abstract =     "A necessary and sufficient condition (exponential
                 nonresonance) is established for every signal obtained
                 from a linear flow on $ R^d $ by means of a linear
                 observable to either vanish identically or else exhibit
                 a strong form of Benford's Law (logarithmic
                 distribution of significant digits). The result extends
                 and unifies all previously known (sufficient)
                 conditions. Exponential nonresonance is shown to be
                 typical for linear flows, both from a topological and a
                 measure-theoretical point of view.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Differential Equations",
  keywords =     "(Continuous) uniform distribution mod 1;
                 (Exponentially) nonresonant set; Benford function;
                 Linear flow; Observable; Q -independence",
}

@InCollection{Berger:2015:SIM,
  author =       "Arno Berger and T. P. Hill",
  title =        "A short introduction to the mathematical theory of
                 {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "23--67",
  year =         "2015",
  DOI =          "https://doi.org/10.1515/9781400866588",
  MRclass =      "37A45 (11K06 60-02 60F15 60G57 62E10)",
  MRnumber =     "3411057",
  bibdate =      "Sat Mar 25 08:23:36 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Bermano:2015:DST,
  author =       "Amit Bermano and Thabo Beeler and Yeara Kozlov and
                 Derek Bradley and Bernd Bickel and Markus Gross",
  title =        "Detailed spatio-temporal reconstruction of eyelids",
  journal =      j-TOG,
  volume =       "34",
  number =       "4",
  pages =        "44:1--44:??",
  month =        aug,
  year =         "2015",
  CODEN =        "ATGRDF",
  DOI =          "https://doi.org/10.1145/2766924",
  ISSN =         "0730-0301 (print), 1557-7368 (electronic)",
  ISSN-L =       "0730-0301",
  bibdate =      "Tue Jul 28 17:22:44 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tog/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tog.bib",
  abstract =     "In recent years we have seen numerous improvements on
                 3D scanning and tracking of human faces, greatly
                 advancing the creation of digital doubles for film and
                 video games. However, despite the high-resolution
                 quality of the reconstruction approaches available,
                 current methods are unable to capture one of the most
                 important regions of the face --- the eye region. In
                 this work we present the first method for detailed
                 spatio-temporal reconstruction of eyelids. Tracking and
                 reconstructing eyelids is extremely challenging, as
                 this region exhibits very complex and unique skin
                 deformation where skin is folded under while opening
                 the eye. Furthermore, eyelids are often only partially
                 visible and obstructed due to self-occlusion and
                 eyelashes. Our approach is to combine a geometric
                 deformation model with image data, leveraging
                 multi-view stereo, optical flow, contour tracking and
                 wrinkle detection from local skin appearance. Our
                 deformation model serves as a prior that enables
                 reconstruction of eyelids even under strong
                 self-occlusions caused by rolling and folding skin as
                 the eye opens and closes. The output is a
                 person-specific, time-varying eyelid reconstruction
                 with anatomically plausible deformations. Our
                 high-resolution detailed eyelids couple naturally with
                 current facial performance capture approaches. As a
                 result, our method can largely increase the fidelity of
                 facial capture and the creation of digital doubles.",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Transactions on Graphics",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J778",
}

@Article{Berzunza:2015:YPR,
  author =       "Gabriel Berzunza",
  title =        "{Yule} processes with rare mutation and their
                 applications to percolation on $b$-ary trees",
  journal =      j-ELECTRON-J-PROBAB,
  volume =       "20",
  number =       "??",
  pages =        "43:1--43:23",
  month =        "????",
  year =         "2015",
  CODEN =        "????",
  ISSN =         "1083-6489",
  ISSN-L =       "1083-6489",
  bibdate =      "Fri Aug 7 10:50:36 MDT 2015",
  bibsource =    "http://ejp.ejpecp.org/index.php/ejp/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ejp.bib",
  URL =          "http://ejp.ejpecp.org/article/view/3789",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronic Journal of Probability",
  journal-URL =  "http://ejp.ejpecp.org/",
}

@Article{Bhole:2015:BAU,
  author =       "Gaurav Bhole and Abhishek Shukla and T. S. Mahesh",
  title =        "{Benford} analysis: A useful paradigm for
                 spectroscopic analysis",
  journal =      j-CHEM-PHYS-LETT,
  volume =       "639",
  number =       "??",
  pages =        "36--40",
  year =         "2015",
  CODEN =        "CHPLBC",
  DOI =          "https://doi.org/10.1016/j.cplett.2015.08.061",
  ISSN =         "0009-2614 (print), 1873-4448 (electronic)",
  ISSN-L =       "0009-2614",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0009261415006582",
  abstract =     "Benford's law is a statistical inference to predict
                 the frequency of significant digits in naturally
                 occurring numerical databases. In such databases this
                 law predicts a higher occurrence of the digit $1$ in
                 the most significant place and decreasing occurrences
                 to other larger digits. Although counter-intuitive at
                 first sight, Benford's law has seen applications in a
                 wide variety of fields like physics, earth-science,
                 biology, finance, etc. In this work, we have explored
                 the use of Benford's law for various spectroscopic
                 applications. Although, we use NMR signals as our
                 databases, the methods described here may also be
                 extended to other spectroscopic techniques. In
                 particular, with the help of Benford analysis, we
                 demonstrate emphasizing weak NMR signals and spectral
                 corrections. We also explore a potential application of
                 Benford analysis in the image-processing of MRI data.",
  acknowledgement = ack-nhfb,
  fjournal =     "Chemical Physics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00092614",
}

@Article{Biau:2015:FDF,
  author =       "Damien Biau",
  title =        "The first-digit frequencies in data of turbulent
                 flows",
  journal =      j-PHYSICA-A,
  volume =       "440",
  number =       "??",
  pages =        "147--154",
  day =          "15",
  month =        dec,
  year =         "2015",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2015.08.016",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "76F20 (82B05)",
  MRnumber =     "3398896",
  bibdate =      "Tue Jan 26 11:15:41 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Brunsch:2015:ISA,
  author =       "Tobias Brunsch and Heiko R{\"o}glin",
  title =        "Improved Smoothed Analysis of Multiobjective
                 Optimization",
  journal =      j-J-ACM,
  volume =       "62",
  number =       "1",
  pages =        "4:1--4:??",
  month =        feb,
  year =         "2015",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/2699445",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Tue Mar 3 12:47:00 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "We present several new results about smoothed analysis
                 of multiobjective optimization problems. Motivated by
                 the discrepancy between worst-case analysis and
                 practical experience, this line of research has gained
                 a lot of attention in the last decade. We consider
                 problems in which d linear and one arbitrary objective
                 function are to be optimized over a set $ S \subseteq
                 \{ 0, 1 \}^n $ of feasible solutions. We improve the
                 previously best known bound for the smoothed number of
                 Pareto-optimal solutions to $ O(n^{2 d} \phi^d) $,
                 where $ \phi $ denotes the perturbation parameter.
                 Additionally, we show that for any constant $c$ the $c$
                 th moment of the smoothed number of Pareto-optimal
                 solutions is bounded by $ O((n^{2 d} \phi^d)^c)$. This
                 improves the previously best known bounds
                 significantly. Furthermore, we address the criticism
                 that the perturbations in smoothed analysis destroy the
                 zero-structure of problems by showing that the smoothed
                 number of Pareto-optimal solutions remains polynomially
                 bounded even for zero-preserving perturbations. This
                 broadens the class of problems captured by smoothed
                 analysis and it has consequences for nonlinear
                 objective functions. One corollary of our result is
                 that the smoothed number of Pareto-optimal solutions is
                 polynomially bounded for polynomial objective
                 functions. Our results also extend to integer
                 optimization problems.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Cacciari:2015:DMC,
  author =       "I. Cacciari and P. Nieri and S. Siano",
  title =        "{$3$D} Digital Microscopy for Characterizing
                 Punchworks on Medieval Panel Paintings",
  journal =      j-JOCCH,
  volume =       "7",
  number =       "4",
  pages =        "19:1--19:??",
  month =        feb,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2594443",
  ISSN =         "1556-4673 (print), 1556-4711 (electronic)",
  ISSN-L =       "1556-4673",
  bibdate =      "Wed Feb 11 13:42:37 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jocch/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jocch.bib",
  abstract =     "This article is devoted to a novel application of the
                 micro-3D modeling based on shape from focus. A 3D
                 portable digital microscope prototype has been used for
                 the first time in order to analyze gold punchwork on
                 medieval panel paintings. In general, the 3D domain
                 provides a more flexible and complete characterization
                 of these decorative elements than traditional
                 photographic documentation. Low-magnification 3D
                 digital microscopy is well suited for analyzing
                 morphologies, depths, and profiles of different punch
                 marks. Here, we used these parameters for interpreting
                 the punching process and recognizing sliding and
                 bouncing effects. The 3D reconstruction of the surface
                 engraved also allowed identifying types of anomalies
                 that could be useful as possible authentication
                 markers. The advantages of the present approach with
                 respect to the photographic documentation are of
                 general valence and can be exploited in order to
                 document, parameterize, and interpret a variety of
                 engraving works on panel paintings and metal
                 artifacts.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "Journal on Computing and Cultural Heritage (JOCCH)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}

@Article{Carrera:2015:TER,
  author =       "C{\'e}sar Carrera",
  title =        "Tracking exchange rate management in {Latin America}",
  journal =      "Review of Financial Economics",
  volume =       "25",
  number =       "??",
  pages =        "35--41",
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.rfe.2015.02.004",
  ISSN =         "1058-3300 (print), 1873-5924 (electronic)",
  ISSN-L =       "1058-3300",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Special Issue on Changing Dynamics in Financial
                 Economics",
  URL =          "http://www.sciencedirect.com/science/article/pii/S105833001500018X",
  abstract =     "One way to track exchange-rate deviations from its
                 long-run value is to examine numerical patterns in
                 exchange rates to see if those patterns appear to have
                 been subjected to some degree of policy management. We
                 apply Benford's Law to exchange rates in Latin American
                 countries, computing and comparing the distribution of
                 exchange-rate observed values with those of Benford's
                 Law. For most cases we find that the exchange rate for
                 the US dollar does not satisfy Benford's Law, however
                 this law holds when the euro is considered. This result
                 may be explained by the fact that these countries are
                 characterized for having different degrees of
                 dollarization and intervention in the US dollar forex
                 market while there is almost no policy intervention in
                 the euro forex market. Our approach is an alternative
                 view of how these characteristics play a role inducing
                 deviations with respect to an implied equilibrium
                 exchange rate.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Exchange rate; Forex; FX intervention;
                 International reserves",
}

@Article{Chaves-Gonzalez:2015:DEP,
  author =       "Jos{\'e} M. Chaves-Gonz{\'a}lez and Miguel A.
                 P{\'e}rez-Toledano",
  title =        "Differential evolution with {Pareto} tournament for
                 the multi-objective next release problem",
  journal =      j-APPL-MATH-COMP,
  volume =       "252",
  number =       "??",
  pages =        "1--13",
  day =          "1",
  month =        feb,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Feb 18 09:36:18 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314016257",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Cuff:2015:WDB,
  author =       "Victoria Cuff and Allison Lewis and Steven J. Miller",
  title =        "The {Weibull} distribution and {Benford's Law}",
  journal =      "Involve",
  volume =       "8",
  number =       "5",
  pages =        "859--874",
  year =         "2015",
  DOI =          "https://doi.org/10.2140/involve.2015.8.859",
  ISSN =         "1944-4176 (print), 1944-4184 (electronic)",
  ISSN-L =       "1944-4176",
  MRclass =      "60F05 (11K06 42A16 60E10 62E15 62P99)",
  MRnumber =     "3404662",
  MRreviewer =   "Nikolai Volodin",
  bibdate =      "Tue Jan 26 11:03:29 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Involve. A Journal of Mathematics",
  journal-URL =  "http://msp.org/involve/",
}

@Article{Dandurand:2015:DCP,
  author =       "Brian Dandurand and Margaret M. Wiecek",
  title =        "Distributed Computation of {Pareto} Sets",
  journal =      j-SIAM-J-OPT,
  volume =       "25",
  number =       "2",
  pages =        "1083--1109",
  month =        "????",
  year =         "2015",
  CODEN =        "SJOPE8",
  DOI =          "https://doi.org/10.1137/130929564",
  ISSN =         "1052-6234 (print), 1095-7189 (electronic)",
  ISSN-L =       "1052-6234",
  bibdate =      "Sat Aug 8 07:33:46 MDT 2015",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIOPT/25/2;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjopt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Optimization",
  journal-URL =  "http://epubs.siam.org/siopt",
  onlinedate =   "January 2015",
}

@Article{delCastillo:2015:LIG,
  author =       "Joan del Castillo and Isabel Serra",
  title =        "Likelihood inference for generalized {Pareto}
                 distribution",
  journal =      j-COMPUT-STAT-DATA-ANAL,
  volume =       "83",
  number =       "??",
  pages =        "116--128",
  month =        mar,
  year =         "2015",
  CODEN =        "CSDADW",
  ISSN =         "0167-9473 (print), 1872-7352 (electronic)",
  ISSN-L =       "0167-9473",
  bibdate =      "Fri Feb 6 11:44:05 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/computstatdataanal2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167947314003065",
  acknowledgement = ack-nhfb,
  fjournal =     "Computational Statistics \& Data Analysis",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01679473",
}

@Article{Ferreira:2015:LPA,
  author =       "Anselmo Ferreira and Luiz C. Navarro and Giuliano
                 Pinheiro and Jefersson A. dos Santos and Anderson
                 Rocha",
  title =        "Laser printer attribution: Exploring new features and
                 beyond",
  journal =      "Forensic Science International",
  volume =       "247",
  number =       "0",
  pages =        "105--125",
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.forsciint.2014.11.030",
  ISSN =         "0379-0738 (print), 1872-6283 (electronic)",
  ISSN-L =       "0379-0738",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib",
  note =         "See also \cite{Jiang:2010:NMS}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0379073814005064",
  abstract =     "With a huge amount of printed documents nowadays,
                 identifying their source is useful for criminal
                 investigations and also to authenticate digital copies
                 of a document. In this paper, we propose novel
                 techniques for laser printer attribution. Our solutions
                 do not need very high resolution scanning of the
                 investigated document and explore the multidirectional,
                 multiscale and low-level gradient texture patterns
                 yielded by printing devices. The main contributions of
                 this work are: (1) the description of printed areas
                 using multidirectional and multiscale co-occurring
                 texture patterns; (2) description of texture on
                 low-level gradient areas by a convolution texture
                 gradient filter that emphasizes textures in specific
                 transition areas and (3) the analysis of printer
                 patterns in segments of interest, which we call frames,
                 instead of whole documents or only printed letters. We
                 show by experiments in a well documented dataset that
                 the proposed methods outperform techniques described in
                 the literature and present near-perfect classification
                 accuracy being very promising for deployment in
                 real-world forensic investigations.",
  acknowledgement = ack-nhfb,
  keywords =     "Banding; Benford's Law; Printer forensics; Texture
                 patterns",
}

@Article{Garrabrant:2015:ALU,
  author =       "Scott Garrabrant and Siddharth Bhaskar and Abram
                 Demski and Joanna Garrabrant and George Koleszarik and
                 Evan Lloyd",
  title =        "Asymptotic Logical Uncertainty and The {Benford}
                 Test",
  journal =      "CoRR",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.48550/arXiv.1510.03370",
  ISSN =         "????",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1510.03370;
                 https://dblp.org/db/journals/corr/corr1510.html#GarrabrantBDGKL15",
  abstract =     "We give an algorithm A which assigns probabilities to
                 logical sentences. For any simple infinite sequence of
                 sentences whose truth-values appear indistinguishable
                 from a biased coin that outputs ``true'' with
                 probability $p$, we have that the sequence of
                 probabilities that A assigns to these sentences
                 converges to $p$.",
  acknowledgement = ack-nhfb,
  dblp-key =     "journals/corr/GarrabrantBDGKL15",
  dblp-mdate =   "2018-08-13",
}

@Article{Goegebeur:2015:ETI,
  author =       "Yuri Goegebeur and Armelle Guillou and Michael
                 Osmann",
  title =        "An estimator for the tail index of an integrated
                 conditional {Pareto--Weibull}-type model",
  journal =      j-STAT-PROB-LETT,
  volume =       "103",
  number =       "??",
  pages =        "8--16",
  month =        aug,
  year =         "2015",
  CODEN =        "SPLTDC",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  bibdate =      "Mon Jun 8 18:57:37 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett2010.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715215001182",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
}

@Article{Goel:2015:PCA,
  author =       "Gagan Goel and Vahab Mirrokni and Renato Paes Leme",
  title =        "Polyhedral Clinching Auctions and the {AdWords}
                 Polytope",
  journal =      j-J-ACM,
  volume =       "62",
  number =       "3",
  pages =        "18:1--18:??",
  month =        jun,
  year =         "2015",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/2757277",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Fri Aug 7 10:12:49 MDT 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jacm.bib",
  abstract =     "A central issue in applying auction theory in practice
                 is the problem of dealing with budget-constrained
                 agents. A desirable goal in practice is to design
                 incentive compatible, individually rational, and Pareto
                 optimal auctions while respecting the budget
                 constraints. Achieving this goal is particularly
                 challenging in the presence of nontrivial combinatorial
                 constraints over the set of feasible allocations.
                 Toward this goal and motivated by AdWords auctions, we
                 present an auction for polymatroidal environments
                 satisfying these properties. Our auction employs a
                 novel clinching technique with a clean geometric
                 description and only needs an oracle access to the
                 submodular function defining the polymatroid. As a
                 result, this auction not only simplifies and
                 generalizes all previous results, it applies to several
                 new applications including AdWords Auctions, bandwidth
                 markets, and video on demand. In particular, our
                 characterization of the AdWords auction as
                 polymatroidal constraints might be of independent
                 interest. This allows us to design the first mechanism
                 for Ad Auctions taking into account simultaneously
                 budgets, multiple keywords and multiple slots. We show
                 that it is impossible to extend this result to generic
                 polyhedral constraints. This also implies an
                 impossibility result for multiunit auctions with
                 decreasing marginal utilities in the presence of budget
                 constraints.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "Journal of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J401",
}

@Article{Gunasekera:2015:GIR,
  author =       "Sumith Gunasekera",
  title =        "Generalized inferences of {$ R = \Pr (X > Y) $} for
                 {Pareto} distribution",
  journal =      j-STAT-PAPERS,
  volume =       "56",
  number =       "2",
  pages =        "333--351",
  month =        may,
  year =         "2015",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-014-0584-8",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Fri Apr 10 15:56:09 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/article/10.1007/s00362-014-0584-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{Han:2015:PSS,
  author =       "Qixing Han and Daqing Jiang",
  title =        "Periodic solution for stochastic non-autonomous
                 multispecies {Lotka--Volterra} mutualism type
                 ecosystem",
  journal =      j-APPL-MATH-COMP,
  volume =       "262",
  number =       "??",
  pages =        "204--217",
  day =          "1",
  month =        jul,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon May 18 12:21:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315005007",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Hu:2015:EES,
  author =       "Yangzi Hu and Fuke Wu",
  title =        "Exponential extinction of a stochastic
                 {Lotka--Volterra} model with expectations in
                 coefficients",
  journal =      j-IMA-J-APPL-MATH,
  volume =       "80",
  number =       "4",
  pages =        "1219--1234",
  month =        aug,
  year =         "2015",
  CODEN =        "IJAMDM",
  DOI =          "https://doi.org/10.1093/imamat/hxu050",
  ISSN =         "0272-4960 (print), 1464-3634 (electronic)",
  ISSN-L =       "0272-4960",
  bibdate =      "Sat Jul 25 19:12:11 MDT 2015",
  bibsource =    "http://imamat.oxfordjournals.org/contentcontent/80/4.toc;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/imajapplmath.bib",
  URL =          "http://imamat.oxfordjournals.org/content/80/4/1219",
  acknowledgement = ack-nhfb,
  fjournal =     "IMA Journal of Applied Mathematics",
  journal-URL =  "http://imamat.oxfordjournals.org/content/by/year",
  onlinedate =   "October 23, 2014",
}

@Article{Hurlimann:2015:BLS,
  author =       "Werner H{\"u}rlimann",
  title =        "{Benford's Law} in Scientific Research",
  journal =      j-INT-J-SCI-ENG-RESEARCH,
  volume =       "6",
  number =       "7",
  pages =        "143--148",
  month =        jul,
  year =         "2015",
  ISSN =         "2229-5518",
  ISSN-L =       "2229-5518",
  bibdate =      "Wed Jul 29 06:32:18 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.ijser.org/onlineResearchPaperViewer.aspx?Benfords-Law-in-Scientific-Research.pdf",
  abstract =     "As departures from Benford's law have been observed in
                 many scientific data sets, there is a theoretical need
                 to understand such discrepancies. We argue that the use
                 of parametric extensions to Benford's law is
                 appropriate and demonstrate this for several first
                 significant digit distributions taken from theoretical
                 scientific laws or extracted from real-world data
                 sets.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Scientific and Engineering
                 Research",
  journal-URL =  "http://www.ijser.org/",
}

@Article{Hurlimann:2015:FDT,
  author =       "Werner H{\"u}rlimann",
  title =        "A first digit theorem for powerful integer powers",
  journal =      j-SPRINGERPLUS,
  volume =       "4",
  number =       "1",
  pages =        "576:1--576:??",
  day =          "6",
  month =        oct,
  year =         "2015",
  CODEN =        "SPRIFB",
  DOI =          "https://doi.org/10.1186/s40064-015-1370-3",
  ISSN =         "2193-1801",
  ISSN-L =       "2193-1801",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1186/s40064-015-1370-3",
  acknowledgement = ack-nhfb,
  fjournal =     "SpringerPlus",
  journal-URL =  "http://link.springer.com/journal/40064",
  keywords =     "Benford's Law",
}

@Article{Hurlimann:2015:URU,
  author =       "Werner H{\"u}rlimann",
  title =        "On the uniform random upper bound family of first
                 significant digit distributions",
  journal =      j-J-INFORMETRICS,
  volume =       "9",
  number =       "2",
  pages =        "349--358",
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.joi.2015.02.007",
  ISSN =         "1751-1577 (print), 1875-5879 (electronic)",
  ISSN-L =       "1751-1577",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1751157715000255",
  abstract =     "The first significant digit patterns arising from a
                 mixture of uniform distributions with a random upper
                 bound are revisited. A closed-form formula for its
                 first significant digit distribution (FSD) is obtained.
                 The one-parameter model of Rodriguez is recovered for
                 an extended truncated Pareto mixing distribution.
                 Considering additionally the truncated Erlang, gamma
                 and Burr mixing distributions, and the generalized
                 Benford law, for which another probabilistic derivation
                 is offered, we study the fitting capabilities of the
                 FSD's for various Benford like data sets from
                 scientific research. Based on the results, we propose
                 the general use of a fine structure index for Benford's
                 law in case the data is well fitted by the truncated
                 Erlang member of the uniform random upper bound family
                 of FSD's.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informetrics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/17511577",
  keywords =     "Benford's law; Erlang distribution; Extended truncated
                 Pareto; Simulation algorithm; Stigler's law; Uniform
                 distribution",
}

@Article{Iafrate:2015:EDN,
  author =       "Joseph R. Iafrate and Steven J. Miller and Frederick
                 W. Strauch",
  title =        "Equipartitions and a distribution for numbers: A
                 statistical model for {Benford's Law}",
  journal =      j-PHYS-REV-E,
  volume =       "91",
  number =       "6",
  pages =        "062138:1--062138:6",
  month =        jun,
  year =         "2015",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/PhysRevE.91.062138",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  MRclass =      "60E99 (82B05)",
  MRnumber =     "3491369",
  bibdate =      "Tue Jan 26 11:15:52 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.aps.org/doi/10.1103/PhysRevE.91.062138",
  acknowledgement = ack-nhfb,
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  numpages =     "6",
}

@Article{Khataei:2015:PPB,
  author =       "Amirsam Khataei and Ali Arya",
  title =        "Personalized presentation builder for persuasive
                 communication",
  journal =      j-COMMUN-DESIGN-Q-REVIEW,
  volume =       "3",
  number =       "3",
  pages =        "25--32",
  month =        may,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2792989.2792993",
  ISSN =         "2166-1200 (print), 2166-1642 (electronic)",
  ISSN-L =       "2166-1200",
  bibdate =      "Wed Jun 17 19:00:11 MDT 2015",
  bibsource =    "http://dl.acm.org/citation.cfm?id=J1351;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/commundesignqreview.bib",
  abstract =     "Presentations are effective ways of communicating
                 information, especially in the field of education, but
                 they might not be equally or fully beneficial and
                 persuasive to all users. Each member of the audience
                 might be interested in a particular topic, come from a
                 different background and profession, and have his or
                 her own personality traits. In this conceptual paper,
                 we first describe our persuasive personalization model;
                 the Individualization Pyramid based on Yale Attitude
                 Change Approach. The model consists of the following
                 main sections: selecting contents by applying
                 segmentation, adjusting comprehensibility of the text,
                 tailoring the language of the text to fit with user's
                 personality and recommending content that is associated
                 with user's personal history within the related
                 subjects. We then propose an enhanced version of our
                 previously published presentation builder, which uses
                 users' digital traces such as those on social media to
                 personalize presentation content. Finally, we highlight
                 the available tools and algorithms to assist us with
                 developing the system.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communication Design Quarterly Review",
  journal-URL =  "http://dl.acm.org/citation.cfm?id=J1351",
}

@Article{Khosravani:2015:DBC,
  author =       "Azar Khosravani and Constantin Rasinariu",
  title =        "$n$-digit {Benford} converges to {Benford}",
  journal =      j-INT-J-MATH-MATH-SCI,
  pages =        "Art. ID 123816, 4",
  year =         "2015",
  DOI =          "https://doi.org/10.1155/2015/123816",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "60F25 (11K45)",
  MRnumber =     "3442627",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
}

@Book{Kossovsky:2015:BLT,
  author =       "Alex Ely Kossovsky",
  title =        "{Benford's Law}: theory, the general law of relative
                 quantities, and forensic fraud detection applications",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xxi + 649",
  year =         "2015",
  DOI =          "https://doi.org/10.1142/9089",
  ISBN =         "981-4583-68-5 (hardcover), 981-4583-69-3 (e-book)",
  ISBN-13 =      "978-981-4583-68-8 (hardcover), 978-981-4583-69-5
                 (e-book)",
  LCCN =         "HV8079.F7 K67 2015",
  bibdate =      "Mon Feb 16 17:20:54 MST 2015",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  abstract =     "Contrary to common intuition that all digits should
                 occur randomly with equal chances in real data,
                 empirical examinations consistently show that not all
                 digits are created equal, but rather that low digits
                 such as {1, 2, 3} occur much more frequently than high
                 digits such as {7, 8, 9} in almost all data types, such
                 as those relating to geology, chemistry, astronomy,
                 physics, and engineering, as well as in accounting,
                 financial, econometrics, and demographics data sets.
                 This intriguing digital phenomenon is known as
                 Benford's Law. This book represents an attempt to give
                 a comprehensive and in-depth account of all the
                 theoretical aspects, results, causes and explanations
                 of Benford's Law, with a strong emphasis on the
                 connection to real-life data and the physical
                 manifestation of the law. In addition to such a bird's
                 eye view of the digital phenomenon, the conceptual
                 distinctions between digits, numbers, and quantities
                 are explored; leading to the key finding that the
                 phenomenon is actually quantitative in nature;
                 originating from the fact that in extreme generality,
                 nature creates many small quantities but very few big
                 quantities, corroborating the motto ``small is
                 beautiful'', and that therefore all this is applicable
                 just as well to data written in the ancient Roman,
                 Mayan, Egyptian, and other digit-less civilizations.
                 Fraudsters are typically not aware of this digital
                 pattern and tend to invent numbers with approximately
                 equal digital frequencies. The digital analyst can
                 easily check reported data for compliance with this
                 digital law, enabling the detection of tax evasion,
                 Ponzi schemes, and other financial scams. The forensic
                 fraud detection section in this book is written in a
                 very concise and reader-friendly style; gathering all
                 known methods and standards in the accounting and
                 auditing industry; summarizing and fusing them into a
                 singular coherent whole; and can be understood without
                 deep knowledge in statistical theory or advanced
                 mathematics. In addition, a digital algorithm is
                 presented, enabling the auditor to detect fraud even
                 when the sophisticated cheater is aware of the law and
                 invents numbers accordingly. The algorithm employs a
                 subtle inner digital pattern within the Benford's
                 pattern itself. This newly discovered pattern is deemed
                 to be nearly universal, being even more prevalent than
                 the Benford phenomenon, as it is found in all random
                 data sets, Benford as well as non-Benford types.",
  acknowledgement = ack-nhfb,
  subject =      "Fraud investigation; Statistical methods; Fraud;
                 Distribution (Probability theory); Forensic statistics;
                 Forensic sciences",
  tableofcontents = "1. Benford's law \\
                 2. Forensic digital analysis and fraud detection \\
                 3. Data compliance tests \\
                 4. Conceptual and mathematical foundations \\
                 5. Benford's law in the physical sciences \\
                 6. Topics in Benford's law \\
                 7. The law of Relative quantities",
}

@Article{Kozubowski:2015:DTP,
  author =       "Tomasz J. Kozubowski and Anna K. Panorska and Matthew
                 L. Forister",
  title =        "A discrete truncated {Pareto} distribution",
  journal =      j-STAT-METHODOL,
  volume =       "26",
  number =       "??",
  pages =        "135--150",
  month =        sep,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.stamet.2015.04.002",
  ISSN =         "1572-3127 (print), 1878-0954 (electronic)",
  ISSN-L =       "1572-3127",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statmethodol.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1572312715000313",
  abstract =     "We propose a new discrete distribution with finite
                 support, which generalizes truncated Pareto and beta
                 distributions as well as uniform and Benford's laws.
                 Although our focus is on basic properties and
                 stochastic representations, we also consider parameter
                 estimation and include an illustration from ecology
                 showing potential applications of this new stochastic
                 model.",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methodology",
  journal-URL =  "http://www.sciencedirect.com/science/journal/15723127/",
  keywords =     "Benford's Law; Beta distribution; Discrete Pareto;
                 Ecology; First digit law; Heavy tail; Maximum
                 likelihood estimation; Power law; Truncated geometric;
                 Truncated Pareto",
}

@Article{Kramer:2015:MJE,
  author =       "Walter Kr{\"a}mer",
  title =        "{Miller, S. J. (ed.): \booktitle{Benford's law. Theory
                 and applications}}",
  journal =      j-STAT-PAPERS,
  volume =       "56",
  number =       "4",
  pages =        "1251--1252",
  month =        nov,
  year =         "2015",
  CODEN =        "STPAE4",
  DOI =          "https://doi.org/10.1007/s00362-015-0717-8",
  ISSN =         "0932-5026 (print), 1613-9798 (electronic)",
  ISSN-L =       "0932-5026",
  bibdate =      "Tue Nov 17 09:38:07 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s00362-015-0717-8",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Papers",
  journal-URL =  "http://link.springer.com/journal/362",
}

@Article{Kudryashov:2015:APE,
  author =       "Nikolay A. Kudryashov and Anastasia S. Zakharchenko",
  title =        "Analytical properties and exact solutions of the
                 {Lotka--Volterra} competition system",
  journal =      j-APPL-MATH-COMP,
  volume =       "254",
  number =       "??",
  pages =        "219--228",
  day =          "1",
  month =        mar,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Feb 23 08:51:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314017743",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Lafouge:2015:DTP,
  author =       "Thierry Lafouge and Abdellatif Agouzal and Genevieve
                 Lallich",
  title =        "The deconstruction of a text: the permanence of the
                 generalized {Zipf} law --- the inter-textual
                 relationship between entropy and effort amount",
  journal =      j-SCIENTOMETRICS,
  volume =       "104",
  number =       "1",
  pages =        "193--217",
  month =        jul,
  year =         "2015",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-015-1600-z",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Wed Sep 2 12:06:12 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-015-1600-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@InCollection{Lee:2015:GBL,
  author =       "Joanne Lee and Wendy K. Tam Cho and George Judge",
  title =        "Generalizing {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "304--316",
  year =         "2015",
  MRclass =      "62P10",
  MRnumber =     "3411066",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Leemis:2015:BLG,
  author =       "Lawrence Leemis",
  title =        "{Benford's Law} geometry",
  crossref =     "Miller:2015:BLT",
  pages =        "109--118",
  year =         "2015",
  MRclass =      "62E17 (60E05)",
  MRnumber =     "3411059",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Lewis:2015:SDA,
  author =       "Peter R. Lewis and Lukas Esterle and Arjun Chandra and
                 Bernhard Rinner and Jim Torresen and Xin Yao",
  title =        "Static, Dynamic, and Adaptive Heterogeneity in
                 Distributed Smart Camera Networks",
  journal =      j-TAAS,
  volume =       "10",
  number =       "2",
  pages =        "8:1--8:??",
  month =        jun,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2764460",
  ISSN =         "1556-4665 (print), 1556-4703 (electronic)",
  ISSN-L =       "1556-4665",
  bibdate =      "Wed Jun 10 08:01:03 MDT 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/taas.bib",
  abstract =     "We study heterogeneity among nodes in self-organizing
                 smart camera networks, which use strategies based on
                 social and economic knowledge to target communication
                 activity efficiently. We compare homogeneous
                 configurations, when cameras use the same strategy,
                 with heterogeneous configurations, when cameras use
                 different strategies. Our first contribution is to
                 establish that static heterogeneity leads to new
                 outcomes that are more efficient than those possible
                 with homogeneity. Next, two forms of dynamic
                 heterogeneity are investigated: nonadaptive mixed
                 strategies and adaptive strategies, which learn online.
                 Our second contribution is to show that mixed
                 strategies offer Pareto efficiency consistently
                 comparable with the most efficient static heterogeneous
                 configurations. Since the particular configuration
                 required for high Pareto efficiency in a scenario will
                 not be known in advance, our third contribution is to
                 show how decentralized online learning can lead to more
                 efficient outcomes than the homogeneous case. In some
                 cases, outcomes from online learning were more
                 efficient than all other evaluated configuration types.
                 Our fourth contribution is to show that online learning
                 typically leads to outcomes more evenly spread over the
                 objective space. Our results provide insight into the
                 relationship between static, dynamic, and adaptive
                 heterogeneity, suggesting that all have a key role in
                 achieving efficient self-organization.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Autonomous and Adaptive Systems
                 (TAAS)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1010",
}

@Article{Li:2015:BBL,
  author =       "Qinglei Li and Zuntao Fu and Naiming Yuan",
  title =        "Beyond {Benford's Law}: Distinguishing Noise from
                 Chaos",
  journal =      j-PLOS-ONE,
  volume =       "10",
  number =       "6",
  pages =        "e0129161:1--e0129161:11",
  day =          "1",
  month =        jun,
  year =         "2015",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0129161",
  ISSN =         "1932-6203",
  bibdate =      "Wed Aug 12 08:58:10 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0129161",
  abstract =     "Determinism and randomness are two inherent aspects of
                 all physical processes. Time series from chaotic
                 systems share several features identical with those
                 generated from stochastic processes, which makes them
                 almost undistinguishable. In this paper, a new method
                 based on Benford's law is designed in order to
                 distinguish noise from chaos by only information from
                 the first digit of considered series. By applying this
                 method to discrete data, we confirm that chaotic data
                 indeed can be distinguished from noise data,
                 quantitatively and clearly.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
}

@Article{Lin:2015:DES,
  author =       "Cheng-Yen Lin and Chung-Wen Huang and Chi-Bang Kuan
                 and Shi-Yu Huang and Jenq-Kuen Lee",
  title =        "The Design and Experiments of a {SID}-Based
                 Power-Aware Simulator for Embedded Multicore Systems",
  journal =      j-TODAES,
  volume =       "20",
  number =       "2",
  pages =        "22:1--22:??",
  month =        feb,
  year =         "2015",
  CODEN =        "ATASFO",
  DOI =          "https://doi.org/10.1145/2699834",
  ISSN =         "1084-4309 (print), 1557-7309 (electronic)",
  ISSN-L =       "1084-4309",
  bibdate =      "Tue Mar 3 14:46:37 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/todaes/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/todaes.bib",
  abstract =     "Embedded multicore systems are playing increasingly
                 important roles in the design of consumer electronics.
                 The objective of such systems is to optimize both
                 performance and power characteristics of mobile
                 devices. However, currently there are no power metrics
                 supporting popular application design platforms (such
                 as SID) that application developers use to develop
                 their applications. This hinders the ability of
                 application developers to optimize power consumption.
                 In this article we present the design and experiments
                 of a SID-based power-aware simulation framework for
                 embedded multicore systems. The proposed power
                 estimation flow includes two phases: IP-level power
                 modeling and power-aware system simulation. The first
                 phase employs PowerMixer$^{IP}$ to construct the power
                 model for the processor IP and other major IPs, while
                 the second phase involves a power abstract
                 interpretation method for summarizing the simulation
                 trace, then, with a CPE module, estimating the power
                 consumption based on the summarized trace information
                 and the input of IP power models. In addition, a
                 Manager component is devised to map each digital signal
                 processor (DSP) component to a host thread and maintain
                 the access to shared resources. The aim is to maintain
                 the simulation performance as the number of simulated
                 DSP components increases. A power-profiling API is also
                 supported that developers of embedded software can use
                 to tune the granularity of power-profiling for a
                 specific code section of the target application. We
                 demonstrate via case studies and experiments how
                 application developers can use our SID-based power
                 simulator for optimizing the power consumption of their
                 applications. We characterize the power consumption of
                 DSP applications with the DSPstone benchmark and
                 discuss how compiler optimization levels with SIMD
                 intrinsics influence the performance and power
                 consumption. A histogram application and an
                 augmented-reality application based on human-face-based
                 RMS (recognition, mining, and synthesis) application
                 are deployed as running examples on multicore systems
                 to demonstrate how our power simulator can be used by
                 developers in the optimization process to illustrate
                 different views of power dissipations of
                 applications.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Design Automation of Electronic
                 Systems",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J776",
}

@Article{Liu:2015:ASN,
  author =       "Qun Liu",
  title =        "Analysis of a stochastic non-autonomous food-limited
                 {Lotka--Volterra} cooperative model",
  journal =      j-APPL-MATH-COMP,
  volume =       "254",
  number =       "??",
  pages =        "1--8",
  day =          "1",
  month =        mar,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Mon Feb 23 08:51:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300314018037",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Liu:2015:DSD,
  author =       "Qun Liu and Qingmei Chen",
  title =        "Dynamics of stochastic delay {Lotka--Volterra} systems
                 with impulsive toxicant input and {L{\'e}vy} noise in
                 polluted environments",
  journal =      j-APPL-MATH-COMP,
  volume =       "256",
  number =       "??",
  pages =        "52--67",
  day =          "1",
  month =        apr,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Feb 27 06:15:38 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315000235",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Liu:2015:SPA,
  author =       "Si Liu and Qiang Chen and Shuicheng Yan and Changsheng
                 Xu and Hanqing Lu",
  title =        "{Snap \& Play}: Auto-Generated Personalized
                 Find-the-Difference Game",
  journal =      j-TIST,
  volume =       "5",
  number =       "4",
  pages =        "65:1--65:??",
  month =        jan,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2668109",
  ISSN =         "2157-6904 (print), 2157-6912 (electronic)",
  ISSN-L =       "2157-6904",
  bibdate =      "Wed Feb 11 12:29:09 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tist.bib",
  abstract =     "In this article, by taking a popular game, the
                 Find-the-Difference (FiDi) game, as a concrete example,
                 we explore how state-of-the-art image processing
                 techniques can assist in developing a personalized,
                 automatic, and dynamic game. Unlike the traditional
                 FiDi game, where image pairs (source image and target
                 image) with five different patches are manually
                 produced by professional game developers, the proposed
                 Personalized FiDi (P-FiDi) electronic game can be
                 played in a fully automatic Snap \& Play mode. Snap
                 means that players first take photos with their digital
                 cameras. The newly captured photos are used as source
                 images and fed into the P-FiDi system to autogenerate
                 the counterpart target images for users to play. Four
                 steps are adopted to autogenerate target images:
                 enhancing the visual quality of source images,
                 extracting some changeable patches from the source
                 image, selecting the most suitable combination of
                 changeable patches and difference styles for the image,
                 and generating the differences on the target image with
                 state-of-the-art image processing techniques. In
                 addition, the P-FiDi game can be easily redesigned for
                 the im-game advertising. Extensive experiments show
                 that the P-FiDi electronic game is satisfying in terms
                 of player experience, seamless advertisement, and
                 technical feasibility.",
  acknowledgement = ack-nhfb,
  articleno =    "65",
  fjournal =     "ACM Transactions on Intelligent Systems and Technology
                 (TIST)",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J1318",
}

@Article{Llamocca:2015:DEP,
  author =       "Daniel Llamocca and Marios Pattichis",
  title =        "Dynamic Energy, Performance, and Accuracy Optimization
                 and Management Using Automatically Generated
                 Constraints for Separable {$2$D} {FIR} Filtering for
                 Digital Video Processing",
  journal =      j-TRETS,
  volume =       "7",
  number =       "4",
  pages =        "4:1--4:??",
  month =        jan,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2629623",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Fri Feb 13 07:24:19 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "There is strong interest in the development of
                 dynamically reconfigurable systems that can meet
                 real-time constraints on energy, performance, and
                 accuracy. The generation of real-time constraints will
                 significantly expand the applicability of dynamically
                 reconfigurable systems to new domains, such as digital
                 video processing. We develop a dynamically
                 reconfigurable 2D FIR filtering system that can meet
                 real-time constraints in energy, performance, and
                 accuracy (EPA). The real-time constraints are
                 automatically generated based on user input, image
                 types associated with video communications, and video
                 content. We first generate a set of Pareto-optimal
                 realizations, described by their EPA values and
                 associated 2D FIR hardware description bitstreams.
                 Dynamic management is then achieved by selecting
                 Pareto-optimal realizations that meet the automatically
                 generated time-varying EPA constraints. We validate our
                 approach using three different 2D Gaussian filters.
                 Filter realizations are evaluated in terms of the
                 required energy per frame, accuracy of the resulting
                 image, and performance in frames per second. We
                 demonstrate dynamic EPA management by applying a
                 Difference of Gaussians (DOG) filter to standard video
                 sequences. For video frame sizes that are equal to or
                 larger than the VGA resolution, compared to a static
                 implementation, our dynamic system provides significant
                 reduction in the total energy consumption
                 ({$>$30}\%).",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{LoBuglio:2015:WDT,
  author =       "David {Lo Buglio} and Vanessa Lardinois and Livio {De
                 Luca}",
  title =        "What Do Thirty-One Columns Say about a ``Theoretical''
                 Thirty-Second?",
  journal =      j-JOCCH,
  volume =       "8",
  number =       "1",
  pages =        "6:1--6:??",
  month =        feb,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2700425",
  ISSN =         "1556-4673 (print), 1556-4711 (electronic)",
  ISSN-L =       "1556-4673",
  bibdate =      "Wed Feb 25 17:50:15 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jocch/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jocch.bib",
  abstract =     "Over the past three decades, the introduction of
                 digital technologies in the field of architectural
                 documentation has profoundly changed tools and
                 acquisition techniques. Most of the developments
                 concern metrical and colorimetric characteristics of
                 the objects studied. These developments, surrounding
                 the practice of architectural survey, tend to respond
                 primarily to the requirements of completeness. In this
                 context, it seems necessary to assess the impact of
                 these instruments on the cognitive value of
                 architectural representation. With a strong
                 technological presence, the study of the built heritage
                 is facing a problem of ``information overload.''
                 Indeed, this strong technological presence fails to
                 strengthen representation in its role as a vehicle of
                 knowledge. Confronted with the intelligibility deficit,
                 this article proposes an original approach for reading
                 morphological features of an artifact by using a
                 bottom-up approach: the meaning of elements (i.e.,
                 their semantic layouts) come from a statistical
                 analysis of the major shape discontinuities of a
                 collection of instances. The idea is to rely on data
                 accumulation to render apparent high-level semantic
                 structures from the comparative analysis of common
                 low-level geometric features. The principles introduced
                 are illustrated by the study of 31 columns of the
                 cloister of the abbey of Saint-Michel-de-Cuxa. To
                 summarize, the first objective is to understand how
                 digital technologies can help us in the analysis of
                 artistic and technical production of Romanesque
                 columns. The second objective is to automatically
                 identify the common semantic articulations of the
                 entire collection to build a reference model for the
                 future assessment of each artifact.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "Journal on Computing and Cultural Heritage (JOCCH)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}

@Article{Luo:2015:IAD,
  author =       "Da Luo and Rui Yang and Jiwu Huang",
  title =        "Identification of {AMR} decompressed audio",
  journal =      "Digital Signal Processing",
  volume =       "37",
  number =       "0",
  pages =        "85--91",
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.dsp.2014.11.003",
  ISSN =         "1051-2004 (print), 1095-4333 (electronic)",
  ISSN-L =       "1051-2004",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1051200414003200",
  abstract =     "More and more conversation recordings from phone calls
                 are used as forensic evidence. To decide whether an
                 unknown speech recording comes from mobile phone or not
                 becomes an important issue in digital audio forensics.
                 The communicating conversation recorded by mobile
                 phones is encoded by Adaptive Multi-Rate (AMR) audio
                 codec, which was adopted as the standard speech codec
                 by 3GPP and widely used in {GSM} and UMTS. Therefore,
                 {AMR} decompressed audio detection can be used to
                 identify the source of the digital audio recording.
                 Furthermore, it is helpful to locate the forgery
                 position of the splicing {AMR} decompressed audio for
                 forensic purposes. In this article, we focus on the
                 identification of {AMR} decompressed audio, namely,
                 given the waveform of an audio, we wish to identify
                 whether it has been previously compressed by {AMR}
                 codec or not. The artifacts introduced by the {AMR}
                 codec will help to detect the source of the recordings.
                 Based on our analysis, we find that the sample
                 repetition rate of the {AMR} decompressed waveform is
                 significantly greater than the regular waveform.
                 Therefore, we employ the sample repetition rate as a
                 feature to identify the {AMR} decompressed audio. The
                 experimental results show that this feature is robust
                 and effective.",
  acknowledgement = ack-nhfb,
  keywords =     "Audio forensics; Benford's Law; Decompression audio
                 identification; Sample repetition rate; {AMR}",
}

@Article{Manack:2015:LDL,
  author =       "Corey Manack and Steven J. Miller",
  title =        "Leading digit laws on linear {Lie} groups",
  journal =      "Research in Number Theory",
  volume =       "1",
  number =       "1",
  pages =        "22:1--22:19",
  month =        dec,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s40993-015-0024-4",
  ISSN =         "2363-9555",
  ISSN-L =       "2363-9555",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s40993-015-0024-4",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/40993",
  keywords =     "Benford's Law; Digit laws; Haar measure; Matrix
                 groups",
}

@Article{Masse:2015:FGS,
  author =       "Bruno Mass{\'e} and Dominique Schneider",
  title =        "Fast growing sequences of numbers and the first digit
                 phenomenon",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "11",
  number =       "3",
  pages =        "705--719",
  month =        may,
  year =         "2015",
  DOI =          "https://doi.org/10.1142/S1793042115500384",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11K31 (11K06)",
  MRnumber =     "3327839",
  MRreviewer =   "Steven Joel Miller",
  bibdate =      "Tue Jan 26 11:14:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042115500384",
  abstract =     "We consider a large class of fast growing sequences of
                 numbers $ U_n $ like the nth superfactorial, the $n$-th
                 hyperfactorial and similar ones. We show that their
                 mantissas are distributed following Benford's law in
                 the sense of the natural density. We prove that this is
                 also verified by, by and is passed down to all the
                 sequences obtained by iterating this design process. We
                 also consider the superprimorial numbers and the
                 products of logarithms of integers.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{McCartney:2015:TSD,
  author =       "Mark McCartney and David H. Glass",
  title =        "A three-state dynamical model for religious
                 affiliation",
  journal =      j-PHYSICA-A,
  volume =       "419",
  number =       "0",
  pages =        "145--152",
  year =         "2015",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2014.09.052",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Wed Jan 28 10:08:12 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437114008206",
  abstract =     "In the last century the western world has seen a rapid
                 increase in the number of people describing themselves
                 as affiliated with no religious group. We construct a
                 set of models using coupled differential equations in
                 which members of a society can be in one of three
                 groups; religiously committed, religiously affiliated
                 or religiously not affiliated. These models are then
                 used to analyse post World War {II} census data for
                 Northern Ireland.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Benford's Law; Group behaviour; Nonlinear models;
                 Religion",
}

@InCollection{Mebane:2015:CVC,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Can vote counts' digits and {Benford's Law} diagnose
                 elections?",
  crossref =     "Miller:2015:BLT",
  pages =        "212--222",
  year =         "2015",
  MRclass =      "62P25 (91F10)",
  MRnumber =     "3411063",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Miller:2015:FAB,
  author =       "Steven J. Miller",
  title =        "{Fourier} analysis and {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "68--105",
  year =         "2015",
  DOI =          "https://doi.org/10.1515/9781400866595",
  MRclass =      "60-02 (42B37 60B20 60F05 60J65 62G30 62N01 62N03)",
  MRnumber =     "3411058",
  MRreviewer =   "Rita Giuliano Antonini",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Miller:2015:HSOa,
  author =       "Steven J. Miller",
  title =        "How a Simple Observation from the 1800s about Patterns
                 in Big Data Sets Can Fight Fraud",
  journal =      "The Conversation",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        dec,
  year =         "2015",
  bibdate =      "Mon Dec 14 09:36:50 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://theconversation.com/how-a-simple-observation-from-the-1800s-about-patterns-in-big-data-sets-can-fight-fraud-42683",
  acknowledgement = ack-nhfb,
}

@Article{Miller:2015:HSOb,
  author =       "Steven J. Miller",
  title =        "How a Simple Observation from the 1800s about Patterns
                 in Big Data Sets Can Fight Fraud",
  journal =      j-SCI-COMPUT,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "10",
  month =        dec,
  year =         "2015",
  CODEN =        "SCHRCU",
  ISSN =         "1930-5753 (print), 1930-6156 (electronic)",
  ISSN-L =       "1930-5753",
  bibdate =      "Mon Dec 14 09:36:50 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.scientificcomputing.com/articles/2015/12/how-simple-observation-1800s-about-patterns-big-data-sets-can-fight-fraud",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific Computing",
  journal-URL =  "http://digital.scientificcomputing.com/scientificcomputing/",
}

@InCollection{Miller:2015:QIB,
  author =       "Steven J. Miller",
  title =        "A quick introduction to {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "3--22",
  year =         "2015",
  DOI =          "https://doi.org/10.1515/9781400866595",
  MRclass =      "60-02 (60E05 62-02)",
  MRnumber =     "3411056",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Mishra:2015:PGMa,
  author =       "Nikita Mishra and Huazhe Zhang and John D. Lafferty
                 and Henry Hoffmann",
  title =        "A Probabilistic Graphical Model-based Approach for
                 Minimizing Energy Under Performance Constraints",
  journal =      j-COMP-ARCH-NEWS,
  volume =       "43",
  number =       "1",
  pages =        "267--281",
  month =        mar,
  year =         "2015",
  CODEN =        "CANED2",
  DOI =          "https://doi.org/10.1145/2786763.2694373",
  ISSN =         "0163-5964 (print), 1943-5851 (electronic)",
  ISSN-L =       "0163-5964",
  bibdate =      "Wed Jun 3 11:27:38 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigarch.bib",
  abstract =     "In many deployments, computer systems are
                 underutilized --- meaning that applications have
                 performance requirements that demand less than full
                 system capacity. Ideally, we would take advantage of
                 this under-utilization by allocating system resources
                 so that the performance requirements are met and energy
                 is minimized. This optimization problem is complicated
                 by the fact that the performance and power consumption
                 of various system configurations are often application
                 --- or even input --- dependent. Thus, practically,
                 minimizing energy for a performance constraint requires
                 fast, accurate estimations of application-dependent
                 performance and power tradeoffs. This paper
                 investigates machine learning techniques that enable
                 energy savings by learning Pareto-optimal power and
                 performance tradeoffs. Specifically, we propose LEO, a
                 probabilistic graphical model-based learning system
                 that provides accurate online estimates of an
                 application's power and performance as a function of
                 system configuration. We compare LEO to (1) offline
                 learning, (2) online learning, (3) a heuristic
                 approach, and (4) the true optimal solution. We find
                 that LEO produces the most accurate estimates and near
                 optimal energy savings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGARCH Computer Architecture News",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J89",
  remark =       "ASPLOS'15 conference proceedings.",
}

@Article{Mishra:2015:PGMb,
  author =       "Nikita Mishra and Huazhe Zhang and John D. Lafferty
                 and Henry Hoffmann",
  title =        "A Probabilistic Graphical Model-based Approach for
                 Minimizing Energy Under Performance Constraints",
  journal =      j-SIGPLAN,
  volume =       "50",
  number =       "4",
  pages =        "267--281",
  month =        apr,
  year =         "2015",
  CODEN =        "SINODQ",
  DOI =          "https://doi.org/10.1145/2775054.2694373",
  ISSN =         "0362-1340 (print), 1523-2867 (print), 1558-1160
                 (electronic)",
  ISSN-L =       "0362-1340",
  bibdate =      "Tue May 12 17:41:19 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/sigplan2010.bib",
  abstract =     "In many deployments, computer systems are
                 underutilized --- meaning that applications have
                 performance requirements that demand less than full
                 system capacity. Ideally, we would take advantage of
                 this under-utilization by allocating system resources
                 so that the performance requirements are met and energy
                 is minimized. This optimization problem is complicated
                 by the fact that the performance and power consumption
                 of various system configurations are often application
                 --- or even input --- dependent. Thus, practically,
                 minimizing energy for a performance constraint requires
                 fast, accurate estimations of application-dependent
                 performance and power tradeoffs. This paper
                 investigates machine learning techniques that enable
                 energy savings by learning Pareto-optimal power and
                 performance tradeoffs. Specifically, we propose LEO, a
                 probabilistic graphical model-based learning system
                 that provides accurate online estimates of an
                 application's power and performance as a function of
                 system configuration. We compare LEO to (1) offline
                 learning, (2) online learning, (3) a heuristic
                 approach, and (4) the true optimal solution. We find
                 that LEO produces the most accurate estimates and near
                 optimal energy savings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM SIGPLAN Notices",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J706",
  remark =       "ASPLOS '15 conference proceedings.",
}

@InCollection{Nigrini:2015:DFE,
  author =       "Mark Nigrini",
  title =        "Detecting fraud and errors using {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "191--211",
  year =         "2015",
  MRclass =      "62P20",
  MRnumber =     "3411062",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Noll:2015:FAO,
  author =       "Tobias N{\"o}ll and Johannes K{\"o}hler and Gerd Reis
                 and Didier Stricker",
  title =        "Fully Automatic, Omnidirectional Acquisition of
                 Geometry and Appearance in the Context of Cultural
                 Heritage Preservation",
  journal =      j-JOCCH,
  volume =       "8",
  number =       "1",
  pages =        "2:1--2:??",
  month =        feb,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2629693",
  ISSN =         "1556-4673 (print), 1556-4711 (electronic)",
  ISSN-L =       "1556-4673",
  bibdate =      "Wed Feb 25 17:50:15 MST 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jocch/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jocch.bib",
  abstract =     "Effective documentation and display of ancient objects
                 is an essential task in the field of cultural heritage
                 conservation. Digitization plays an important role in
                 the process of creating, preserving, and accessing
                 objects in digital space. Up to the present day,
                 industrial scanners are used for this task, which focus
                 mainly on the detailed reconstruction of the object's
                 geometry only. However, particularly important for a
                 faithful digital presentation of the object is the
                 appearance information-that is, a description of the
                 used materials and how they interact with incident
                 light. Using the world's first full-spherical scanner,
                 we propose a user-friendly reconstruction process that
                 is specifically tailored to the needs of digitizing and
                 representing cultural heritage artifacts. More
                 precisely, our hardware specifically addresses the
                 problem that invaluable or fragile artifacts may not be
                 turned over during acquisition. Nevertheless, we can
                 digitize the object completely, including its bottom.
                 Further, by integrating appearance information into our
                 digitization, we achieve a far more faithful digital
                 replica with a quality comparable to a real picture of
                 the object. But in contrast to a static picture, our
                 representation allows one to interactively change the
                 viewing and lighting directions freely. In addition,
                 the results are very memory efficient, consuming only
                 several megabytes per scanned object. In cooperation
                 with museums and a private collector, we digitized
                 several cultural heritage artifacts to demonstrate the
                 feasibility of the proposed process.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "Journal on Computing and Cultural Heritage (JOCCH)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}

@Article{Obradovic:2015:GFT,
  author =       "Marko Obradovi{\'c} and Milan Jovanovi{\'c} and Bojana
                 Milosevi{\'c}",
  title =        "Goodness-of-fit tests for {Pareto} distribution based
                 on a characterization and their asymptotics",
  journal =      j-STATISTICS,
  volume =       "49",
  number =       "5",
  pages =        "1026--1041",
  year =         "2015",
  CODEN =        "MOSSD5",
  DOI =          "https://doi.org/10.1080/02331888.2014.919297",
  ISSN =         "0233-1888 (print), 1029-4910 (electronic)",
  ISSN-L =       "0233-1888",
  bibdate =      "Wed Aug 19 08:16:20 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statistics.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics: A Journal of Theoretical and Applied
                 Statistics",
  journal-URL =  "http://www.tandfonline.com/loi/gsta20",
}

@InCollection{Perez-Gonzalez:2015:ABL,
  author =       "Fernando P{\'e}rez-Gonz{\'a}lez and Tu-Thach Quach and
                 Chaouki T. Abdallah and Gregory L. Heileman and Steven
                 J. Miller",
  title =        "Application of {Benford's Law} to images",
  crossref =     "Miller:2015:BLT",
  pages =        "338--370",
  year =         "2015",
  MRclass =      "62H35",
  MRnumber =     "3411068",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Raman:2015:CSC,
  author =       "Raghu Raman and Smrithi Venkatasubramanian and
                 Krishnashree Achuthan and Prema Nedungadi",
  title =        "Computer Science {(CS)} Education in {Indian} Schools:
                 Situation Analysis using {Darmstadt} Model",
  journal =      j-TOCE,
  volume =       "15",
  number =       "2",
  pages =        "7:1--7:??",
  month =        may,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2716325",
  ISSN =         "1946-6226",
  bibdate =      "Tue May 12 06:10:11 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/toce;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/toce.bib",
  abstract =     "Computer science (CS) and its enabling technologies
                 are at the heart of this information age, yet its
                 adoption as a core subject by senior secondary students
                 in Indian schools is low and has not reached critical
                 mass. Though there have been efforts to create core
                 curriculum standards for subjects like Physics,
                 Chemistry, Biology, and Math, CS seems to have been
                 kept outside the purview of such efforts leading to its
                 marginalization. As a first step, using the Darmstadt
                 model from the ITiCSE working group that provides a
                 systematic categorization approach to CS education in
                 schools, we coded and analyzed the CS situation for the
                 Indian schools. Next, we focused on the motivation
                 category of the Darmstadt model and investigated
                 behavioral intentions of secondary school students and
                 teachers from 332 schools in India. Considering the CS
                 subject as an educational innovation, using Rogers'
                 Theory of Diffusion of Innovations, we propose a
                 pedagogical framework for innovation attributes that
                 can significantly predict-adoption of the CS subject
                 among potential-adopter students and teachers. Data was
                 analyzed to answer research questions about student and
                 teacher intentions, influence of gender, school
                 management, and school location in adopting CS.
                 Interestingly, girls, urban students, teachers, and
                 private schools were seen favoring the adoption of CS.
                 An important issue that needed to be addressed,
                 however, was the interchangeable use of terms like CS,
                 Informatics, ICT, and digital literacy. Through our
                 article, we offer a promising picture of the
                 educational policy directives and the academic
                 environment in India that is rapidly growing and
                 embracing CS as a core subject of study in schools. We
                 also analyze the factors that influence the adoption of
                 CS by school students and teachers and conclude that
                 there is a very positive response for CS among
                 educators and students in India.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Computing Education",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1193",
}

@Article{Ribeiro:2015:MPE,
  author =       "Marco Tulio Ribeiro and Nivio Ziviani and Edleno
                 {Silva De Moura} and Itamar Hata and Anisio Lacerda and
                 Adriano Veloso",
  title =        "Multiobjective {Pareto}-Efficient Approaches for
                 Recommender Systems",
  journal =      j-TIST,
  volume =       "5",
  number =       "4",
  pages =        "53:1--53:??",
  month =        jan,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2629350",
  ISSN =         "2157-6904 (print), 2157-6912 (electronic)",
  ISSN-L =       "2157-6904",
  bibdate =      "Wed Feb 11 12:29:09 MST 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tist.bib",
  abstract =     "Recommender systems are quickly becoming ubiquitous in
                 applications such as e-commerce, social media channels,
                 and content providers, among others, acting as an
                 enabling mechanism designed to overcome the information
                 overload problem by improving browsing and consumption
                 experience. A typical task in many recommender systems
                 is to output a ranked list of items, so that items
                 placed higher in the rank are more likely to be
                 interesting to the users. Interestingness measures
                 include how accurate, novel, and diverse are the
                 suggested items, and the objective is usually to
                 produce ranked lists optimizing one of these measures.
                 Suggesting items that are simultaneously accurate,
                 novel, and diverse is much more challenging, since this
                 may lead to a conflicting-objective problem, in which
                 the attempt to improve a measure further may result in
                 worsening other measures. In this article, we propose
                 new approaches for multiobjective recommender systems
                 based on the concept of Pareto efficiency-a state
                 achieved when the system is devised in the most
                 efficient manner in the sense that there is no way to
                 improve one of the objectives without making any other
                 objective worse off. Given that existing multiobjective
                 recommendation algorithms differ in their level of
                 accuracy, diversity, and novelty, we exploit the
                 Pareto-efficiency concept in two distinct manners: (i)
                 the aggregation of ranked lists produced by existing
                 algorithms into a single one, which we call
                 Pareto-efficient ranking, and (ii) the weighted
                 combination of existing algorithms resulting in a
                 hybrid one, which we call Pareto-efficient
                 hybridization. Our evaluation involves two real
                 application scenarios: music recommendation with
                 implicit feedback (i.e., Last.fm) and movie
                 recommendation with explicit feedback (i.e.,
                 MovieLens). We show that the proposed Pareto-efficient
                 approaches are effective in suggesting items that are
                 likely to be simultaneously accurate, diverse, and
                 novel. We discuss scenarios where the system achieves
                 high levels of diversity and novelty without
                 compromising its accuracy. Further, comparison against
                 multiobjective baselines reveals improvements in terms
                 of accuracy (from 10.4\% to 10.9\%), novelty (from
                 5.7\% to 7.5\%), and diversity (from 1.6\% to 4.2\%).",
  acknowledgement = ack-nhfb,
  articleno =    "53",
  fjournal =     "ACM Transactions on Intelligent Systems and Technology
                 (TIST)",
  journal-URL =  "http://portal.acm.org/citation.cfm?id=J1318",
}

@InCollection{Roukema:2015:CBL,
  author =       "Boudewijn F. Roukema",
  title =        "Complementing {Benford's Law} for small {$N$}: a local
                 bootstrap",
  crossref =     "Miller:2015:BLT",
  pages =        "223--232",
  year =         "2015",
  MRclass =      "62P25 (62G09)",
  MRnumber =     "3411064",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Rubino:2015:ILB,
  author =       "Irene Rubino and Claudia Barberis and Jetmir Xhembulla
                 and Giovanni Malnati",
  title =        "Integrating a Location-Based Mobile Game in the Museum
                 Visit: Evaluating Visitors' Behaviour and Learning",
  journal =      j-JOCCH,
  volume =       "8",
  number =       "3",
  pages =        "15:1--15:??",
  month =        may,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2724723",
  ISSN =         "1556-4673 (print), 1556-4711 (electronic)",
  ISSN-L =       "1556-4673",
  bibdate =      "Tue May 12 07:01:13 MDT 2015",
  bibsource =    "http://www.acm.org/pubs/contents/journals/jocch/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jocch.bib",
  abstract =     "Location-based systems currently represent a suitable
                 solution to enhance cultural experiences inside
                 museums, as they can satisfy visitors' needs through
                 the provision of contextualized contents and services.
                 In this framework, a promising approach to captivate
                 the attention of teenagers-a hard to please target
                 audience-is represented by mobile serious games, such
                 as playful activities aiming to primarily fulfil
                 educational purposes. The use of a mobile digital tool
                 during the visit definitely discloses new opportunities
                 for contextual learning scenarios; however, so far,
                 only a few studies have analysed the impact of
                 different communication approaches on visitors' degree
                 of exploration and acquisition of knowledge. This work
                 aims to enrich this field of research, presenting the
                 conceptual framework; the design principles; and the
                 evaluation results of ``Gossip at palace,'' a
                 location-based mobile game integrating a storytelling
                 approach. The game was developed for an Italian
                 historical residence to communicate its 18th-century
                 history to teenagers, capitalizing on narrative and
                 game mechanics to foster young visitors' motivations to
                 explore the museum and facilitate their meaning-making
                 process. Following a mixed-methods perspective, the
                 article firstly describes to what extent the components
                 of the application were appreciated by teenagers as
                 well as by other visitor segments. Secondly, it
                 provides an insight on the effectiveness of the game in
                 facilitating the acquisition of historical knowledge by
                 participants, enriched by considerations on the methods
                 to be adopted when evaluating mobile learning in
                 informal educational settings. Thirdly, players' degree
                 of use of the digital game throughout the visit is
                 compared to analogous patterns registered for people
                 using a multimedia mobile guide in the same venue. On
                 the one hand, the study pointed out that the game
                 facilitated a wider exploration of the museum; on the
                 other, it highlighted that players mainly gained a
                 superficial knowledge of the proposed contents.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "Journal on Computing and Cultural Heritage (JOCCH)",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J1157",
}

@InCollection{Schurger:2015:LPB,
  author =       "Klaus Sch{\"u}rger",
  title =        "{L{\'e}vy} processes and {Benford's Law}",
  crossref =     "Miller:2015:BLT",
  pages =        "135--173",
  year =         "2015",
  MRclass =      "60G51 (60F10 60F15 62G10)",
  MRnumber =     "3411061",
  MRreviewer =   "Sreenivasan Ravi",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Serra:2015:POA,
  author =       "Edoardo Serra and Sushil Jajodia and Andrea Pugliese
                 and Antonino Rullo and V. S. Subrahmanian",
  title =        "{Pareto}-Optimal Adversarial Defense of Enterprise
                 Systems",
  journal =      j-TISSEC,
  volume =       "17",
  number =       "3",
  pages =        "11:1--11:??",
  month =        mar,
  year =         "2015",
  CODEN =        "ATISBQ",
  DOI =          "https://doi.org/10.1145/2699907",
  ISSN =         "1094-9224 (print), 1557-7406 (electronic)",
  ISSN-L =       "1094-9224",
  bibdate =      "Fri Mar 27 17:03:46 MDT 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tissec.bib",
  abstract =     "The National Vulnerability Database (NVD) maintained
                 by the US National Institute of Standards and
                 Technology provides valuable information about
                 vulnerabilities in popular software, as well as any
                 patches available to address these vulnerabilities.
                 Most enterprise security managers today simply patch
                 the most dangerous vulnerabilities-an adversary can
                 thus easily compromise an enterprise by using less
                 important vulnerabilities to penetrate an enterprise.
                 In this article, we capture the vulnerabilities in an
                 enterprise as a Vulnerability Dependency Graph (VDG)
                 and show that attacks graphs can be expressed in them.
                 We first ask the question: What set of vulnerabilities
                 should an attacker exploit in order to maximize his
                 expected impact? We show that this problem can be
                 solved as an integer linear program. The defender would
                 obviously like to minimize the impact of the worst-case
                 attack mounted by the attacker-but the defender also
                 has an obligation to ensure a high productivity within
                 his enterprise. We propose an algorithm that finds a
                 Pareto-optimal solution for the defender that allows
                 him to simultaneously maximize productivity and
                 minimize the cost of patching products on the
                 enterprise network. We have implemented this framework
                 and show that runtimes of our computations are all
                 within acceptable time bounds even for large VDGs
                 containing 30K edges and that the balance between
                 productivity and impact of attacks is also
                 acceptable.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Information and System Security",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J789",
}

@InProceedings{Singh:2015:ABL,
  author =       "N. Singh and R. Bansal",
  booktitle =    "Signal Processing and Communication (ICSC), 2015
                 International Conference on",
  title =        "Analysis of {Benford's Law} in digital image
                 forensics",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "413--418",
  month =        mar,
  year =         "2015",
  DOI =          "https://doi.org/10.1109/ICSPCom.2015.7150688",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford law; Benford's law; compression; data
                 compression; data detection; data recovery; digital
                 image forensics; Digital images; Discrete cosine
                 transforms; Discrete wavelet transforms; Forensics;
                 Image coding; image coding; image compression; image
                 forensics; image registration; JPEG2000; Q-factor;
                 tampering detection; Transform coding",
}

@Article{Slepkov:2015:BLT,
  author =       "Aaron D. Slepkov and Kevin B. Ironside and David
                 DiBattista",
  title =        "{Benford's Law}: Textbook Exercises and
                 Multiple-Choice Testbanks",
  journal =      j-PLOS-ONE,
  volume =       "10",
  number =       "2",
  pages =        "e0117972:1--e0117972:13",
  day =          "17",
  month =        feb,
  year =         "2015",
  CODEN =        "POLNCL",
  DOI =          "https://doi.org/10.1371/journal.pone.0117972",
  ISSN =         "1932-6203",
  bibdate =      "Wed Aug 12 08:59:52 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0117972",
  abstract =     "Benford's Law describes the finding that the
                 distribution of leading (or leftmost) digits of
                 innumerable datasets follows a well-defined logarithmic
                 trend, rather than an intuitive uniformity. In practice
                 this means that the most common leading digit is 1,
                 with an expected frequency of 30.1\%, and the least
                 common is 9, with an expected frequency of 4.6\%.
                 Currently, the most common application of Benford's Law
                 is in detecting number invention and tampering such as
                 found in accounting-, tax-, and voter-fraud. We
                 demonstrate that answers to end-of-chapter exercises in
                 physics and chemistry textbooks conform to Benford's
                 Law. Subsequently, we investigate whether this fact can
                 be used to gain advantage over random guessing in
                 multiple-choice tests, and find that while testbank
                 answers in introductory physics closely conform to
                 Benford's Law, the testbank is nonetheless secure
                 against such a Benford's attack for banal reasons.",
  acknowledgement = ack-nhfb,
  fjournal =     "PLoS One",
  journal-URL =  "http://www.plosone.org/",
}

@Article{VanCaneghem:2015:NFSa,
  author =       "Tom {Van Caneghem}",
  title =        "{NPO} Financial Statement Quality: An Empirical
                 Analysis Based on {Benford's Law}",
  journal =      "VOLUNTAS: International Journal of Voluntary and
                 Nonprofit Organizations",
  volume =       "26",
  number =       "1",
  pages =        "1--24",
  month =        feb,
  year =         "2015",
  DOI =          "https://doi.org/10.1007/s11266-015-9629-4",
  ISSN =         "0957-8765 (print), 1573-7888 (electronic)",
  ISSN-L =       "0957-8765",
  bibdate =      "Wed Aug 12 10:03:53 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11266-015-9629-4",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://link.springer.com/journal/11266",
  keywords =     "Benford's Law; Digital analysis; Financial reporting;
                 Financial statements; Non-profit organizations",
}

@Article{VanCaneghem:2015:NFSb,
  author =       "Tom {Van Caneghem}",
  title =        "{NPO} Financial Statement Quality: An Empirical
                 Analysis Based on {Benford's Law}",
  journal =      "{VOLUNTAS}: International Journal of Voluntary and
                 Nonprofit Organizations",
  volume =       "27",
  number =       "6",
  pages =        "2685--2708",
  month =        aug,
  year =         "2015",
  DOI =          "https://doi.org/10.1007/s11266-015-9629-4",
  ISSN =         "0957-8765 (print), 1573-7888 (electronic)",
  ISSN-L =       "0957-8765",
  bibdate =      "Wed Jun 20 15:13:31 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://link.springer.com/journal/11266",
}

@Article{Wang:2015:SPW,
  author =       "Xiaohuan Wang",
  title =        "Stability of planar waves in a {Lotka--Volterra}
                 system",
  journal =      j-APPL-MATH-COMP,
  volume =       "259",
  number =       "??",
  pages =        "313--326",
  day =          "15",
  month =        may,
  year =         "2015",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Apr 24 18:27:24 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2015.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300315002398",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}

@Article{Whyman:2015:ICC,
  author =       "G. Whyman and E. Shulzinger and Ed. Bormashenko",
  title =        "Intuitive considerations clarifying the origin and
                 applicability of the {Benford Law}",
  journal =      "arXiv.org",
  volume =       "??",
  number =       "??",
  pages =        "12",
  day =          "25",
  month =        oct,
  year =         "2015",
  bibdate =      "Tue Jan 26 09:53:36 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1510.07220v2",
  acknowledgement = ack-nhfb,
}

@Article{Woods:2015:PDP,
  author =       "Louis Woods and Gustavo Alonso and Jens Teubner",
  title =        "Parallelizing Data Processing on {FPGAs} with Shifter
                 Lists",
  journal =      j-TRETS,
  volume =       "8",
  number =       "2",
  pages =        "7:1--7:??",
  month =        apr,
  year =         "2015",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2629551",
  ISSN =         "1936-7406 (print), 1936-7414 (electronic)",
  ISSN-L =       "1936-7406",
  bibdate =      "Tue May 19 17:05:20 MDT 2015",
  bibsource =    "http://portal.acm.org/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/trets.bib",
  abstract =     "Parallelism is currently seen as a mechanism to
                 minimize the impact of the power and heat dissipation
                 problems encountered in modern hardware. Data
                 parallelism-based on partitioning the data-and pipeline
                 parallelism-based on partitioning the computation-are
                 the two main approaches to leverage parallelism on a
                 wide range of hardware platforms. Unfortunately, not
                 all data processing problems are susceptible to either
                 of those strategies. An example is the skyline operator
                 [B{\"o}rzs{\"o}nyi et al. 2001], which computes the set
                 of Pareto-optimal points within a multidimensional
                 dataset. Existing approaches to parallelize the skyline
                 operator are based on data parallelism. As a result,
                 they suffer from a high overhead when merging
                 intermediate results because of the lack of a global
                 view of the problem inherent to partitioning the input
                 data. In this article, we show how to combine pipeline
                 with data parallelism on a Field-Programmable Gate
                 Array (FPGA) for a more efficient utilization of the
                 available hardware parallelism. As we show in our
                 experiments, skyline computation using our proposed
                 technique scales linearly with the number of processing
                 elements, and the performance we achieve on a rather
                 small FPGA is comparable to that of a 64-core high-end
                 server running a state-of-the-art data parallel
                 implementation of skyline [Park et al. 2009]. The
                 proposed approach to parallelize the skyline operator
                 can be generalized to a wider range of data processing
                 problems. We demonstrate this through a novel, highly
                 parallel data structure, a shifter list, that can be
                 efficiently implemented on an FPGA. The resulting
                 template is easy to parametrize to implement a variety
                 of computationally intensive operators such as frequent
                 items, n -closest pairs, or K-means.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Reconfigurable Technology and
                 Systems (TRETS)",
  journal-URL =  "http://portal.acm.org/toc.cfm?id=J1151",
}

@Article{Yang:2015:ERP,
  author =       "Ziyun Yang and Xiaobo Dong",
  title =        "Earnings roundup in private and public bank holding
                 companies",
  journal =      "Advances in Accounting",
  volume =       "31",
  number =       "1",
  pages =        "96--99",
  year =         "2015",
  DOI =          "https://doi.org/10.1016/j.adiac.2015.03.004",
  ISSN =         "0882-6110",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S088261101500005X",
  abstract =     "In this study, we compare the relative tendencies of
                 public versus private firms to round up earnings in a
                 setting of the banking industry. This industry consists
                 of a large number of public and private bank holding
                 companies (BHCs) that face the same regulation
                 environment. In both the full sample and the
                 size-matched sample, we find evidence that public BHCs
                 show a greater tendency to round up the second digit of
                 earnings than do private BHCs. Our study contributes to
                 the current debate on the financial reporting quality
                 of public versus private firms by providing evidence
                 supporting the opportunistic behavior hypothesis.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; Earnings roundup; Reporting quality",
}

@Article{Zhao:2015:UCA,
  author =       "Peng Zhao and Engui Fan",
  title =        "A unified construction for the algebro-geometric
                 quasiperiodic solutions of the {Lotka--Volterra} and
                 relativistic {Lotka--Volterra} hierarchy",
  journal =      j-J-MATH-PHYS,
  volume =       "56",
  number =       "4",
  pages =        "043501",
  month =        apr,
  year =         "2015",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.4916676",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Tue Aug 4 09:20:02 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2015.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}

@Article{Zornig:2015:ZLR,
  author =       "Peter Z{\"o}rnig",
  title =        "{Zipf}'s law for randomly generated frequencies:
                 explicit tests for the goodness-of-fit",
  journal =      j-J-STAT-COMPUT-SIMUL,
  volume =       "85",
  number =       "11",
  pages =        "2202--2213",
  year =         "2015",
  CODEN =        "JSCSAJ",
  DOI =          "https://doi.org/10.1080/00949655.2014.925113",
  ISSN =         "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
  ISSN-L =       "0094-9655",
  bibdate =      "Tue Jun 9 05:53:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Computation and Simulation",
  journal-URL =  "http://www.tandfonline.com/loi/gscs20",
}

@Article{Alves:2016:ABI,
  author =       "Alexandre Donizeti Alves and Horacio Hideki Yanasse
                 and Nei Yoshihiro Soma",
  title =        "An analysis of bibliometric indicators to {JCR}
                 according to {Benford's Law}",
  journal =      j-SCIENTOMETRICS,
  volume =       "107",
  number =       "3",
  pages =        "1489--1499",
  month =        jun,
  year =         "2016",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-016-1908-3",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Mon May 16 16:03:17 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/content/pdf/10.1007/s11192-016-1908-3.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
  keywords =     "Journal Citation Reports (JCR)",
}

@Article{Amir:2016:SNE,
  author =       "Ariel Amir and Mikhail Lemeshko and Tadashi Tokieda",
  title =        "Surprises in Numerical Expressions of Physical
                 Constants",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "123",
  number =       "6",
  pages =        "609--612",
  month =        jun,
  year =         "2016",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.4169/amer.math.monthly.123.6.609",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jun 20 14:16:05 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/amermathmonthly2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.jstor.org/stable/10.4169/amer.math.monthly.123.6.609",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
  keywords =     "Benford's Law; experimental mathematics",
  remark =       "This paper looks at the probability that a particular
                 numerical physical constant is generated by a simple
                 expression involving a few mathematical constants. It
                 also discusses Benford's Law.",
}

@Article{Ausloos:2016:QQP,
  author =       "Marcel Ausloos and Olgica Nedic and Agata Fronczak and
                 Piotr Fronczak",
  title =        "Quantifying the quality of peer reviewers through
                 {Zipf}'s law",
  journal =      j-SCIENTOMETRICS,
  volume =       "106",
  number =       "1",
  pages =        "347--368",
  month =        jan,
  year =         "2016",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-015-1704-5",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Sat Jan 16 07:09:36 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/article/10.1007/s11192-015-1704-5",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Ausloos:2016:RDC,
  author =       "Marcel Ausloos and Rosella Castellano and Roy
                 Cerqueti",
  title =        "Regularities and discrepancies of credit default
                 swaps: a data science approach through {Benford}'s
                 law",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "90",
  pages =        "8--17",
  month =        sep,
  year =         "2016",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2016.03.002",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  bibdate =      "Tue May 22 16:45:20 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
}

@Article{Berger:2016:CBL,
  author =       "Arno Berger and Gideon Eshun",
  title =        "A characterization of {Benford's Law} in discrete-time
                 linear systems",
  journal =      j-J-DYN-DIFFER-EQU,
  volume =       "28",
  number =       "2",
  pages =        "431--469",
  year =         "2016",
  CODEN =        "JDDEEH",
  DOI =          "https://doi.org/10.1007/s10884-014-9393-y",
  ISSN =         "1040-7294 (print), 1572-9222 (electronic)",
  ISSN-L =       "1040-7294",
  MRclass =      "37A45 (11J71 37A05)",
  MRnumber =     "3500397",
  MRreviewer =   "Joseph Andrew Vandehey",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Dynamics and Differential Equations",
}

@Article{Bormashenko:2016:BLA,
  author =       "Ed. Bormashenko and E. Shulzinger and G. Whyman and
                 Ye. Bormashenko",
  title =        "{Benford's Law}, its applicability and breakdown in
                 the {IR} spectra of polymers",
  journal =      j-PHYSICA-A,
  volume =       "444",
  number =       "??",
  pages =        "524--529",
  year =         "2016",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2015.10.090",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0378437115009498",
  abstract =     "Infrared spectra of various polymers were treated
                 statistically. It was established that for the
                 absorbance spectra the Benford distribution of leading
                 digits takes place, whereas the distribution of leading
                 digits for transmittance spectra is random. This
                 observation may be explained by the fact that the value
                 of transmittance $ T_r $ is restricted $ 0 < T_r < 1 $,
                 due to the physical reasons, whereas the value of
                 absorbance is not. Moreover, the transmittance and
                 absorbance $A$ are interrelated by the logarithmic
                 dependence $ A = \log T_r$. This observation supplies
                 the idea that the Benford law is valid in the
                 situations, when logarithmic dependencies take place.
                 Amalgamation of spectral data obtained for various
                 polymers brings the distribution of the leading digits
                 in the absorbance domain into proximity to the Benford
                 Law.",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
  keywords =     "Absorbance; Benford's Law; Infrared spectra of
                 polymers; Transmittance",
}

@Article{Chen:2016:LBS,
  author =       "Evan Chen and Peter S. Park and Ashvin A.
                 Swaminathan",
  title =        "On logarithmically {Benford} sequences",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "144",
  number =       "11",
  pages =        "4599--4608",
  year =         "2016",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/proc/13112",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "11F11 (11N05)",
  MRnumber =     "3544512",
  MRreviewer =   "Ping Xi",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Friar:2016:UBL,
  author =       "J. L. Friar and T. Goldman and J. P{\'e}rez-Mercader",
  title =        "Ubiquity of {Benford's Law} and emergence of the
                 reciprocal distribution",
  journal =      j-PHYS-LET-A,
  volume =       "380",
  number =       "22--23",
  pages =        "1895--1899",
  year =         "2016",
  CODEN =        "PYLAAG",
  DOI =          "https://doi.org/10.1016/j.physleta.2016.03.045",
  ISSN =         "0375-9601 (print), 1873-2429 (electronic)",
  ISSN-L =       "0375-9601",
  MRclass =      "60E05 (94A15)",
  MRnumber =     "3489018",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Letters. A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03759601",
}

@InCollection{Frunza:2016:CBL,
  author =       "Marius-Christian Frunza",
  editor =       "Marius-Christian Frunza",
  booktitle =    "Solving Modern Crime in Financial Markets",
  title =        "{Benford's Law}",
  chapter =      "2K",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  bookpages =    "528",
  pages =        "233--245",
  year =         "2016",
  DOI =          "https://doi.org/10.1016/B978-0-12-804494-0.00017-6",
  ISBN =         "0-12-804494-2 (hardcover), 0-12-804532-9 (e-book)",
  ISBN-13 =      "978-0-12-804494-0 (hardcover), 978-0-12-804532-9
                 (e-book)",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/B9780128044940000176",
  abstract =     "Since the seminal work published by Nigrini in 1992,
                 Benford's Law has been employed as a forensic
                 accounting tool that is currently used as evidence in
                 many courts. The application to cases of fraud on
                 financial markets is still new, but successful
                 applications have been illustrated, in particular in
                 the case of the LIBOR manipulation. The field of
                 application for Benford's Law in the financial markets
                 is growing as many data sets can be the target of
                 manipulation or misrepresentation. Therefore, the test
                 assessing conformity with Benford's Law can emphasize
                 fictitious figures resulting from manual handling of
                 data in areas like fund performance metrics,
                 benchmarks, and index values or prices of niche
                 commodity markets.",
  acknowledgement = ack-nhfb,
  keywords =     "Chi-square test; Digit manipulation; First digit;
                 Second digit",
}

@InCollection{Garrabrant:2016:ALU,
  author =       "Scott Garrabrant and Tsvi Benson-Tilsen and Siddharth
                 Bhaskar and Abram Demski and Joanna Garrabrant and
                 George Koleszarik and Evan Lloyd",
  booktitle =    "Artificial General Intelligence ({AGI 2016})",
  title =        "Asymptotic Logical Uncertainty and the {Benford}
                 Test",
  volume =       "9782",
  publisher =    "Springer International Publishing",
  address =      "Cham, Switzerland",
  pages =        "202--211",
  year =         "2016",
  DOI =          "https://doi.org/10.1007/978-3-319-41649-6_20",
  ISBN =         "3-319-41648-0 (print), 3-319-41649-9 (e-book)",
  ISBN-13 =      "978-3-319-41648-9 (print), 978-3-319-41649-6
                 (e-book)",
  bibdate =      "Wed Jun 20 15:26:46 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@Article{Goodman:2016:PPB,
  author =       "William Goodman",
  title =        "The promises and pitfalls of {Benford}'s law",
  journal =      j-SIGNIF,
  volume =       "13",
  number =       "3",
  pages =        "38--41",
  month =        jun,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1111/j.1740-9713.2016.00919.x",
  ISSN =         "1740-9705 (print), 1740-9713 (electronic)",
  ISSN-L =       "1740-9705",
  bibdate =      "Thu Aug 13 12:04:02 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/significance.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Signif.",
  fjournal =     "Significance",
  journal-URL =  "https://rss.onlinelibrary.wiley.com/journal/17409713",
  onlinedate =   "06 June 2016",
}

@Book{Guttag:2016:ICP,
  author =       "John Guttag",
  title =        "Introduction to Computation and Programming Using
                 {Python}: with Application to Understanding Data",
  publisher =    pub-MIT,
  address =      pub-MIT:adr,
  edition =      "Second",
  pages =        "xvii + 447",
  year =         "2016",
  ISBN =         "0-262-52962-9 (paperback), 0-262-33738-X (e-book)",
  ISBN-13 =      "978-0-262-52962-4 (paperback), 978-0-262-33738-0
                 (e-book)",
  LCCN =         "QA76.73.P98 G88 2016",
  bibdate =      "Tue Jun 5 11:01:20 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "This book introduces students with little or no prior
                 programming experience to the art of computational
                 problem solving using Python and various Python
                 libraries, including PyLab. It provides students with
                 skills that will enable them to make productive use of
                 computational techniques, including some of the tools
                 and techniques of data science for using computation to
                 model and interpret data. The book is based on an MIT
                 course (which became the most popular course offered
                 through MIT's OpenCourseWare) and was developed for use
                 not only in a conventional classroom but in a massive
                 open online course (MOOC). This new edition has been
                 updated for Python 3, reorganized to make it easier to
                 use for courses that cover only a subset of the
                 material, and offers additional material including five
                 new chapters. Students are introduced to Python and the
                 basics of programming in the context of such
                 computational concepts and techniques as exhaustive
                 enumeration, bisection search, and efficient
                 approximation algorithms. Although it covers such
                 traditional topics as computational complexity and
                 simple algorithms, the book focuses on a wide range of
                 topics not found in most introductory texts, including
                 information visualization, simulations to model
                 randomness, computational techniques to understand
                 data, and statistical techniques that inform (and
                 misinform) as well as two related but relatively
                 advanced topics: optimization problems and dynamic
                 programming. This edition offers expanded material on
                 statistics and machine learning and new chapters on
                 Frequentist and Bayesian statistics.",
  acknowledgement = ack-nhfb,
  subject =      "Python (Computer program language); Textbooks;
                 Computer programming",
  tableofcontents = "Preface \\
                 1. Introduction \\
                 2: Introduction to Python: The basic elements of Python
                 \\
                 Objects, expressions, and numerical types \\
                 Variables and assignment \\
                 Python IDE's \\
                 Branching programs \\
                 Strings and input \\
                 Input \\
                 A digression about character encoding \\
                 Iteration \\
                 3: Some simple numerical programs: Exhaustive
                 enumeration \\
                 For loops \\
                 Approximate solutions and bisection search \\
                 Few words about using floats \\
                 Newton--Raphson \\
                 4: Functions, scoping, and abstraction: Functions and
                 scoping \\
                 Function definitions \\
                 Keyword arguments and default values \\
                 Scoping \\
                 Specifications \\
                 Recursion \\
                 Fibonacci numbers \\
                 Palindromes \\
                 Global variables \\
                 Modules \\
                 Files \\
                 5: Structured types, mutability, and higher-order
                 functions: Tuples \\
                 Sequences and multiple assignment \\
                 Ranges \\
                 Lists and mutability \\
                 Cloning \\
                 List comprehension \\
                 Functions as objects \\
                 Strings, tuples, ranges, and lists \\
                 Dictionaries \\
                 6: Testing and debugging: Testing \\
                 Black-box testing \\
                 Glass-box testing \\
                 Conducting tests \\
                 Debugging \\
                 Learning to debug \\
                 Designing the experiment \\
                 When the going gets tough \\
                 When you have found ``the'' bug \\
                 7: Exceptions and assertions: Handling exceptions \\
                 Exceptions as a control flow mechanism \\
                 Assertions \\
                 8: Classes and object-oriented programming: Abstract
                 data types and classes \\
                 Designing programs using abstract data types \\
                 Using classes to keep track of students and faculty \\
                 Inheritance \\
                 Multiple levels of inheritance \\
                 Substitution principle \\
                 Encapsulation and information hiding \\
                 Generators \\
                 Mortgages, an extended example \\
                 9: A simplistic introduction to algorithmic complexity:
                 Thinking about computational complexity \\
                 Asymptotic notation \\
                 Some important complexity classes \\
                 Constant complexity \\
                 Logarithmic complexity \\
                 Linear complexity \\
                 Log-linear complexity \\
                 Polynomial complexity \\
                 Exponential complexity \\
                 Comparisons of complexity classes \\
                 10: Some simple algorithms and data structures: Search
                 algorithms \\
                 Linear search and using indirection to access elements
                 \\
                 Binary search and exploiting assumptions \\
                 Sorting algorithms \\
                 Merge sort \\
                 Exploiting functions as parameters \\
                 Sorting in Python \\
                 Hash tables \\
                 11: Plotting and more about classes: Plotting using
                 PyLab \\
                 Plotting mortgages, an extended example \\
                 12: Knapsack and graph optimization problems: Knapsack
                 problems \\
                 Greedy algorithms \\
                 Optimal solution to the 0/1 Knapsack problem \\
                 Graph optimization problems \\
                 Some classic graph-theoretic problems \\
                 Shortest path: depth-first search and breadth-first
                 search \\
                 13: Dynamic programming: Fibonacci sequences, revisited
                 \\
                 Dynamic programming and the 0/1 Knapsack problem \\
                 Dynamic programming and divide-and-conquer \\
                 14: Random walks and more about data visualization:
                 Random walks \\
                 The drunkard's walk \\
                 Biased random walks \\
                 Treacherous fields \\
                 15: Stochastic programs, probability, and
                 distributions: Stochastic programs \\
                 Calculating simple probabilities \\
                 Inferential statistics \\
                 Distributions \\
                 Probability distributions \\
                 Normal distributions \\
                 Continuous and discrete uniform distributions \\
                 Binomial and multinomial distributions \\
                 Exponential and geometric distributions \\
                 Benford's distribution \\
                 Hashing and collisions \\
                 How often does the better team win? \\
                 16: Monte Carlo stimulation: Pascal's problem \\
                 Pass or don't pass? \\
                 Using table lookup to improve performance \\
                 Finding pi \\
                 Some closing remarks about simulation models \\
                 17: Sampling and confidence intervals: Sampling the
                 Boston Marathon \\
                 Central limit theorem \\
                 Standard error of the mean \\
                 18: Understanding experimental data: The behavior of
                 springs \\
                 Using linear regression to find a fit \\
                 The behavior of projectiles \\
                 Coefficient of determination \\
                 Using a computational model \\
                 Fitting exponentially distributed data \\
                 When theory is missing \\
                 19: Randomized trials and hypothesis checking: Checking
                 significance \\
                 Beware of P-values \\
                 One-tail and one-sample tests \\
                 Significant or not? \\
                 Which N? \\
                 Multiple hypotheses \\
                 20: Conditional probability and Bayesian statistics. :
                 Conditional probabilities \\
                 Bayes' theorem \\
                 Bayesian updating \\
                 21: Lies, damned lies, and statistics: Garbage in
                 garbage out (GIGO) \\
                 Tests are imperfect \\
                 Pictures can be deceiving \\
                 Cum hoc ergo propter hoc \\
                 Statistical measures don't tell the whole story \\
                 Sampling bias \\
                 Context matters \\
                 Beware of extrapolation \\
                 Texas sharpshooter fallacy \\
                 Percentages can confuse \\
                 Statistically significant differences can be
                 insignificant \\
                 Regressive fallacy \\
                 Just beware \\
                 22: A quick look at machine learning: Feature vectors
                 \\
                 Distance metrics \\
                 23: Clustering: Class cluster \\
                 K-means clustering \\
                 A contrived example \\
                 A less contrived example \\
                 24: Classification methods: Evaluating classifiers \\
                 Predicting the gender of runners \\
                 K-nearest neighbors \\
                 Regression-based classifiers \\
                 Surviving the Titanic \\
                 Wrapping up \\
                 Python 3.5 quick reference",
}

@Article{Hill:2016:HLI,
  author =       "Theodore P. Hill and Ronald F. Fox",
  title =        "{Hubble's Law} Implies {Benford's Law} for Distances
                 to Galaxies",
  journal =      j-J-ASTROPHYS-ASTRON,
  volume =       "37",
  number =       "1",
  pages =        "??--??",
  month =        feb,
  year =         "2016",
  CODEN =        "JASRD7",
  DOI =          "https://doi.org/10.1007/s12036-016-9373-1",
  ISSN =         "0250-6335 (print), 0973-7758 (electronic)",
  ISSN-L =       "0250-6335",
  bibdate =      "Wed Jun 20 15:21:17 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "See \cite{Alexopoulos:2014:BLA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Astrophysics and Astronomy",
  journal-URL =  "http://www.springerlink.com/content/0250-6335",
  pagecount =    "4",
}

@Article{Hoppe:2016:BLD,
  author =       "Fred M. Hoppe",
  title =        "{Benford's Law} and distractors in multiple choice
                 exams",
  journal =      j-INT-J-MATH-EDU-SCI-TECH,
  volume =       "47",
  number =       "4",
  pages =        "606--612",
  year =         "2016",
  CODEN =        "IJMEBM",
  DOI =          "https://doi.org/10.1080/0020739X.2015.1091515",
  ISSN =         "0020-739x (print), 1464-5211 (electronic)",
  ISSN-L =       "0020-739X",
  MRclass =      "60C05",
  MRnumber =     "3484057",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematical Education in
                 Science and Technology",
  journal-URL =  "http://www.tandfonline.com/loi/tmes20",
}

@Article{Jameson:2016:BLC,
  author =       "Marie Jameson and Jesse Thorner and Lynnelle Ye",
  title =        "{Benford's Law} for coefficients of newforms",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "12",
  number =       "2",
  pages =        "483--494",
  month =        mar,
  year =         "2016",
  DOI =          "https://doi.org/10.1142/S1793042116500299",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11F11 (11F30 11K06)",
  MRnumber =     "3461444",
  MRreviewer =   "Bingrong Huang",
  bibdate =      "Sat Mar 25 08:28:06 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042116500299",
  abstract =     "Let $ f(z) = \sum_{n = 1}^\infty \lambda_f(n) e^P{2
                 \pi i n z} \in S_k^{\mathrm {new}}(\Gamma_0 (N)) $ be a
                 newform of even weight $ k \geq 2 $ on $ \Gamma_0 (N) $
                 without complex multiplication. Let $P$ denote the set
                 of all primes. We prove that the sequence $ \{
                 \lambda_f(p) \}_{p \in P}$ does not satisfy Benford s
                 Law in any integer base $ b \geq 2$. However, given a
                 base $ b \geq 2$ and a string of digits $S$ in base
                 $b$, the set $ A_{\lambda_f}(b, S) \coloneq \{ p
                 \mathrm {prime : the first digits of } \lambda_f(p)
                 \mathrm {in base} b \mathrm {are given by} S \} $ has
                 logarithmic density equal to $ \log_b(1 + S^{ 1})$.
                 Thus, $ \{ \lambda_f(p) \}_{p \in P}$ follows Benford's
                 Law with respect to logarithmic density. Both results
                 rely on the now-proven Sato -Tate Conjecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Karthik:2016:ETS,
  author =       "Deepak Karthik and Gil Stelzer and Sivan Gershanov and
                 Danny Baranes and Mali Salmon-Divon",
  title =        "Elucidating tissue specific genes using the {Benford}
                 distribution",
  journal =      "{BMC} Genomics",
  volume =       "17",
  number =       "1",
  month =        aug,
  year =         "2016",
  DOI =          "https://doi.org/10.1186/s12864-016-2921-x",
  ISSN =         "1471-2164",
  ISSN-L =       "1471-2164",
  bibdate =      "Wed Jun 20 15:15:23 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  journal-URL =  "https://link.springer.com/journal/12864",
}

@Article{Li:2016:QNS,
  author =       "Qinglei Li and Zuntao Fu",
  title =        "Quantifying non-stationarity effects on organization
                 of atmospheric turbulent eddy motion by {Benford}'s
                 law",
  journal =      j-COMM-NONLIN-SCI-NUM-SIM,
  volume =       "33",
  number =       "??",
  pages =        "91--98",
  month =        apr,
  year =         "2016",
  DOI =          "https://doi.org/10.1016/j.cnsns.2015.09.006",
  ISSN =         "1007-5704 (print), 1878-7274 (electronic)",
  ISSN-L =       "1007-5704",
  MRclass =      "86A10 (62M10)",
  MRnumber =     "3417171",
  bibdate =      "Tue Jan 26 11:05:08 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Commun. Nonlinear Sci. Numer. Simul.",
  fjournal =     "Communications in Nonlinear Science and Numerical
                 Simulation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/10075704",
}

@Article{Mir:2016:CAC,
  author =       "Tariq Ahmad Mir",
  title =        "Citations to articles citing {Benford}'s law: a
                 {Benford} analysis",
  journal =      "CoRR",
  volume =       "abs/1602.01205",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.48550/arXiv.1602.01205",
  ISSN =         "????",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://arxiv.org/abs/1602.01205;
                 https://dblp.org/db/journals/corr/corr1602.html#Mir16",
  abstract =     "The occurrence of first significant digits of numbers
                 in large data is often governed by a logarithmically
                 decreasing distribution called Benford's law (BL),
                 reported first by S. Newcomb (SN) and many decades
                 later independently by F. Benford (FB). Due to its
                 counter-intuitiveness the law was ignored for decades
                 as a mere curious observation. However, an indication
                 of its remarkable resurgence is the huge swell in the
                 number of citations received by the papers of SN/FB.
                 The law has come a long way, from obscurity to now
                 being a regular subject of books, peer reviewed papers,
                 patents, blogs and news. Here, we use Google Scholar
                 (GS) to collect the data on the number of citations
                 received by the articles citing the original paper of
                 SN/FB and then investigate whether the leading digits
                 of this citations data are distributed according to the
                 law they discovered. We find that the citations data of
                 literature on BL is in remarkable agreement with the
                 predictions of the law.",
  acknowledgement = ack-nhfb,
  dblp-key =     "journals/corr/Mir16",
  dblp-mdate =   "2018-08-13",
}

@Article{Mir:2016:LDD,
  author =       "T. A. Mir",
  title =        "The leading digit distribution of the worldwide
                 illicit financial flows",
  journal =      j-QUAL-QUANT,
  volume =       "50",
  number =       "1",
  pages =        "271--281",
  month =        jan,
  year =         "2016",
  CODEN =        "QQEJAV",
  DOI =          "https://doi.org/10.1007/s11135-014-0147-z",
  ISSN =         "0033-5177 (print), 1573-7845 (electronic)",
  ISSN-L =       "0033-5177",
  bibdate =      "Tue Jan 26 07:28:33 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://link.springer.com/article/10.1007/s11135-014-0147-z",
  acknowledgement = ack-nhfb,
  fjournal =     "Quality \& Quantity",
  journal-URL =  "http://www.springer.com/social+sciences/journal/11135",
  keywords =     "Benford's Law",
}

@InProceedings{Neubert:2016:IPP,
  author =       "T. Neubert and M. Hildebrandt and J. Dittmann",
  booktitle =    "2016 First International Workshop on Sensing,
                 Processing and Learning for Intelligent Machines
                 (SPLINE)",
  title =        "Image pre-processing detection: Evaluation of
                 {Benford's Law}, spatial and frequency domain feature
                 performance",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1--5",
  month =        jul,
  year =         "2016",
  DOI =          "https://doi.org/10.1109/SPLIM.2016.7528405",
  bibdate =      "Sat Sep 10 11:43:16 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; Computer science; data integrity; Data
                 models; Feature extraction; frequency domain feature
                 performance; Frequency-domain analysis; image data
                 integrity; image filtering; image forensics; image
                 preprocessing blind detection; image preprocessing
                 filters; learning (artificial intelligence); Pattern
                 recognition; sensor intrinsic preprocessing; spatial
                 domain feature performance; statistical analysis;
                 statistical pattern recognition; supervised learning;
                 Transform coding",
}

@Article{Sheng:2016:DCA,
  author =       "Guorui Sheng and Tao Li and Qingtang Su and Beijing
                 Chen and Yi Tang",
  title =        "Detection of content-aware image resizing based on
                 {Benford}'s law",
  journal =      j-SOFT-COMP,
  volume =       "21",
  number =       "19",
  pages =        "5693--5701",
  month =        apr,
  year =         "2016",
  DOI =          "https://doi.org/10.1007/s00500-016-2146-6",
  ISSN =         "1432-7643 (print), 1433-7479 (electronic)",
  ISSN-L =       "1432-7643",
  bibdate =      "Wed Jun 20 15:03:09 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Soft computing: newsletter of the {Canadian Society
                 for Fuzzy Information and Neural Systems}",
}

@Article{Sheng:2016:DSC,
  author =       "Guorui Sheng and Tiegang Gao",
  title =        "Detection of Seam-Carving Image Based on {Benford's
                 Law} for Forensic Applications",
  journal =      "International Journal of Digital Crime and Forensics",
  volume =       "8",
  number =       "1",
  pages =        "51--61",
  month =        "????",
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.4018/IJDCF.2016010104",
  ISSN =         "1941-6210 (print), 1941-6229 (electronic)",
  ISSN-L =       "1941-6210",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/ijdcf/ijdcf8.html#ShengG16",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Digit. Crime Forensics",
  dblp-key =     "journals/ijdcf/ShengG16",
  dblp-mdate =   "2020-08-12",
  fjournal =     "International Journal of Digital Crime and Forensics",
  journal-URL =  "https://www.igi-global.com/gateway/journal/1112",
}

@Article{Stoerk:2016:SCB,
  author =       "Thomas Stoerk",
  title =        "Statistical corruption in {Beijing}'s air quality data
                 has likely ended in 2012",
  journal =      j-ATMOS-ENV,
  volume =       "127",
  number =       "??",
  pages =        "365--371",
  year =         "2016",
  CODEN =        "ATENBP",
  DOI =          "https://doi.org/10.1016/j.atmosenv.2015.12.055",
  ISSN =         "1352-2310 (print), 1873-2844 (electronic)",
  ISSN-L =       "1352-2310",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1352231015306336",
  abstract =     "This research documents changes in likely misreporting
                 in official air quality data from Beijing for the years
                 2008--2013. It is shown that, consistent with prior
                 research, the official Chinese data report suspiciously
                 few observations that exceed the politically important
                 Blue Sky Day threshold, a particular air pollution
                 level used to evaluate local officials, and an excess
                 of observations just below that threshold. Similar
                 data, measured by the US Embassy in Beijing, do not
                 show this irregularity. To document likely
                 misreporting, this analysis proposes a new way of
                 comparing air quality data via Benford's Law, a
                 statistical regularity known to fit air pollution data.
                 Using this method to compare the official data to the
                 US Embassy data for the first time, I find that the
                 Chinese data fit Benford's Law poorly until a change in
                 air quality measurements at the end of 2012. From 2013
                 onwards, the Chinese data fit Benford's Law closely.
                 The US Embassy data, by contrast, exhibit no variation
                 over time in the fit with Benford's Law, implying that
                 the underlying pollution processes remain unchanged.
                 These findings suggest that misreporting of air quality
                 data for Beijing has likely ended in 2012.
                 Additionally, I use aerosol optical density data to
                 show the general applicability of this method of
                 detecting likely misreporting in air pollution data.",
  acknowledgement = ack-nhfb,
  fjournal =     "Atmospheric Environment",
  keywords =     "Air pollution; Air quality data; Beijing; Benford's
                 Law; Misreporting; PM10; PM2.5",
}

@Article{Whyman:2016:ICC,
  author =       "G. Whyman and E. Shulzinger and Ed. Bormashenko",
  title =        "Intuitive considerations clarifying the origin and
                 applicability of the {Benford Law}",
  journal =      "Results in Physics",
  volume =       "6",
  number =       "??",
  pages =        "3--6",
  year =         "2016",
  DOI =          "https://doi.org/10.1016/j.rinp.2015.11.010",
  ISSN =         "2211-3797",
  bibdate =      "Tue Jan 26 09:03:59 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S2211379715000728",
  abstract =     "The diverse applications of the Benford law attract
                 investigators working in various fields of physics,
                 biology and sociology. At the same time, the groundings
                 of the Benford law remain obscure. Our paper
                 demonstrates that the Benford law arises from the
                 positional (place-value) notation accepted for
                 representing various sets of data. An alternative to
                 Benford formulae to predict the distribution of digits
                 in statistical data is derived. Application of these
                 formulae to the statistical analysis of infrared
                 spectra of polymers is presented. Violations of the
                 Benford Law are discussed.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law; Infrared spectra; Leading digit
                 phenomenon; Positional notation; Statistical data",
}

@Article{Yang:2016:WSZ,
  author =       "Yue Yang and Jianwen Zhu",
  title =        "Write Skew and {Zipf} Distribution: Evidence and
                 Implications",
  journal =      j-TOS,
  volume =       "12",
  number =       "4",
  pages =        "21:1--21:??",
  month =        aug,
  year =         "2016",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1145/2908557",
  ISSN =         "1553-3077 (print), 1553-3093 (electronic)",
  ISSN-L =       "1553-3077",
  bibdate =      "Sat Mar 25 07:00:07 MDT 2017",
  bibsource =    "http://www.acm.org/pubs/contents/journals/tos/;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/tos.bib",
  abstract =     "Understanding workload characteristics is essential to
                 storage systems design and performance optimization.
                 With the emergence of flash memory as a new viable
                 storage medium, the new design concern of flash
                 endurance arises, necessitating a revisit of workload
                 characteristics, in particular, of the write behavior.
                 Inspired by Web caching studies where a Zipf-like
                 access pattern is commonly found, we hypothesize that
                 write count distribution at the block level may also
                 follow Zipf's Law. To validate this hypothesis, we
                 study 48 block I/O traces collected from a wide variety
                 of real and benchmark applications. Through extensive
                 analysis, we demonstrate that the Zipf-like pattern
                 indeed widely exists in write traffic provided its
                 disguises are removed by statistical processing. This
                 finding implies that write skew in a large class of
                 applications could be analytically expressed and, thus,
                 facilitates design tradeoff explorations adaptive to
                 workload characteristics.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Storage",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J960",
}

@Article{Berger:2017:WLB,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "What is \ldots{} {Benford's Law}?",
  journal =      j-NAMS,
  volume =       "64",
  number =       "2",
  pages =        "132--134",
  month =        feb,
  year =         "2017",
  CODEN =        "AMNOAN",
  DOI =          "https://doi.org/10.1090/noti1477",
  ISSN =         "0002-9920 (print), 1088-9477 (electronic)",
  ISSN-L =       "0002-9920",
  MRclass =      "60C05 (60E05)",
  MRnumber =     "3587717",
  bibdate =      "Mon Jan 30 16:18:54 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/nams2010.bib",
  URL =          "http://www.ams.org/publications/journals/notices/201702/rnoti-p132.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Notices Amer. Math. Soc.",
  fjournal =     "Notices of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/notices/",
}

@InCollection{Best:2017:BBG,
  author =       "Andrew Best and Patrick Dynes and Xixi Edelsbrunner
                 and Brian McDonald and Steven J. Miller and Kimsy Tor
                 and Caroline Turnage-Butterbaugh and Madeleine
                 Weinstein",
  editor =       "M. Nathanson",
  booktitle =    "Springer Proceedings in Mathematics \& Statistics",
  title =        "{Benford} Behavior of Generalized {Zeckendorf}
                 Decompositions",
  publisher =    "Springer International Publishing",
  address =      "Cham, Switzerland",
  pages =        "25--37",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-68032-3_3",
  MRclass =      "11B39 (11B05 11K06 60F05 62E20)",
  MRnumber =     "3754894",
  MRreviewer =   "Vilius Stakenas",
  bibdate =      "Wed Jun 20 15:07:06 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Corazza:2017:LET,
  author =       "Marco Corazza and Andrea Ellero and Alberto Zorzi",
  title =        "L'importanza di Essere ``{UNO}'' (ovvero la legge di
                 {Benford}). ({Italian}) [The importance of Being
                 ``one'' (i.e., the {Benford} law)]",
  journal =      "Lettera Matematica Pristem",
  volume =       "103",
  number =       "1",
  pages =        "31--38",
  month =        dec,
  year =         "2017",
  DOI =          "https://doi.org/10.1007/s10031-017-0051-5",
  ISSN =         "1593-5884 (print), 1970-6820 (electronic)",
  ISSN-L =       "1593-5884",
  bibdate =      "Wed Jun 20 15:01:02 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Daniels:2017:BLQ,
  author =       "Jeremy Daniels and Samantha-Jo Caetano and Dirk Huyer
                 and Andrew Stephen and John Fernandes and Alice Lytwyn
                 and Fred M. Hoppe",
  title =        "{Benford's Law} for Quality Assurance of Manner of
                 Death Counts in Small and Large Databases",
  journal =      "Journal of Forensic Sciences",
  volume =       "62",
  number =       "5",
  pages =        "1326--1331",
  month =        jun,
  year =         "2017",
  DOI =          "https://doi.org/10.1111/1556-4029.13437",
  ISSN =         "0022-1198 (print), 1556-4029 (electronic)",
  ISSN-L =       "0022-1198",
  bibdate =      "Wed Jun 20 14:41:06 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Fellman:2017:BP,
  author =       "Johan Fellman",
  title =        "{Benford} paradox",
  journal =      j-ARKHIMEDES,
  volume =       "??",
  number =       "4",
  pages =        "26--33",
  year =         "2017",
  CODEN =        "AKMDA5",
  ISSN =         "0004-1920",
  MRclass =      "60E99",
  MRnumber =     "3931184",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Arkhimedes",
}

@Article{Hullemann:2017:ABL,
  author =       "S. H{\"u}llemann and G. Sch{\"u}pfer and J. Mauch",
  title =        "Application of {Benford}'s law: a valuable tool for
                 detecting scientific papers with fabricated data?",
  journal =      "Der Anaesthesist",
  volume =       "66",
  number =       "10",
  pages =        "795--802",
  month =        jun,
  year =         "2017",
  DOI =          "https://doi.org/10.1007/s00101-017-0333-1",
  ISSN =         "0003-2417 (print), 1432-055X (electronic)",
  ISSN-L =       "0003-2417",
  bibdate =      "Wed Jun 20 14:24:42 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@InCollection{Iorliam:2017:UBL,
  author =       "Aamo Iorliam and Anthony T. S. Ho and Adrian Waller
                 and Xi Zhao",
  editor =       "Y. Shi and H. Kim and F. Perez-Gonzalez and F. Liu",
  booktitle =    "Digital Forensics and Watermarking (IWDW 2016)",
  title =        "Using {Benford's Law} Divergence and Neural Networks
                 for Classification and Source Identification of
                 Biometric Images",
  volume =       "10082",
  publisher =    "Springer International Publishing",
  address =      "Cham, Switzerland",
  pages =        "88--105",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-53465-7_7",
  bibdate =      "Wed Jun 20 15:08:25 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       ser-LNCS,
  acknowledgement = ack-nhfb,
}

@InCollection{Klepac:2017:CDS,
  author =       "Goran Klepac",
  editor =       "A. Sangaiah and A. Thangavelu and Sundaram V.
                 Meenakshi",
  booktitle =    "Cognitive Computing for Big Data Systems Over {IoT}",
  title =        "Cognitive Data Science Automatic Fraud Detection
                 Solution, Based on {Benford's Law}, Fuzzy Logic with
                 Elements of Machine Learning",
  publisher =    "Springer International Publishing",
  address =      "Cham, Switzerland",
  pages =        "79--95",
  month =        dec,
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-319-70688-7_4",
  ISBN =         "3-319-70687-X (print), 3-319-70688-8 (electronic)",
  ISBN-13 =      "978-3-319-70687-0 (print), 978-3-319-70688-7
                 (electronic)",
  bibdate =      "Wed Jun 20 14:57:48 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes on Data Engineering and Communications
                 Technologies",
  acknowledgement = ack-nhfb,
}

@InCollection{Mochty:2017:ABL,
  author =       "Ludwig Mochty",
  editor =       "B. Kaluza and K. Braun and H. Beschorner and B.
                 Rolfes",
  booktitle =    "Betriebswirtschaftliche Fragen zu Steuern,
                 Finanzierung, Banken und Management",
  title =        "{Die Achillesferse des Benford's Law: KMUs}.
                 ({German}) [{The} {Achilles} heel of {Benford's Law}:
                 {SMEs}]",
  publisher =    "Springer Fachmedien Wiesbaden",
  address =      "Wiesbaden, Germany",
  pages =        "39--55",
  year =         "2017",
  DOI =          "https://doi.org/10.1007/978-3-658-16730-1_3",
  bibdate =      "Wed Jun 20 15:11:20 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Misc{Oransky:2017:TCT,
  author =       "Ivar Oransky",
  title =        "Two in 100 clinical trials in eight major journals
                 likely contain inaccurate data: Study",
  howpublished = "Web site article.",
  day =          "5",
  month =        jun,
  year =         "2017",
  bibdate =      "Wed Jun 20 14:31:24 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://retractionwatch.com/2017/06/05/two-100-clinical-trials-eight-major-journals-likely-contain-inaccurate-data-study/",
  acknowledgement = ack-nhfb,
}

@Article{Shukla:2017:BDE,
  author =       "Abhishek Shukla and Ankit Kumar Pandey and Anirban
                 Pathak",
  title =        "{Benford}'s Distribution in Extrasolar World: Do the
                 Exoplanets Follow {Benford}'s Distribution?",
  journal =      j-J-ASTROPHYS-ASTRON,
  volume =       "38",
  number =       "1",
  month =        mar,
  year =         "2017",
  CODEN =        "JASRD7",
  DOI =          "https://doi.org/10.1007/s12036-017-9427-z",
  ISSN =         "0250-6335 (print), 0973-7758 (electronic)",
  ISSN-L =       "0250-6335",
  bibdate =      "Wed Jun 20 15:05:03 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Astrophysics and Astronomy",
  journal-URL =  "http://www.springerlink.com/content/0250-6335",
}

@Article{Tseng:2017:MBL,
  author =       "Hsiang-chi Tseng and Wei-neng Huang and Ding-wei
                 Huang",
  title =        "Modified {Benford's Law} for two-exponent
                 distributions",
  journal =      j-SCIENTOMETRICS,
  volume =       "110",
  number =       "3",
  pages =        "1403--1413",
  month =        mar,
  year =         "2017",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-016-2217-6",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Tue Feb 21 09:16:43 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2010.bib",
  URL =          "http://link.springer.com/accesspage/article/10.1007/s11192-016-2217-6",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Article{Barabesi:2018:GFT,
  author =       "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli
                 and Domenico Perrotta",
  title =        "Goodness-of-Fit Testing for the {Newcomb--Benford Law}
                 With Application to the Detection of Customs Fraud",
  journal =      j-J-BUS-ECON-STAT,
  volume =       "36",
  number =       "2",
  pages =        "346--358",
  year =         "2018",
  DOI =          "https://doi.org/10.1080/07350015.2016.1172014",
  ISSN =         "0735-0015 (print), 1537-2707 (electronic)",
  ISSN-L =       "0735-0015",
  MRclass =      "62G10",
  MRnumber =     "3790219",
  bibdate =      "Mon Jun 15 17:20:33 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jbuseconstat.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/07350015.2016.1172014",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Business \& Economic Statistics",
  journal-URL =  "https://amstat.tandfonline.com/loi/ubes20",
  onlinedate =   "28 Apr 2017",
}

@Article{Becker:2018:BLC,
  author =       "Thealexa Becker and David Burt and Taylor C. Corcoran
                 and Alec Greaves-Tunnell and Joseph R. Iafrate and Joy
                 Jing and Steven J. Miller and Jaclyn D. Porfilio and
                 Ryan Ronan and Jirapat Samranvedhya and Frederick W.
                 Strauch and Blaine Talbut",
  title =        "{Benford}'s law and continuous dependent random
                 variables",
  journal =      j-ANN-PHYS,
  volume =       "388",
  pages =        "350--381",
  year =         "2018",
  CODEN =        "APNYA6",
  DOI =          "https://doi.org/10.1016/j.aop.2017.11.013",
  ISSN =         "0003-4916 (print), 1096-035x (electronic)",
  ISSN-L =       "0003-4916",
  MRclass =      "60A10 (11K06 60E10)",
  MRnumber =     "3759655",
  MRreviewer =   "Ad Ridder",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00034916",
}

@Article{Berger:2018:BFA,
  author =       "Arno Berger and Chuang Xu",
  title =        "Best Finite Approximations of {Benford's Law}",
  journal =      j-J-THEOR-PROBAB,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        apr,
  year =         "2018",
  CODEN =        "JTPREO",
  DOI =          "https://doi.org/10.1007/s10959-018-0827-z",
  ISSN =         "0894-9840 (print), 1572-9230 (electronic)",
  ISSN-L =       "0894-9840",
  bibdate =      "Wed Jun 20 14:46:04 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Probability",
  journal-URL =  "http://link.springer.com/journal/10959",
  xxnote =       "Check; not yet assigned volume / number / pages
                 data.",
}

@Article{Berger:2018:SUR,
  author =       "Arno Berger and Isaac Twelves",
  title =        "On the significands of uniform random variables",
  journal =      j-J-APPL-PROBAB,
  volume =       "55",
  number =       "2",
  pages =        "353--367",
  month =        jun,
  year =         "2018",
  CODEN =        "JPRBAM",
  DOI =          "https://doi.org/10.1017/jpr.2018.23",
  ISSN =         "0021-9002 (print), 1475-6072 (electronic)",
  ISSN-L =       "0021-9002",
  bibdate =      "Sat Mar 16 09:23:51 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/japplprobab.bib",
  URL =          "https://www.cambridge.org/core/journals/journal-of-applied-probability/article/on-the-significands-of-uniform-random-variables/0D08D0EEC38F52E431CF41290651603A",
  abstract =     "For all $ \alpha > 0 $ and real random variables $X$,
                 we establish sharp bounds for the smallest and the
                 largest deviation of $ \alpha X$ from the logarithmic
                 distribution also known as Benford's law. In the case
                 of uniform $X$, the value of the smallest possible
                 deviation is determined explicitly. Our elementary
                 calculation puts into perspective the recurring claims
                 that a random variable conforms to Benford's law, at
                 least approximately, whenever it has large spread.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Appl. Probab.",
  fjournal =     "Journal of Applied Probability",
  journal-URL =  "https://www.cambridge.org/core/journals/journal-of-applied-probability",
  onlinedate =   "26 July 2018",
}

@Article{Corazza:2018:IBO,
  author =       "Marco Corazza and Andrea Ellero and Alberto Zorzi",
  title =        "The importance of being ``one'' (or {Benford}'s law)",
  journal =      "Lettera Matematica",
  volume =       "6",
  number =       "1",
  pages =        "33--39",
  day =          "01",
  month =        mar,
  year =         "2018",
  DOI =          "https://doi.org/10.1007/s40329-018-0218-4",
  ISSN =         "2281-5937 (print), 2281-6917 (electronic)",
  ISSN-L =       "2281-6917",
  MRclass =      "60E05 (62P99)",
  MRnumber =     "3775303",
  bibdate =      "Wed Jun 20 14:53:18 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Translated from the Italian.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; First significant digit; Power
                 sequences; Tax evasion; Vote rigging",
}

@Article{Ferrer-i-Cancho:2018:OZM,
  author =       "Ramon Ferrer-i-Cancho and Michael S. Vitevitch",
  title =        "The origins of {Zipf}'s meaning-frequency law",
  journal =      j-J-ASSOC-INF-SCI-TECHNOL,
  volume =       "69",
  number =       "11",
  pages =        "1369--1379",
  month =        nov,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1002/asi.24057",
  ISSN =         "2330-1643 (print), 2330-1643 (electronic)",
  ISSN-L =       "2330-1643",
  bibdate =      "Thu Mar 28 08:58:20 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jaist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Information Science and
                 Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "30 July 2018",
}

@Article{Hartmann:2018:AVK,
  author =       "Sandro Hartmann and Daniel Brinkert",
  title =        "{Aufdeckung von Versicherungsbetrug bei
                 Kfz-Sch{\"a}den mit Hilfe des Benford-Tests}.
                 ({German}) [{Detection} of insurance fraud for vehicle
                 damage using the {Benford} test]",
  journal =      "{Zeitschrift f{\"u}r die gesamte
                 Versicherungswissenschaft}",
  volume =       "107",
  number =       "1",
  pages =        "41--59",
  month =        jan,
  year =         "2018",
  DOI =          "https://doi.org/10.1007/s12297-017-0396-8",
  ISSN =         "0044-2585 (print), 1865-9748 (electronic)",
  ISSN-L =       "0044-2585",
  bibdate =      "Wed Jun 20 14:52:07 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Book{Holt:2018:WEW,
  author =       "Jim Holt",
  title =        "When {Einstein} walked with {G{\"o}del}: excursions to
                 the edge of thought",
  publisher =    pub-FARRAR,
  address =      pub-FARRAR:adr,
  pages =        "xi + 368",
  year =         "2018",
  ISBN =         "0-374-14670-5 (hardcover), 0-374-71784-2 (e-book)",
  ISBN-13 =      "978-0-374-14670-2 (hardcover), 978-0-374-71784-1
                 (e-book)",
  LCCN =         "PS3608.O4943595 A6 2018",
  bibdate =      "Fri May 18 13:58:57 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lovelace-ada-augusta.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/von-neumann-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/einstein.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "A collection of essays on philosophy, mathematics, and
                 science, and the people who pursue them.",
  acknowledgement = ack-nhfb,
  author-dates = "1954--",
  remark =       "Chapter 8 discusses the influence of Zipf's Law on
                 Mandelbrot's discovery of fractals.",
  shorttableofcontents = "Part I: The moving image of eternity \\
                 Part II: Numbers in the brain, in platonic heaven, and
                 in society \\
                 Part III: Mathematics, pure and impure \\
                 Part IV: Higher dimensions, abstract maps \\
                 Part V: Infinity, large and small \\
                 Part VI: Heroism, tragedy, and the computer age \\
                 Part VII: The cosmos reconsidered \\
                 Part VIII: Quick studies: A selection of shorter essays
                 \\
                 Part IX: God, sainthood, truth and bullshit",
  tableofcontents = "Part I: The moving image of eternity \\
                 1: When Einstein walked with G{\"o}del \\
                 2: Time --- the grand illusion? \\
                 Part II: Numbers in the brain, in platonic heaven, and
                 in society \\
                 3: Numbers guy: the neuroscience of math \\
                 4: The Riemann Zeta conjecture and the laughter of the
                 primes \\
                 5: Sir Francis Galton, the father of
                 statistics\ldots{}and eugenics \\
                 Part III: Mathematics, pure and impure \\
                 6: A mathematical romance \\
                 7: The avatars of higher mathematics \\
                 8: Beno{\^\i}t Mandelbrot and the discovery of fractals
                 \\
                 Part IV: Higher dimensions, abstract maps \\
                 9: Geometrical creatures \\
                 10: A comedy of colors \\
                 Part V: Infinity, large and small \\
                 11: Infinite visions: Georg Cantor v. David Foster
                 Wallace \\
                 12: Worshipping infinity: why the Russians do and the
                 French don't \\
                 13: The dangerous idea of the infinitesimal \\
                 Part VI: Heroism, tragedy, and the computer age \\
                 14: The Ada perplex: was Byron's daughter the first
                 coder? \\
                 15: Alan Turing in life, logic, and death \\
                 16: Dr. Strangelove makes a thinking machine \\
                 17: Smarter, happier, more productive \\
                 Part VII: The cosmos reconsidered \\
                 18: The string theory wars: is beauty truth? \\
                 19: Einstein, ``Spooky action,'' and the reality of
                 space \\
                 20: How will the Universe end? \\
                 Part VII: Quick studies: a selection of shorter essays
                 \\
                 Little big man \\
                 Doom soon \\
                 Death: bad? \\
                 The looking-glass war \\
                 Astrology and the demarcation problem \\
                 G{\"o}del takes on the U.S. Constitution \\
                 The law of least action \\
                 Emmy Noether's beautiful theorem \\
                 Is logic coercive? \\
                 Newcomb's problem and the paradox of choice \\
                 The right not to exist \\
                 Can't anyone get Heisenberg right? \\
                 Overconfidence and the Monty Hall problem \\
                 The cruel law of eponymy \\
                 The mind of a rock \\
                 Part IX: God, sainthood, truth, and bullshit \\
                 21: Dawkins and the deity \\
                 22: On moral sainthood \\
                 23: Truth and reference: a philosophical feud \\
                 24: Say anything \\
                 Further Reading \\
                 Acknowledgments \\
                 Index",
}

@InCollection{Humenberger:2018:BGW,
  author =       "Hans Humenberger",
  editor =       "Hans-Stefan Siller and Gilbert Greefrath and Werner
                 Blum",
  booktitle =    "Neue Materialien f{\"u}r einen realit{\"a}tsbezogenen
                 Mathematikunterricht 4: 25 Jahre ISTRON-Gruppe - eine
                 Best-of-Auswahl aus der ISTRON-Schriftenreihe",
  title =        "{Das Benford-Gesetz`` --- warum ist die Eins als
                 f{\"u}hrende Ziffer von Zahlen bevorzugt?}. ({German})
                 [{The} ``{Benford Law}'' --- why is one preferred as
                 the leading digit of numbers?]",
  chapter =      "12",
  publisher =    "Springer Fachmedien Wiesbaden",
  address =      "Wiesbaden",
  pages =        "161--176",
  year =         "2018",
  DOI =          "https://doi.org/10.1007/978-3-658-17599-3_12",
  ISBN =         "978-36581-7-5-9-9-3",
  ISBN-13 =      "978-3-658-17599-3",
  bibdate =      "Wed Jun 20 14:56:18 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}

@Article{Lacasa:2018:NBL,
  author =       "Lucas Lacasa",
  title =        "{Newcomb--Benford} law helps customs officers to
                 detect fraud in international trade",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "116",
  number =       "1",
  pages =        "11--13",
  month =        dec,
  year =         "2018",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.1819470116",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  bibdate =      "Wed Aug 28 15:42:44 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.pnas.org/cgi/doi/10.1073/pnas.1819470116",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/content/by/year",
}

@Article{Lee:2018:PIB,
  author =       "Edward D. Lee",
  title =        "Partisan Intuition Belies Strong, Institutional
                 Consensus and Wide {Zipf's Law} for Voting Blocs in {US
                 Supreme Court}",
  journal =      j-J-STAT-PHYS,
  volume =       "173",
  number =       "6",
  pages =        "1722--1733",
  month =        dec,
  year =         "2018",
  CODEN =        "JSTPSB",
  DOI =          "https://doi.org/10.1007/s10955-018-2156-0",
  ISSN =         "0022-4715 (print), 1572-9613 (electronic)",
  ISSN-L =       "0022-4715",
  bibdate =      "Fri Mar 1 07:23:36 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatphys2010.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Statistical Physics",
  journal-URL =  "http://link.springer.com/journal/10955",
}

@Article{Mir:2018:BLS,
  author =       "Tariq Ahmad Mir and Marcel Ausloos",
  title =        "{Benford}'s law: a ``sleeping beauty'' sleeping in the
                 dirty pages of logarithmic tables",
  journal =      j-J-ASSOC-INF-SCI-TECHNOL,
  volume =       "69",
  number =       "3",
  pages =        "349--358",
  month =        mar,
  year =         "2018",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1002/asi.23845",
  ISSN =         "2330-1643 (print), 2330-1643 (electronic)",
  ISSN-L =       "2330-1643",
  bibdate =      "Tue May 22 14:36:54 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jaist.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Association for Information Science and
                 Technology",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2330-1643",
  onlinedate =   "17 September 2017",
}

@Article{Riccioni:2018:RPF,
  author =       "Jessica Riccioni and Roy Cerqueti",
  title =        "Regular paths in financial markets: investigating the
                 {Benford}'s law",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "107",
  pages =        "186--194",
  year =         "2018",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2018.01.008",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  MRclass =      "91B24",
  MRnumber =     "3759502",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
}

@Article{Aleksandrova:2019:BLD,
  author =       "Elena B. Aleksandrova and Daria S. Lavrova and A. V.
                 Yarmak",
  title =        "{Benford's Law} in the Detection of {DoS} Attacks on
                 Industrial Systems",
  journal =      "Automatic Control and Computer Sciences",
  volume =       "53",
  number =       "8",
  pages =        "954--962",
  month =        "????",
  year =         "2019",
  CODEN =        "ACCSCE",
  DOI =          "https://doi.org/10.3103/S0146411619080030",
  ISSN =         "0146-4116 (print), 1558-108X (electronic)",
  ISSN-L =       "0146-4116",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/accs/accs53.html#AleksandrovaLY19",
  acknowledgement = ack-nhfb,
  ajournal =     "Autom. Control. Comput. Sci.",
  dblp-key =     "journals/accs/AleksandrovaLY19",
  dblp-mdate =   "2021-10-14",
  fjournal =     "Automatic Control and Computer Sciences",
}

@Article{Benjamin:2019:LSB,
  author =       "Arthur T. Benjamin",
  title =        "The long and the short of {Benford}'s law",
  journal =      "Math Horizons",
  volume =       "26",
  number =       "4",
  pages =        "8--9",
  year =         "2019",
  DOI =          "https://doi.org/10.1080/10724117.2019.1568086",
  ISSN =         "1072-4117",
  MRclass =      "60E05",
  MRnumber =     "3925688",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Math Horiz.",
  fjournal =     "Math Horizons",
}

@Article{Berger:2019:BFA,
  author =       "Arno Berger and Chuang Xu",
  title =        "Best Finite Approximations of {Benford's Law}",
  journal =      j-J-THEOR-PROBAB,
  volume =       "32",
  number =       "3",
  pages =        "1525--1553",
  month =        sep,
  year =         "2019",
  CODEN =        "JTPREO",
  DOI =          "https://doi.org/10.1007/s10959-018-0827-z",
  ISSN =         "0894-9840 (print), 1572-9230 (electronic)",
  ISSN-L =       "0894-9840",
  MRclass =      "60B10 (60E15 62E15)",
  MRnumber =     "3979679",
  bibdate =      "Tue Jul 9 09:42:45 MDT 2019",
  bibsource =    "http://link.springer.com/journal/10959/32/3;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jtheorprobab.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Theoretical Probability",
  journal-URL =  "http://link.springer.com/journal/10959",
}

@Article{Cai:2019:LBL,
  author =       "Zhaodong Cai and A. J. Hildebrand and Junxian Li",
  title =        "A local {Benford Law} for a class of arithmetic
                 sequences",
  journal =      j-INT-J-NUMBER-THEORY,
  volume =       "15",
  number =       "3",
  pages =        "613--638",
  month =        apr,
  year =         "2019",
  DOI =          "https://doi.org/10.1142/S1793042119500325",
  ISSN =         "1793-0421 (print), 1793-7310 (electronic)",
  ISSN-L =       "1793-0421",
  MRclass =      "11K31 (11B05 11K06 11N05)",
  MRnumber =     "3925756",
  MRreviewer =   "Vilius Stakenas",
  bibdate =      "Tue Jul 21 10:35:38 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fibquart.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijnt.bib",
  URL =          "https://www.worldscientific.com/doi/10.1142/S1793042119500325",
  abstract =     "It is well known that sequences such as the Fibonacci
                 numbers and the factorials satisfy Benford's Law; that
                 is, leading digits in these sequences occur with
                 frequencies given by $ P(d) = \log_{10} (1 + 1 / d) $,
                 $ d = 1, 2, \ldots, 9 $. In this paper, we investigate
                 leading digit distributions of arithmetic sequences
                 from a local point of view. We call a sequence locally
                 Benford distributed of order $k$ if, roughly speaking,
                 $k$-tuples of consecutive leading digits behave like
                 $k$ independent Benford-distributed digits. This notion
                 refines that of a Benford distributed sequence, and it
                 provides a way to quantify the extent to which the
                 Benford distribution persists at the local level.
                 Surprisingly, most sequences known to satisfy Benford's
                 Law have rather poor local distribution properties. In
                 our main result we establish, for a large class of
                 arithmetic sequences, a ``best-possible'' local Benford
                 Law; that is, we determine the maximal value k such
                 that the sequence is locally Benford distributed of
                 order k. The result applies, in particular, to
                 sequences of the form $ \{ a^n \} $, $ \{ a^{n^d} \} $,
                 and $ \{ n^\beta a^{n^\alpha } \} $, as well as the
                 sequence of factorials $ \{ n! \} $ and similar
                 iterated product sequences.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Number Theory (IJNT)",
  journal-URL =  "https://www.worldscientific.com/worldscinet/ijnt",
}

@Article{Cerioli:2019:NBL,
  author =       "Andrea Cerioli and Lucio Barabesi and Andrea Cerasa
                 and Mario Menegatti and Domenico Perrotta",
  title =        "{Newcomb--Benford} law and the detection of frauds in
                 international trade",
  journal =      j-PROC-NATL-ACAD-SCI-USA,
  volume =       "116",
  number =       "1",
  pages =        "106--115",
  year =         "2019",
  CODEN =        "PNASA6",
  DOI =          "https://doi.org/10.1073/pnas.1806617115",
  ISSN =         "0027-8424 (print), 1091-6490 (electronic)",
  ISSN-L =       "0027-8424",
  MRclass =      "91B60 (62P99 91B24)",
  MRnumber =     "3900205",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the National Academy of Sciences of the
                 United States of America",
  journal-URL =  "http://www.pnas.org/content/by/year",
}

@Article{Durst:2019:BLB,
  author =       "Rebecca F. Durst and Steven J. Miller",
  title =        "{Benford}'s law beyond independence: tracking
                 {Benford} behavior in copula models",
  journal =      "Involve",
  volume =       "12",
  number =       "7",
  pages =        "1193--1218",
  year =         "2019",
  DOI =          "https://doi.org/10.2140/involve.2019.12.1193",
  ISSN =         "1944-4176",
  MRclass =      "60E99",
  MRnumber =     "4023347",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Involve. A Journal of Mathematics",
}

@Article{Ruankong:2019:CTB,
  author =       "Pongpol Ruankong and Songkiat Sumetkijakan",
  title =        "Chains of truncated beta distributions and {Benford}'s
                 law",
  journal =      "Unif. Distrib. Theory",
  volume =       "14",
  number =       "2",
  pages =        "27--32",
  year =         "2019",
  ISSN =         "1336-913X",
  MRclass =      "60A10",
  MRnumber =     "4063899",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Uniform Distribution Theory",
}

@Article{Zunini:2019:BL,
  author =       "Mar{\'{}\i}a Caputi Zunini",
  title =        "{Benford}'s law",
  journal =      "Publ. Mat. Urug.",
  volume =       "17",
  pages =        "285--290",
  year =         "2019",
  ISSN =         "0797-1443",
  MRclass =      "62E99",
  MRnumber =     "4018784",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Publicaciones Matem\'{a}ticas del Uruguay",
}

@Article{Barabesi:2020:GBL,
  author =       "Lucio Barabesi and Luca Pratelli",
  title =        "On the {Generalized Benford law}",
  journal =      j-STAT-PROB-LETT,
  volume =       "160",
  number =       "??",
  pages =        "Article 108702",
  month =        may,
  year =         "2020",
  CODEN =        "SPLTDC",
  DOI =          "https://doi.org/10.1016/j.spl.2020.108702",
  ISSN =         "0167-7152 (print), 1879-2103 (electronic)",
  ISSN-L =       "0167-7152",
  MRclass =      "60E05 (60F05 62E15)",
  MRnumber =     "4058264",
  bibdate =      "Mon Aug 3 15:37:29 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/statproblett2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167715220300055",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistics \& Probability Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01677152",
}

@Article{Cai:2020:SAB,
  author =       "Zhaodong Cai and Matthew Faust and A. J. Hildebrand
                 and Junxian Li and Yuan Zhang",
  title =        "The surprising accuracy of {Benford}'s law in
                 mathematics",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "127",
  number =       "3",
  pages =        "217--237",
  year =         "2020",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.1080/00029890.2020.1690387",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "11K31 (11K38 11Y55 60F99)",
  MRnumber =     "4067893",
  MRreviewer =   "Russell Jay Hendel",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}

@Article{DAlessandro:2020:BLM,
  author =       "Angelo D'Alessandro",
  title =        "{Benford}'s law and metabolomics: A tale of numbers
                 and blood",
  journal =      "Transfusion and Apheresis Science",
  volume =       "59",
  number =       "6",
  pages =        "103019",
  month =        dec,
  year =         "2020",
  DOI =          "https://doi.org/10.1016/j.transci.2020.103019",
  ISSN =         "1473-0502 (print), 1878-1683 (electronic)",
  ISSN-L =       "1473-0502",
  bibdate =      "Thu May 20 15:42:53 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{DaSilva:2020:BBS,
  author =       "St{\'e}phane Blondeau {Da Silva}",
  title =        "{Benford} or Not {Benford}: A Systematic But Not
                 Always Well-Founded Use of an Elegant Law in
                 Experimental Fields",
  journal =      j-COMMUN-MATH-STAT,
  volume =       "8",
  number =       "2",
  pages =        "167--201",
  month =        jun,
  year =         "2020",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s40304-018-00172-1",
  ISSN =         "2194-6701 (print), 2194-671X (electronic)",
  ISSN-L =       "2194-6701",
  MRclass =      "60E05",
  MRnumber =     "4102358",
  bibdate =      "Fri Jul 24 15:51:38 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communmathstat.bib",
  URL =          "http://link.springer.com/article/10.1007/s40304-018-00172-1",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Mathematics and Statistics",
  journal-URL =  "http://link.springer.com/journal/40304",
}

@Article{daSilva:2020:VNB,
  author =       "A. J. da Silva and S. Floquet and D. O. C. Santos and
                 R. F. Lima",
  title =        "On the validation of the {Newcomb--Benford} law and
                 the {Weibull} distribution in neuromuscular
                 transmission",
  journal =      j-PHYSICA-A,
  volume =       "553",
  pages =        "124606, 15",
  year =         "2020",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2020.124606",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "92C42 (62P10 92C37)",
  MRnumber =     "4096745",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Durst:2020:IGD,
  author =       "R. F. Durst and C. Huynh and A. Lott and S. J. Miller
                 and E. A. Palsson and W. Touw and G. Vriend",
  title =        "The inverse gamma distribution and {Benford}'s law",
  journal =      "PUMP J. Undergrad. Res.",
  volume =       "3",
  pages =        "95--109",
  year =         "2020",
  ISSN =         "2765-8724",
  MRclass =      "60F05 (42A16 60E10 62E15)",
  MRnumber =     "4143770",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "The PUMP Journal of Undergraduate Research",
}

@Article{Ectors:2020:ZPL,
  author =       "Wim Ectors and Bruno Kochan and Davy Janssens and Tom
                 Bellemans and Geert Wets",
  title =        "{Zipf}'s power law in activity schedules and the
                 effect of aggregation",
  journal =      j-FUT-GEN-COMP-SYS,
  volume =       "107",
  number =       "??",
  pages =        "1014--1025",
  month =        jun,
  year =         "2020",
  CODEN =        "FGSEVI",
  DOI =          "https://doi.org/10.1016/j.future.2018.04.095",
  ISSN =         "0167-739X (print), 1872-7115 (electronic)",
  ISSN-L =       "0167-739X",
  bibdate =      "Fri Jun 19 07:44:14 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/futgencompsys.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0167739X17321891",
  acknowledgement = ack-nhfb,
  fjournal =     "Future Generation Computer Systems",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0167739X",
}

@Article{Fang:2020:SCP,
  author =       "Guojun Fang and Qihong Chen",
  title =        "Several common probability distributions obey
                 {Benford}'s law",
  journal =      j-PHYSICA-A,
  volume =       "540",
  pages =        "123129, 8",
  year =         "2020",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2019.123129",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "60E05",
  MRnumber =     "4041619",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A. Statistical Mechanics and its
                 Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Huang:2020:TFL,
  author =       "Yasheng Huang and Zhiyong Niu and Clair Yang",
  title =        "Testing firm-level data quality in {China} against
                 {Benford}'s law",
  journal =      j-ECONOM-LETT,
  volume =       "192",
  pages =        "109182, 4",
  year =         "2020",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/j.econlet.2020.109182",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "91G70",
  MRnumber =     "4095772",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01651765",
}

@Article{Kazemitabar:2020:MCD,
  author =       "Jalil Kazemitabar and Javad Kazemitabar",
  title =        "Measuring the conformity of distributions to
                 {Benford's Law}",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "49",
  number =       "14",
  pages =        "3530--3536",
  year =         "2020",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610926.2019.1590599",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  MRclass =      "60E05",
  MRnumber =     "4107617",
  bibdate =      "Fri Jul 24 10:15:17 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/03610926.2019.1590599",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
  onlinedate =   "28 Mar 2019",
}

@Article{Koch:2020:BLC,
  author =       "Christoffer Koch and Ken Okamura",
  title =        "{Benford's Law} and {COVID-19} reporting",
  journal =      j-ECONOM-LETT,
  volume =       "196",
  pages =        "109573",
  month =        nov,
  year =         "2020",
  CODEN =        "ECLEDS",
  DOI =          "https://doi.org/10.1016/j.econlet.2020.109573",
  ISSN =         "0165-1765 (print), 1873-7374 (electronic)",
  ISSN-L =       "0165-1765",
  MRclass =      "92B10 (92D30)",
  MRnumber =     "4150786",
  bibdate =      "Thu May 20 15:46:14 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Economics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01651765",
}

@Article{Lee:2020:CFC,
  author =       "Kang-Bok Lee and Sumin Han and Yeasung Jeong",
  title =        "{COVID-19}, flattening the curve, and {Benford}'s
                 law",
  journal =      j-PHYSICA-A,
  volume =       "559",
  pages =        "125090",
  month =        dec,
  year =         "2020",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2020.125090",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  MRclass =      "92D30 (62P10)",
  MRnumber =     "4138406",
  bibdate =      "Thu May 20 15:48:54 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@InProceedings{Lindstrom:2020:VRC,
  author =       "Peter Lindstrom",
  title =        "Variable-Radix Coding of the Reals",
  crossref =     "Cornea:2020:ISC",
  pages =        "111--116",
  month =        jun,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020.00024",
  ISSN =         "2576-2265",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Recently proposed real number systems like Posits and
                 Elias codes make use of tapered accuracy resulting from
                 variable-length coding of exponents and significands.
                 Several quite different interpretations of these number
                 systems have been provided, though most often these
                 rely on some combination of fixed- and variable-length
                 codes for exponent and significand. We provide a new
                 perspective on these number systems that unifies known
                 representations while suggesting new ones. Our
                 framework is based on multibit radix representations
                 that encode the exponent in unary, the leading nonzero
                 digit in a variable-length code, and the remaining
                 digits in fixed-length binary code. We show how Posits,
                 the various Elias codes, and IEEE 754 like
                 representations can be expressed in this framework.
                 Moreover, we show that Posits and the Elias and codes
                 represent the leading digit using the canonical Huffman
                 code for a probability distribution given by Benford's
                 law, which governs the probability of leading digits.
                 We further show that Posits correspond to the use of a
                 fixed radix while Elias and codes are based on simple
                 sequences of increasing radix. Our approach provides
                 for an intuitive and uniform framework for representing
                 numbers that reveals a visual mapping between codewords
                 and the binary representation of real numbers obscured
                 by prior frameworks. This new interpretation suggests a
                 generalization of Posits and other number systems and
                 provides simple rules for designing
                 information-theoretically optimal codes.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's law; Binary codes; Digital arithmetic; Elias
                 codes; Encoding; floating point; Huffman code; Indexes;
                 posits; Probability distribution; Proposals; real
                 number systems; tapered accuracy; Visualization",
}

@Article{Ma:2020:ERD,
  author =       "Chengcheng Ma and Baoyuan Wu and Shibiao Xu and Yanbo
                 Fan and Yong Zhang and Xiaopeng Zhang and Zhifeng Li",
  title =        "Effective and Robust Detection of Adversarial Examples
                 via {Benford--Fourier} Coefficients",
  journal =      "CoRR",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2020",
  CODEN =        "????",
  DOI =          "https://doi.org/10.48550/arXiv.2005.05552",
  ISSN =         "????",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://arxiv.org/abs/2005.05552 [;]
                 db/journals/corr/corr2005.html#abs-2005-05552",
  abstract =     "Adversarial examples have been well known as a serious
                 threat to deep neural networks (DNNs). In this work, we
                 study the detection of adversarial examples, based on
                 the assumption that the output and internal responses
                 of one DNN model for both adversarial and benign
                 examples follow the generalized Gaussian distribution
                 (GGD), but with different parameters (i.e., shape
                 factor, mean, and variance). GGD is a general
                 distribution family to cover many popular distributions
                 (e.g., Laplacian, Gaussian, or uniform). It is more
                 likely to approximate the intrinsic distributions of
                 internal responses than any specific
                 distribution. Besides, since the shape factor is more
                 robust to different databases rather than the other two
                 parameters, we propose to construct discriminative
                 features via the shape factor for adversarial
                 detection, employing the magnitude of Benford-Fourier
                 coefficients (MBF), which can be easily estimated using
                 responses. Finally, a support vector machine is trained
                 as the adversarial detector through leveraging the MBF
                 features. Extensive experiments in terms of image
                 classification demonstrate that the proposed detector
                 is much more effective and robust on detecting
                 adversarial examples of different crafting methods and
                 different sources, compared to state-of-the-art
                 adversarial detection methods.",
  acknowledgement = ack-nhfb,
  dblp-key =     "journals/corr/abs-2005-05552",
  dblp-mdate =   "2022-04-22",
}

@Article{Volcic:2020:UDB,
  author =       "Aljo{\v{s}}a Vol{\v{c}}i{\v{c}}",
  title =        "Uniform distribution, {Benford}'s law and
                 scale-invariance",
  journal =      j-BOLL-UNIONE-MAT-ITAL,
  volume =       "13",
  number =       "4",
  pages =        "539--543",
  year =         "2020",
  CODEN =        "BLUMAM",
  DOI =          "https://doi.org/10.1007/s40574-020-00245-6",
  ISSN =         "1972-6724",
  MRclass =      "60A10 (28D05)",
  MRnumber =     "4172954",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Bollettino dell'Unione Matematica Italiana",
}

@Article{Barabesi:2021:FBL,
  author =       "Lucio Barabesi and Andrea Cerioli and Domenico
                 Perrotta",
  title =        "Forum on {Benford}'s law and statistical methods for
                 the detection of frauds [{Editorial}]",
  journal =      "Stat. Methods Appl.",
  volume =       "30",
  number =       "3",
  pages =        "767--778",
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s10260-021-00588-0",
  ISSN =         "1618-2510",
  MRclass =      "Expansion",
  MRnumber =     "4308363",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methods \& Applications. Journal of the
                 Italian Statistical Society",
}

@Article{Berger:2021:MBL,
  author =       "Arno Berger and Theodore P. Hill",
  title =        "The mathematics of {Benford}'s law: a primer",
  journal =      "Stat. Methods Appl.",
  volume =       "30",
  number =       "3",
  pages =        "779--795",
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s10260-020-00532-8",
  ISSN =         "1618-2510",
  MRclass =      "Expansion",
  MRnumber =     "4308364",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methods \& Applications. Journal of the
                 Italian Statistical Society",
}

@Article{Cerqueti:2021:DVS,
  author =       "Roy Cerqueti and Mario Maggi",
  title =        "Data validity and statistical conformity with
                 {Benford}'s {Law}",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "144",
  pages =        "Paper No. 110740, 7",
  year =         "2021",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2021.110740",
  ISSN =         "0960-0779 (print), 1873-2887 (electronic)",
  ISSN-L =       "0960-0779",
  MRclass =      "62R07",
  MRnumber =     "4220694",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chaos, Solitons \& Fractals",
}

@Article{daSilvaAzevedo:2021:BLB,
  author =       "Caio {da Silva Azevedo} and Rodrigo Franco
                 Gon{\c{c}}alves and Vagner Luiz Gava and Mauro {de
                 Mesquita Spinola}",
  title =        "A {Benford's Law} based methodology for fraud
                 detection in social welfare programs: {Bolsa Familia}
                 analysis",
  journal =      j-PHYSICA-A,
  volume =       "567",
  pages =        "125626",
  month =        apr,
  year =         "2021",
  CODEN =        "PHYADX",
  DOI =          "https://doi.org/10.1016/j.physa.2020.125626",
  ISSN =         "0378-4371 (print), 1873-2119 (electronic)",
  ISSN-L =       "0378-4371",
  bibdate =      "Thu May 20 15:52:27 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Physica A",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03784371",
}

@Article{Farris:2021:RRB,
  author =       "Madeleine Farris and Noah Luntzlara and Steven J.
                 Miller and Lily Shao and Mengxi Wang",
  title =        "Recurrence relations and {Benford}'s law",
  journal =      "Stat. Methods Appl.",
  volume =       "30",
  number =       "3",
  pages =        "797--817",
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s10260-020-00547-1",
  ISSN =         "1618-2510",
  MRclass =      "11K06 (60F05 65Q30)",
  MRnumber =     "4308365",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methods \& Applications. Journal of the
                 Italian Statistical Society",
}

@Article{Galveas:2021:FAS,
  author =       "Daniel Galv{\^e}as and Fernando Barros and Carlos
                 Alessandro Fuzo",
  title =        "A forensic analysis of {SARS-CoV-2} cases and
                 {COVID-19} mortality misreporting in the {Brazilian}
                 population",
  journal =      "Public Health",
  month =        may,
  year =         "2021",
  CODEN =        "PUHEAE",
  DOI =          "https://doi.org/10.1016/j.puhe.2021.05.010",
  ISSN =         "0033-3506 (print), 1476-5616 (electronic)",
  ISSN-L =       "0033-3506",
  bibdate =      "Thu May 20 15:54:19 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Article{Jianu:2021:RFI,
  author =       "Ionel Jianu and Iulia Jianu",
  title =        "Reliability of Financial Information from the
                 Perspective of {Benford's Law}",
  journal =      j-ENTROPY,
  volume =       "23",
  number =       "5",
  pages =        "557--??",
  month =        may,
  year =         "2021",
  CODEN =        "ENTRFG",
  DOI =          "https://doi.org/10.3390/e23050557",
  ISSN =         "????",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/entropy/entropy23.html#JianuJ21",
  acknowledgement = ack-nhfb,
  dblp-key =     "journals/entropy/JianuJ21",
  dblp-mdate =   "2021-06-01",
  fjournal =     "Entropy",
  journal-URL =  "https://www.mdpi.com/journal/entropy/",
}

@Article{Marchand:2021:BLC,
  author =       "Chase Marchand and Dalton Maahs",
  title =        "{Benford's Law} and {COVID-19} Data",
  journal =      j-CHANCE,
  volume =       "34",
  number =       "2",
  pages =        "31--38",
  year =         "2021",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.2021.1915031",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Mon May 17 16:10:57 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/chance.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance: a magazine for people interested in the
                 analysis of data",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
  onlinedate =   "26 Apr 2021",
}

@Article{Mocnik:2021:BLG,
  author =       "Franz-Benjamin Mocnik",
  title =        "{Benford}'s law and geographical information --- the
                 example of {OpenStreetMap}",
  journal =      "International Journal of Geographical Information
                 Science",
  volume =       "35",
  number =       "9",
  pages =        "1746--1772",
  month =        "????",
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/13658816.2020.1829627",
  ISSN =         "1365-8816 (print), 1365-8824 (electronic)",
  ISSN-L =       "1365-8816",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/gis/gis35.html#Mocnik21",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Geogr. Inf. Sci.",
  dblp-key =     "journals/gis/Mocnik21",
  dblp-mdate =   "2021-09-16",
  fjournal =     "International Journal of Geographical Information
                 Science",
}

@Article{Mumic:2021:MTD,
  author =       "Nermina Mumic and Peter Filzmoser",
  title =        "A multivariate test for detecting fraud based on
                 {Benford}'s law, with application to music streaming
                 data",
  journal =      "Stat. Methods Appl.",
  volume =       "30",
  number =       "3",
  pages =        "819--840",
  year =         "2021",
  DOI =          "https://doi.org/10.1007/s10260-021-00582-6",
  ISSN =         "1618-2510",
  MRclass =      "Expansion",
  MRnumber =     "4308366",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Statistical Methods \& Applications. Journal of the
                 Italian Statistical Society",
}

@Article{Tosic:2021:UBL,
  author =       "Aleksandar To{\v{s}}i{\'c} and Jernej
                 Vi{\v{c}}i{\v{c}}",
  title =        "Use of {Benford}'s law on academic publishing
                 networks",
  journal =      j-J-INFORMETRICS,
  volume =       "15",
  number =       "3",
  pages =        "Article 101163",
  month =        aug,
  year =         "2021",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1016/j.joi.2021.101163",
  ISSN =         "1751-1577 (print), 1875-5879 (electronic)",
  ISSN-L =       "1751-1577",
  bibdate =      "Thu May 20 15:50:31 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jinformetrics.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S1751157721000341",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Informetrics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/17511577/",
}

@Article{Wase:2021:BLB,
  author =       "Viktor Wase",
  title =        "{Benford's Law} in the {Beale} ciphers",
  journal =      j-CRYPTOLOGIA,
  volume =       "45",
  number =       "3",
  pages =        "282--286",
  year =         "2021",
  CODEN =        "CRYPE6",
  DOI =          "https://doi.org/10.1080/01611194.2020.1821409",
  ISSN =         "0161-1194 (print), 1558-1586 (electronic)",
  ISSN-L =       "0161-1194",
  bibdate =      "Wed Jun 9 08:58:59 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/cryptologia.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/01611194.2020.1821409",
  acknowledgement = ack-nhfb,
  fjournal =     "Cryptologia",
  journal-URL =  "https://www.tandfonline.com/loi/ucry20",
}

@Article{Barabesi:2022:CTB,
  author =       "Lucio Barabesi and Andrea Cerasa and Andrea Cerioli
                 and Domenico Perrotta",
  title =        "On Characterizations and Tests of {Benford's Law}",
  journal =      j-J-AM-STAT-ASSOC,
  volume =       "117",
  number =       "540",
  pages =        "1887--1903",
  year =         "2022",
  CODEN =        "JSTNAL",
  DOI =          "https://doi.org/10.1080/01621459.2021.1891927",
  ISSN =         "0162-1459 (print), 1537-274X (electronic)",
  ISSN-L =       "0162-1459",
  bibdate =      "Wed Mar 22 07:55:40 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jamstatassoc2020.bib;
                 http://www.tandfonline.com/toc/uasa20/117/540",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the American Statistical Association",
  journal-URL =  "http://www.tandfonline.com/loi/uasa20",
  onlinedate =   "06 Apr 2021",
}

@InCollection{Neves:2021:ABL,
  author =       "Gilberto A. Neves and Catarina S. Nunes and Paula
                 Odete Fernandes",
  booktitle =    "Optimization, Learning Algorithms and Applications:
                 First International Conference, {OL2A 2021},
                 Bragan{\c{c}}a, Portugal, July 19--21, 2021, Revised
                 Selected Papers",
  title =        "Application of {Benford}'s law to the tourism demand:
                 the case of the {Island of Sal, Cape Verde}",
  volume =       "1488",
  publisher =    "Springer",
  address =      "Cham, Switzerland",
  pages =        "587--598",
  year =         "2021",
  DOI =          "https://doi.org/10.1007/978-3-030-91885-9_43",
  ISBN =         "3-030-91884-X; 3-030-91885-8",
  ISBN-13 =      "978-3-030-91884-2; 978-3-030-91885-9",
  MRnumber =     "4432720",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Commun. Comput. Inf. Sci.",
  URL =          "https://doi.org/10.1007/978-3-030-91885-9_43",
  acknowledgement = ack-nhfb,
}

@Article{Cangiotti:2022:BLN,
  author =       "Nicol{\`o} Cangiotti and Mattia Sensi",
  title =        "{Benford}'s law: a number-theoretical perspective",
  journal =      "Palestine Journal of Mathematics",
  volume =       "11",
  number =       "3",
  pages =        "379--385",
  year =         "2022",
  ISSN =         "2219-5688",
  ISSN-L =       "2219-5688",
  MRclass =      "62E10 (11K06 11K16 62A99)",
  MRnumber =     "4447060",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "Palest. J. Math.",
  fjournal =     "Palestine Journal of Mathematics",
}

@Article{Chen:2022:ASU,
  author =       "Tianyi Chen and Charalampos E. Tsourakakis",
  title =        "{AntiBenford} Subgraphs: Unsupervised Anomaly
                 Detection in Financial Networks",
  journal =      "CoRR",
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  month =        "????",
  year =         "2022",
  CODEN =        "????",
  DOI =          "https://doi.org/10.48550/arXiv.2205.13426",
  ISSN =         "????",
  bibdate =      "Wed Mar 29 09:27:49 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/corr/corr2205.html#abs-2205-13426",
  acknowledgement = ack-nhfb,
  DBLP-key =     "journals/corr/abs-2205-13426",
  DBLP-mdate =   "2022-10-02",
}

@Article{DaSilva:2022:AOB,
  author =       "St{\'e}phane Blondeau {Da Silva}",
  title =        "An alternative to the oversimplifying {Benford}'s law
                 in experimental fields",
  journal =      j-SANKHYA-B,
  volume =       "84",
  number =       "2",
  pages =        "778--808",
  year =         "2022",
  CODEN =        "SANBBV",
  DOI =          "https://doi.org/10.1007/s13571-022-00287-0",
  ISSN =         "0976-8386,0976-8394",
  MRclass =      "99-01",
  MRnumber =     "4502751",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://doi.org/10.1007/s13571-022-00287-0",
  acknowledgement = ack-nhfb,
  fjournal =     "Sankhya B. The Indian Journal of Statistics",
}

@Article{Groharing:2022:BLC,
  author =       "Brooks Groharing and David McCune",
  title =        "{Benford's Law} and County-Level Votes in {US}
                 {Presidential} Elections",
  journal =      j-CHANCE,
  volume =       "35",
  number =       "2",
  pages =        "4--10",
  year =         "2022",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.2022.2066408",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Sat Jun 4 14:19:58 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/chance.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066408",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
}

@Article{Mbona:2022:FSU,
  author =       "Innocent Mbona and Jan H. P. Eloff",
  title =        "Feature selection using {Benford}'s law to support
                 detection of malicious social media bots",
  journal =      j-INFO-SCI,
  volume =       "582",
  pages =        "369--381",
  month =        jan,
  year =         "2022",
  CODEN =        "ISIJBC",
  DOI =          "https://doi.org/10.1016/j.ins.2021.09.038",
  ISSN =         "0020-0255 (print), 1872-6291 (electronic)",
  ISSN-L =       "0020-0255",
  MRclass =      "62H25 (91D30)",
  MRnumber =     "4318332",
  bibdate =      "Tue Feb 22 14:31:21 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://dblp.org/db/journals/isci/isci582.html#MbonaE22",
  acknowledgement = ack-nhfb,
  DBLP-key =     "journals/isci/MbonaE22",
  DBLP-mdate =   "2021-12-01",
  fjournal =     "Information Sciences. An International Journal",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200255",
}

@Article{Miraglia:2022:AIC,
  author =       "Jorge E. Miraglia and Maria Silvia Gravielle",
  title =        "Atomic ionization, capture, and stopping cross
                 sections by ion impact examined with the {Benford
                 law}",
  journal =      j-ADV-QUANTUM-CHEM,
  volume =       "85",
  pages =        "??--??",
  year =         "2022",
  CODEN =        "AQCHA9",
  DOI =          "https://doi.org/10.1016/bs.aiq.2022.04.006",
  ISSN =         "0065-3276",
  ISSN-L =       "0065-3276",
  bibdate =      "Wed Sep 21 07:26:09 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/advquantumchem.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.sciencedirect.com/science/article/pii/S0065327622000107",
  acknowledgement = ack-nhfb,
  ajournal =     "Adv. Quantum Chem.",
  fjournal =     "Advances in Quantum Chemistry",
  journal-URL =  "http://www.sciencedirect.com/science/bookseries/00653276/",
}

@InCollection{Nelson:2022:BLM,
  author =       "Sybil Prince Nelson and Brian Wickman and Jack Null
                 and Eric Gazin",
  booktitle =    "Mathematics and computation in music",
  title =        "{Benford}'s law and music note frequencies",
  volume =       "13267",
  publisher =    "Springer",
  address =      "Cham, Switzerland",
  pages =        "383--389",
  year =         "2022",
  DOI =          "https://doi.org/10.1007/978-3-031-07015-0\_34",
  ISBN =         "978-30310-7-0-1-4-3; 978-30310-7-0-1-5-0",
  ISBN-13 =      "978-3-031-07014-3; 978-3-031-07015-0",
  MRclass =      "00A65",
  MRnumber =     "4485599",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Lecture Notes in Comput. Sci.",
  URL =          "https://doi.org/10.1007/978-3-031-07015-0_34",
  acknowledgement = ack-nhfb,
}

@Article{Pollack:2022:DSB,
  author =       "Paul Pollack and Akash Singha Roy",
  title =        "{Dirichlet}, {Sierpi{\'n}ski}, and {Benford}",
  journal =      j-J-NUMBER-THEORY,
  volume =       "239",
  number =       "??",
  pages =        "352--364",
  month =        oct,
  year =         "2022",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2021.12.010",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Fri Jun 3 11:42:55 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X22000099",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Velleman:2022:ECD,
  author =       "Paul Velleman and Howard Wainer",
  title =        "Exploring {COVID} Data with {Benford}'s and {Zipf}'s
                 Laws",
  journal =      j-CHANCE,
  volume =       "35",
  number =       "2",
  pages =        "11--15",
  year =         "2022",
  CODEN =        "CNDCE4",
  DOI =          "https://doi.org/10.1080/09332480.2022.2066410",
  ISSN =         "0933-2480 (print), 1867-2280 (electronic)",
  ISSN-L =       "0933-2480",
  bibdate =      "Sat Jun 4 14:19:58 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/chance.bib",
  URL =          "http://www.tandfonline.com/doi/full/10.1080/09332480.2022.2066410",
  acknowledgement = ack-nhfb,
  fjournal =     "Chance",
  journal-URL =  "http://chance.amstat.org/;
                 http://link.springer.com/journal/144;
                 http://www.tandfonline.com/loi/ucha20",
}

@Article{Barabesi:2023:SMB,
  author =       "Lucio Barabesi and Andrea Cerioli and Marco {Di
                 Marzio}",
  title =        "Statistical models and the {Benford} hypothesis: a
                 unified framework",
  journal =      j-TEST,
  volume =       "32",
  number =       "4",
  pages =        "1479--1507",
  month =        dec,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11749-023-00881-y",
  ISSN =         "1133-0686 (print), 1863-8260 (electronic)",
  ISSN-L =       "1133-0686",
  bibdate =      "Wed Aug 14 12:02:10 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/test.bib",
  URL =          "https://link.springer.com/article/10.1007/s11749-023-00881-y",
  acknowledgement = ack-nhfb,
  ajournal =     "TEST",
  fjournal =     "TEST: An Official Journal of the Spanish Society of
                 Statistics and Operations Research",
  journal-URL =  "http://link.springer.com/journal/11749",
}

@Article{Cerqueti:2023:BLE,
  author =       "Roy Cerqueti and Davide Provenzano",
  title =        "{Benford}'s law for economic data reliability: the
                 case of tourism flows in {Sicily}",
  journal =      j-CHAOS-SOLITONS-FRACTALS,
  volume =       "173",
  pages =        "1--10",
  year =         "2023",
  CODEN =        "CSFOEH",
  DOI =          "https://doi.org/10.1016/j.chaos.2023.113635",
  ISSN =         "0960-0779,1873-2887",
  ISSN-L =       "0960-0779",
  MRclass =      "62R07 (62P20)",
  MRnumber =     "4598410",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://doi.org/10.1016/j.chaos.2023.113635",
  acknowledgement = ack-nhfb,
  articleno =    "113635",
  fjournal =     "Chaos, Solitons \& Fractals",
  pagecount =    "10",
}

@Article{Cerqueti:2023:STB,
  author =       "Roy Cerqueti and Claudio Lupi",
  title =        "Severe testing of {Benford}'s law",
  journal =      j-TEST,
  volume =       "32",
  number =       "2",
  pages =        "677--694",
  month =        jun,
  year =         "2023",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1007/s11749-023-00848-z",
  ISSN =         "1133-0686 (print), 1863-8260 (electronic)",
  ISSN-L =       "1133-0686",
  bibdate =      "Wed Oct 11 15:13:55 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/test.bib",
  URL =          "https://link.springer.com/article/10.1007/s11749-023-00848-z",
  acknowledgement = ack-nhfb,
  ajournal =     "TEST",
  fjournal =     "TEST: An Official Journal of the Spanish Society of
                 Statistics and Operations Research",
  journal-URL =  "http://link.springer.com/journal/11749",
}

@Article{Chandee:2023:BLM,
  author =       "Vorrapan Chandee and Xiannan Li and Paul Pollack and
                 Akash Singha Roy",
  title =        "On {Benford}'s law for multiplicative functions",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "151",
  number =       "11",
  pages =        "4607--4619",
  year =         "2023",
  CODEN =        "PAMYAR",
  DOI =          "https://doi.org/10.1090/proc/16480",
  ISSN =         "0002-9939,1088-6826",
  ISSN-L =       "0002-9939",
  MRclass =      "11N60 (11K65)",
  MRnumber =     "4634867",
  MRreviewer =   "Christoph Aistleitner",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://doi.org/10.1090/proc/16480",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}

@Article{Kazemitabar:2023:GFC,
  author =       "Javad Kazemitabar",
  title =        "A general framework for constructing distributions
                 satisfying {Benford}'s law",
  journal =      j-COMMUN-STAT-SIMUL-COMPUT,
  volume =       "52",
  number =       "12",
  pages =        "6160--6167",
  year =         "2023",
  CODEN =        "CSSCDB",
  DOI =          "https://doi.org/10.1080/03610918.2022.2032153",
  ISSN =         "0361-0918",
  ISSN-L =       "0361-0918",
  bibdate =      "Sat May 18 14:28:31 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstatsimulcomput2020.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Simulation and
                 Computation",
  journal-URL =  "http://www.tandfonline.com/loi/lssp20",
  onlinedate =   "18 May 2022",
}

@Article{Kim:2023:EFA,
  author =       "Phuoc Nguyen Kim and Jonatan Contreras and Martine
                 Ceberio and Nguyen Ngoc Thach",
  title =        "Economic and financial applications of {Benford's
                 Law}: from traditional use in audits to help in deep
                 learning",
  journal =      "Internat. J. Uncertain. Fuzziness Knowledge-Based
                 Systems",
  volume =       "31",
  pages =        "197--207",
  year =         "2023",
  DOI =          "https://doi.org/10.1142/S0218488523400111",
  ISSN =         "0218-4885,1793-6411",
  MRclass =      "91B99 (68T07)",
  MRnumber =     "4700940",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://doi.org/10.1142/S0218488523400111",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Uncertainty, Fuzziness and
                 Knowledge-Based Systems",
}

@Article{Kondo:2023:HTZ,
  author =       "Illenin O. Kondo and Logan T. Lewis and Andrea
                 Stella",
  title =        "Heavy tailed but not {Zipf}: Firm and establishment
                 size in the {United States}",
  journal =      j-J-APPL-ECONOMETRICS,
  volume =       "38",
  number =       "5",
  pages =        "767--785",
  month =        aug,
  year =         "2023",
  CODEN =        "JAECET",
  DOI =          "https://doi.org/10.1002/jae.2976",
  ISSN =         "0883-7252 (print), 1099-1255 (electronic)",
  ISSN-L =       "0883-7252",
  bibdate =      "Mon Oct 16 14:44:43 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jappleconometrics.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Appl. Econometrics",
  fjournal =     "Journal of Applied Econometrics",
  journal-URL =  "https://onlinelibrary.wiley.com/journal/10991255;
                 https://www.jstor.org/journal/japplecon",
  onlinedate =   "23 April 2023",
}

@Article{Murtagh:2023:WBL,
  author =       "Jack Murtagh",
  title =        "What is {Benford's Law}? {Why} This Unexpected Pattern
                 of Numbers is Everywhere",
  journal =      j-SCI-AMER,
  volume =       "??",
  number =       "??",
  pages =        "??--??",
  day =          "8",
  month =        may,
  year =         "2023",
  CODEN =        "SCAMAC",
  ISSN =         "0036-8733 (print), 1946-7087 (electronic)",
  ISSN-L =       "0036-8733",
  bibdate =      "Mon May 08 09:47:36 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://www.scientificamerican.com/article/what-is-benfords-law-why-this-unexpected-pattern-of-numbers-is-everywhere/",
  acknowledgement = ack-nhfb,
  fjournal =     "Scientific American",
  journal-URL =  "http://www.nature.com/scientificamerican",
}

@Article{Campanelli:2024:EDS,
  author =       "Leonardo Campanelli",
  title =        "On the {Euclidean} distance statistic of {Benford}'s
                 law",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "53",
  number =       "2",
  pages =        "451--474",
  year =         "2024",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1080/03610926.2022.2082480",
  ISSN =         "0361-0926,1532-415X",
  ISSN-L =       "0361-0926",
  MRclass =      "99-01",
  MRnumber =     "4669200",
  bibdate =      "Tue May 21 16:59:59 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2020.bib",
  URL =          "https://doi.org/10.1080/03610926.2022.2082480",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics. Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}

@Article{Fang:2024:BLR,
  author =       "Xinyu Fang and Steven J. Miller and Maxwell Sun and
                 Amanda Verga",
  title =        "{Benford}'s law and random integer decomposition with
                 congruence stopping condition",
  journal =      j-J-NUMBER-THEORY,
  volume =       "264",
  number =       "??",
  pages =        "307--356",
  month =        nov,
  year =         "2024",
  CODEN =        "JNUTA9",
  DOI =          "https://doi.org/10.1016/j.jnt.2024.05.005",
  ISSN =         "0022-314X (print), 1096-1658 (electronic)",
  ISSN-L =       "0022-314X",
  bibdate =      "Tue Aug 6 14:07:34 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/jnumbertheory2020.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0022314X24001367",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Number Theory",
  fjournal =     "Journal of Number Theory",
  journal-URL =  "http://www.sciencedirect.com/science/journal/0022314X",
}

@Article{Gupta:2024:ADQ,
  author =       "Solanki Gupta and Vivek Kumar Singh and Sumit Kumar
                 Banshal",
  title =        "Altmetric data quality analysis using {Benford}'s
                 law",
  journal =      j-SCIENTOMETRICS,
  volume =       "129",
  number =       "7",
  pages =        "4597--4621",
  month =        jul,
  year =         "2024",
  CODEN =        "SCNTDX",
  DOI =          "https://doi.org/10.1007/s11192-024-05061-9",
  ISSN =         "0138-9130 (print), 1588-2861 (electronic)",
  ISSN-L =       "0138-9130",
  bibdate =      "Mon Aug 5 13:03:44 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/scientometrics2020.bib",
  URL =          "https://link.springer.com/article/10.1007/s11192-024-05061-9",
  acknowledgement = ack-nhfb,
  ajournal =     "Scientometrics",
  fjournal =     "Scientometrics",
  journal-URL =  "http://link.springer.com/journal/11192",
}

@Book{Mebane:20xx:EF,
  author =       "Walter R. {Mebane, Jr.}",
  title =        "Election Forensics",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "20xx",
  bibdate =      "Sat Sep 10 14:28:31 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  note =         "Book in preparation.",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
}

%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Apers:1989:VLD,
  editor =       "P. M. G. (Petrus Maria Gerardus) Apers and Gio
                 Wiederhold",
  booktitle =    "Very large data bases: proceedings: proceedings of the
                 Fifteenth International Conference on Very Large Data
                 Bases, August 22--25, 1989, Amsterdam, The
                 Netherlands",
  title =        "Very large data bases: proceedings: proceedings of the
                 Fifteenth International Conference on Very Large Data
                 Bases, August 22--25, 1989, Amsterdam, The
                 Netherlands",
  publisher =    pub-MORGAN-KAUFMANN,
  address =      pub-MORGAN-KAUFMANN:adr,
  pages =        "xii + 467",
  year =         "1989",
  ISBN =         "1-55860-101-5",
  ISBN-13 =      "978-1-55860-101-7",
  LCCN =         "QA 76.9 D3 I61 1989",
  bibdate =      "Sat Dec 7 13:05:35 MST 1996",
  bibsource =    "DBLP; http://dblp.uni-trier.de;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  keywords =     "database management -- congresses",
}

@Book{Gell-Mann:1997:QJA,
  author =       "Murray Gell-Mann",
  booktitle =    "The quark and the jaguar: adventures in the simple and
                 the complex",
  title =        "The quark and the jaguar: adventures in the simple and
                 the complex",
  publisher =    pub-W-H-FREEMAN,
  address =      pub-W-H-FREEMAN:adr,
  pages =        "xviii + 392",
  year =         "1997",
  ISBN =         "0-7167-2725-0 (paperback)",
  ISBN-13 =      "978-0-7167-2725-5 (paperback)",
  LCCN =         "QC774.G45 A3 1994",
  bibdate =      "Fri Aug 8 06:26:36 MDT 2014",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib",
  URL =          "http://www.gbv.de/dms/bowker/toc/9780716725817.pdf;
                 http://www.zentralblattmath.org/zmath/en/search/?an=0833.00011",
  abstract =     "From one of the architects of the new science of
                 simplicity and complexity comes a highly personal,
                 unifying vision of the natural world. As a theoretical
                 physicist, Murray Gell-Mann has explored nature at its
                 most fundamental level. His achievements include the
                 1969 Nobel Prize for work leading up to his discovery
                 of the quark --- the basic building block of all atomic
                 nuclei throughout the universe. But Gell-Mann is a man
                 of many intellectual passions, with lifelong interests
                 in fields that seek to understand existence at its most
                 complex: natural history, biological evolution, the
                 history of language, and the study of creative
                 thinking. These seemingly disparate pursuits come
                 together in Gell-Mann's current work at the Santa Fe
                 Institute, where scientists are investigating the
                 similarities and differences among complex adaptive
                 systems --- systems that learn or evolve by utilizing
                 acquired information. They include a child learning his
                 or her native language, a strain of bacteria becoming
                 resistant to an antibiotic, the scientific community
                 testing new theories, or an artist implementing a
                 creative idea. The Quark and the Jaguar is Gell-Mann's
                 own story of finding the connections between the basic
                 laws of physics and the complexity and diversity of the
                 natural world. The simple: a quark inside an atom. The
                 complex: a jaguar prowling its jungle territory in the
                 night. Exploring the relationship between them becomes
                 a series of exciting intellectual adventures.",
  acknowledgement = ack-nhfb,
  subject =      "Gell-Mann, Murray; Travel; Ecuador; Particles (Nuclear
                 physics); Nuclear physicists; United States; Biography;
                 Description and travel",
  tableofcontents = "Part 1. The Simple and the Complex \\
                 1. Prologue: An Encounter in the Jungle \\
                 2. Early Light \\
                 3. Information and Crude Complexity \\
                 4. RANDomness \\
                 5. A Child Learning a Language \\
                 6. Bacteria Developing Drug Resistance \\
                 7. The Scientific Enterprise \\
                 8. The Power of Theory \\
                 9. What Is Fundamental? \\
                 Part 2. The Quantum Universe \\
                 10. Simplicity and Randomness in the Quantum Mechanics
                 Universe \\
                 11. A Contemporary View of Quantum Mechanics \\
                 12. Quantum Mechanics and Flapdoodle \\
                 13. Quarks and All That: The Standard Model \\
                 14. Superstring Theory: Unification at Last? \\
                 15. Time's Arrow's: Forward and Backward Time \\
                 Part 3. Selection and Fitness \\
                 16. Selection at Work in Biological Evolution and
                 Elsewhere \\
                 17. From Learning to Creative Thinking \\
                 18. Superstition and Skepticism \\
                 19. Adaptive and Maladaptive Schema \\
                 20. Machines That Learn or Simulate Learning \\
                 Part 4. Diversity and Sustainability \\
                 21. Diversities Under Threat \\
                 22. Transitions to a More Sustainable World \\
                 23. Afterword \\
                 Index",
}

@Proceedings{ACM:2000:PIC,
  editor =       "{ACM}",
  booktitle =    "{Proceedings of the 2000 International Conference on
                 Software Engineering: ICSE 2000, the new millennium:
                 June 4--11, 2000, Limerick, Ireland}",
  title =        "{Proceedings of the 2000 International Conference on
                 Software Engineering: ICSE 2000, the new millennium:
                 June 4--11, 2000, Limerick, Ireland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xviii + 843",
  year =         "2000",
  ISBN =         "1-58113-206-9, 0-7803-6325-6 (casebound),
                 0-7803-6326-4 (microfiche)",
  ISBN-13 =      "978-1-58113-206-9, 978-0-7803-6325-0 (casebound),
                 978-0-7803-6326-7 (microfiche)",
  LCCN =         "QA76 N271 2000",
  bibdate =      "Sun Feb 17 08:56:25 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
}

@Proceedings{Raidl:2003:AEC,
  editor =       "Gunther Raidl",
  booktitle =    "{Applications of evolutionary computing: EvoWorkshops
                 2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and
                 EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}",
  title =        "{Applications of evolutionary computing: EvoWorkshops
                 2003: EvoBIO, EvoCOP, EvoIASP, EvoMUSART, EvoROB, and
                 EvoSTIM, Essex, UK, April 14--16, 2003: Proceedings}",
  volume =       "2611",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxi + 708",
  year =         "2003",
  CODEN =        "LNCSD9",
  DOI =          "????",
  ISBN =         "3-540-00976-0 (softcover)",
  ISBN-13 =      "978-3-540-00976-4 (softcover)",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  LCCN =         "QA76.618 .E899 2003",
  bibdate =      "Thu Aug 21 09:09:03 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/mandelbrot-benoit.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/lncs.bib",
  series =       ser-LNCS,
  URL =          "http://link.springer-ny.com/link/service/series/0558/tocs/t2611.htm;
                 http://www.springerlink.com/content/978-3-540-00976-4;
                 http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=2611",
  acknowledgement = ack-nhfb,
  keywords =     "evolutionary computation --- congresses; evolutionary
                 programming (computer science) --- congresses",
}

@Article{Rybski:2023:ALZ,
  author =       "Diego Rybski and Antonio Ciccone",
  title =        "{Auerbach}, {Lotka}, and {Zipf}: pioneers of power-law
                 city-size distributions",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "77",
  number =       "6",
  pages =        "601--613",
  month =        nov,
  year =         "2023",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s00407-023-00314-0",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  bibdate =      "Wed Mar 27 09:47:28 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  URL =          "https://link.springer.com/article/10.1007/s00407-023-00314-0",
  acknowledgement = ack-nhfb,
  ajournal =     "Arch. Hist. Exact Sci.",
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
}

@Book{Warren:2003:HD,
  author =       "Henry S. Warren",
  booktitle =    "Hacker's delight",
  title =        "Hacker's delight",
  publisher =    pub-AW,
  address =      pub-AW:adr,
  pages =        "xiv + 306",
  year =         "2003",
  ISBN =         "0-201-91465-4",
  ISBN-13 =      "978-0-201-91465-8",
  LCCN =         "QA76.6 .W375 2003",
  bibdate =      "Tue Jan 03 18:20:34 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "While this book does not specifically address
                 computational aspects of floating-point arithmetic
                 (apart from the nine-page Chapter 15), it has extensive
                 coverage of, and clever algorithms for, integer
                 arithmetic operations that are fundamental for
                 implementing hardware floating-arithmetic and software
                 multiple-precision arithmetic.",
  URL =          "http://www.awprofessional.com/bookstore/product.asp?isbn=0201914654;
                 http://www.hackersdelight.org/;
                 http://www.hackersdelight.org/hackerTOC.pdf;
                 http://www.informit.com/content/images/chap3_0201914654/elementLinks/0201914654.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "DEC PDP-10; division by constants; Gray code; Hilbert
                 curves; IEEE 754 floating-point arithmetic; integer
                 cube root; integer division; integer exponentiation;
                 integer logarithm; integer square root; prime numbers;
                 unusual number bases",
  remark =       "Foreword by Guy L. Steele, Jr., who begins ``When I
                 first got a summer job at MIT's Project MAC almost 30
                 years ago, I was delighted to be able to work with the
                 DEC PDP-10 computer, which was more fun to program in
                 assembly language than any other computer, bar none,
                 because of its rich yet tractable set of instructions
                 for performing bit tests, bit masking, field
                 manipulation, and operations on integers. Though the
                 PDP-10 has not been manufactured for quite some years,
                 there remains a thriving cult of enthusiasts who keep
                 old PDP-10 hardware running and who run old PDP-10
                 software---entire operating systems and their
                 applications---by using personal computers to simulate
                 the PDP-10 instruction set.''",
  subject =      "Computer programming; Computer hackers",
  tableofcontents = "Preface\par

                 1. Introduction\par

                 Notation\par

                 Instruction Set and Execution Time Model\par

                 2. Basis\par

                 Manipulating Rightmost Bits \\
                 Addition Combined with Logical Operations \\
                 Inequalities among Logical and Arithmetic Expressions
                 \\
                 Absolute Value Function \\
                 Sign Extension \\
                 Shift Right Signed from Unsigned \\
                 Sign Function \\
                 Three-Valued Compare \\
                 Transfer of Sign \\
                 Decoding a `Zero Means 2**n' Field \\
                 Comparison Predicates \\
                 Overflow Detection \\
                 Condition Code Result of Add, Subtract, and Multiply
                 \\
                 Rotate Shifts \\
                 Double-Length Add/Subtract \\
                 Double-Length Shifts \\
                 Multibyte Add, Subtract, Absolute Value \\
                 Doz, Max, Min \\
                 Exchanging Registers \\
                 Alternating among Two or More Values\par

                 3. Power-of-2 Boundaries\par

                 Rounding Up/Down to a Multiple of a Known Power of 2
                 \\
                 Rounding Up/Down to the Next Power of 2 \\
                 Detecting a Power-of-2 Boundary Crossing\par

                 4. Arithmetic Bounds\par

                 Checking Bounds of Integers \\
                 Propagating Bounds through Adds and Subtracts \\
                 Propagating Bounds through Logical Operations \\
                 Signed Bounds\par

                 5. Counting Bits\par

                 Counting 1-bits \\
                 Parity \\
                 Counting Leading 0's \\
                 Counting Trailing 0's\par

                 6. Searching Words\par

                 Find First 0-Byte \\
                 Find First String of 1-Bits of a Given Length\par

                 7. Rearranging Bits and Bytes\par

                 Reversing Bits and Bytes \\
                 Shuffling Bits \\
                 Transposing a Bit Matrix \\
                 Compress, or Generalized Extract \\
                 General Permutations, Sheep and Goats Operation \\
                 Rearrangements and Index Transformations\par

                 8. Multiplication\par

                 Multiword Multiplication \\
                 High-Order Half of 64-Bit Product \\
                 High-Order Product Signed from/to Unsigned \\
                 Multiplication by Constants\par

                 9. Integer Division\par

                 Preliminaries \\
                 Multiword Division \\
                 Unsigned Short Division from Signed Division \\
                 Unsigned Long Division\par

                 10. Integer Division by Constants\par

                 Signed Division by a Known Power of 2 \\
                 Signed Remainder from Division by a Known Power of 2
                 \\
                 Signed Division and Remainder by Non-powers of 2 \\
                 Signed Division by Divisors >= 2 \\
                 Signed Division by Divisors <= -2 \\
                 Incorporation into a Compiler \\
                 Miscellaneous Topics \\
                 Unsigned Division \\
                 Unsigned Division by Divisors >= 1 \\
                 Incorporation into a Compiler (Unsigned) \\
                 Miscellaneous Topics (Unsigned) \\
                 Applicability to Modulus and Floor Division \\
                 Similar Methods \\
                 Sample Magic Numbers \\
                 Exact Division by Constants \\
                 Test for Zero Remainder after Division by a
                 Constant\par

                 11. Some Elementary Functions\par

                 Integer Square Root \\
                 Integer Cube Root \\
                 Integer Exponentiation \\
                 Integer Logarithm\par

                 12. Unusual Bases for Number Systems\par

                 Base -2 \\
                 Base -1 + i \\
                 Other Bases \\
                 What is the Most Efficient Base?\par

                 13. Gray Code \\
                 Gray Code \\
                 Incrementing a Gray Coded Integer \\
                 Negabinary Gray Code \\
                 Brief History and Applications\par

                 14. Hilbert's Curve\par

                 A Recursive Algorithm for Generating the Hilbert Curve
                 \\
                 Coordinates from Distance along the Hilbert Curve \\
                 Distance from Coordinates on the Hilbert Curve \\
                 Incrementing the Coordinates on the Hilbert Curve \\
                 Non-recursive Generating Algorithms \\
                 Other Space-Filling Curves \\
                 Applications\par

                 15. Floating-Point\par

                 IEEE Format \\
                 Comparing Floating-Point Numbers Using Integer
                 Operations \\
                 The Distribution of Leading Digits \\
                 Table of Miscellaneous Values\par

                 16. Formulas for Primes\par

                 Introduction \\
                 Willans's Formulas \\
                 Wormell's Formula \\
                 Formulas for Other Difficult Functions\par

                 Appendix A. Arithmetic Tables for a 4-Bit
                 Machine\par

                 Appendix B. Newton's Method\par

                 Bibliography.",
}

@Proceedings{Gama:2005:MLE,
  editor =       "Jo{\~a}ao Gama and Rui Camacho and Pavel Brazdil and
                 Al{\'\i}pio M{\'a}rio Jorge and Lu{\'\i}s Torgo",
  booktitle =    "{Machine learning --- ECML 2005: 16th European
                 Conference on Machine Learning, Porto, Portugal,
                 October 3--7, 2005: proceedings}",
  title =        "{Machine learning --- ECML 2005: 16th European
                 Conference on Machine Learning, Porto, Portugal,
                 October 3--7, 2005: proceedings}",
  volume =       "3720",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxiii + 769",
  year =         "2005",
  ISBN =         "3-540-29243-8",
  ISBN-13 =      "978-3-540-29243-2",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  LCCN =         "Q325.5 .E26 2005",
  bibdate =      "Tue Nov 15 08:57:03 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       ser-LNCS # " and " # ser-LNAI,
  URL =          "http://www.loc.gov/catdir/enhancements/fy0663/2005933045-d.html;
                 http://www.springerlink.com/openurl.asp?genre=issue\%26issn=0302-9743\%26volume=3720",
  acknowledgement = ack-nhfb,
  meetingname =  "ECML 2005 (2005: Porto, Portugal)",
  subject =      "Machine learning; Congresses",
}

@Proceedings{Neumann:2005:CAE,
  editor =       "L{\'a}szl{\'o} Neumann and Mateu Sbert and Bruce Gooch
                 and Werner Purgathofer",
  booktitle =    "{Computational aesthetics 2005: Eurographics Workshop
                 on Computational Aesthetics in Graphics, Visualization
                 and Imaging, Girona, Spain, 18--20 May 2005}",
  title =        "{Computational aesthetics 2005: Eurographics Workshop
                 on Computational Aesthetics in Graphics, Visualization
                 and Imaging, Girona, Spain, 18--20 May 2005}",
  publisher =    "Eurographics Association",
  address =      "Aire-la-Ville, Switzerland",
  pages =        "245",
  year =         "2005",
  ISBN =         "3-905673-27-4",
  ISBN-13 =      "978-3-905673-27-2",
  ISSN =         "1816-0859",
  bibdate =      "Tue Nov 15 06:34:24 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Computational aesthetics",
  acknowledgement = ack-nhfb,
}

@Book{Alvarez:2008:EFD,
  editor =       "R. Michael Alvarez and Thad E. (Thad Edward) Hall and
                 Susan D. Hyde",
  booktitle =    "Election Fraud: Detecting and Deterring Electoral
                 Manipulation",
  title =        "Election Fraud: Detecting and Deterring Electoral
                 Manipulation",
  publisher =    "Brookings Institution Press",
  address =      "Washington, DC, USA",
  pages =        "xiii + 255",
  year =         "2008",
  ISBN =         "0-8157-0138-1 (hardcover), 0-8157-0139-X (paperback)",
  ISBN-13 =      "978-0-8157-0138-5 (hardcover), 978-0-8157-0139-2
                 (paperback)",
  LCCN =         "JK1994 .E43 2008",
  bibdate =      "Sat Sep 10 14:23:39 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/toc/ecip0810/2008005719.html",
  abstract =     "Brings together experts on election law, election
                 administration, and U.S. and comparative politics to
                 examine the U.S. understanding of election fraud. With
                 survey data, incident reports, and state-collected
                 fraud allegations, measures the extent and nature of
                 election fraud in U.S. Analyzes techniques for
                 detecting and potentially deterring fraud..",
  acknowledgement = ack-nhfb,
  keywords =     "Benford's Law",
  subject =      "Elections; Corrupt practices; United States;
                 Prevention; Ballot; Security measures; Case studies",
  tableofcontents = "Corruption of the election process under U.S.
                 federal law / Craig C. Donsanto \\
                 International principles for election integrity / Thad
                 E. Hall and Tova Andrea Wang \\
                 Beyond election fraud: manipulation, violence, and
                 foreign power intervention / Gamze {\eth}Cavdar \\
                 Measuring perceptions of election threats: survey data
                 from voters and elites / R. Michael Alvarez and Thad E.
                 Hall \\
                 Caught in the act: recent federal election fraud cases
                 / Delia Bailey \\
                 Correlates of fraud: studying state election fraud
                 allegations / R. Michael Alvarez and Frederick J.
                 Boehmke \\
                 Fraud or failure? what incident reports reveal about
                 election anomalies and irregularities / D. Roderick
                 Kiewiet \ldots{} [et al.] \\
                 Identifying and preventing signature fraud on ballot
                 measure petitions / Todd Donovan and Daniel A. Smith
                 \\
                 The case of the 2002 general election / R. Michael
                 Alvarez and Jonathan N. Katz \\
                 Election forensics: the second-digit Benford's law test
                 and recent American presidential elections / Walter R.
                 Mebane, Jr. \\
                 On the trail of fraud: estimating the flow of votes
                 between Russia's elections / Mikhail Myagkov, Peter C.
                 Ordeshook, and Dimitry Shaikin \\
                 How international election observers detect and deter
                 fraud / Susan D. Hyde \\
                 Unintended consequences of election monitoring /
                 Alberto Simpser",
}

@Book{Horgan:2009:PRI,
  author =       "Jane M. Horgan",
  booktitle =    "Probability with {R}: an introduction with computer
                 science applications",
  title =        "Probability with {R}: an introduction with computer
                 science applications",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xviii + 393",
  year =         "2009",
  ISBN =         "0-470-28073-5 (cloth)",
  ISBN-13 =      "978-0-470-28073-7 (cloth)",
  LCCN =         "QA76.9.M35 H863 2009",
  bibdate =      "Wed Sep 15 09:37:35 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/toc/ecip0819/2008022817.html;
                 http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470280735.html",
  acknowledgement = ack-nhfb,
  subject =      "computer science; mathematics; probabilities; R
                 (computer programming language)",
}

@Proceedings{Paredaens:2009:PTE,
  editor =       "Jan Paredaens and Jianwen Su",
  booktitle =    "{Proceedings of the twenty-eighth ACM
                 SIGMOD-SIGACT-SIGART symposium on Principles of
                 database systems: PODS'09, Providence, Rhode Island,
                 June 29--July 1, 2009}",
  title =        "{Proceedings of the twenty-eighth ACM
                 SIGMOD-SIGACT-SIGART symposium on Principles of
                 database systems, PODS'09, Providence, Rhode Island,
                 June 29--July 1, 2009}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "x + 288",
  year =         "2009",
  ISBN =         "1-60558-553-X",
  ISBN-13 =      "978-1-60558-553-6",
  LCCN =         "????",
  bibdate =      "Thu Jul 02 12:41:14 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Nigrini:2011:FAM,
  author =       "Mark J. (Mark John) Nigrini",
  booktitle =    "Forensic analytics: methods and techniques for
                 forensic accounting investigations",
  title =        "Forensic analytics: methods and techniques for
                 forensic accounting investigations",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xvi + 463",
  year =         "2011",
  DOI =          "https://doi.org/10.1002/9781118386798",
  ISBN =         "0-470-89046-0, 1-118-08763-1 (e-book), 1-118-08766-6
                 (e-book), 1-118-08768-2 (e-book), 1-118-38679-5
                 (e-book)",
  ISBN-13 =      "978-0-470-89046-2, 978-1-118-08763-3 (e-book),
                 978-1-118-08766-4 (e-book), 978-1-118-08768-8 (e-book),
                 978-1-118-38679-8 (e-book)",
  LCCN =         "HV6768 .N54 2011",
  bibdate =      "Sat Feb 23 17:38:11 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "Wiley corporate F and A",
  URL =          "http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-d.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1107/2011007210-t.html;
                 http://catdir.loc.gov/catdir/enhancements/fy1109/2011007210-b.html",
  abstract =     "The book will review and discuss (with Access and
                 Excel examples) the methods and techniques that
                 investigators can use to uncover anomalies in corporate
                 and public sector data. These anomalies would include
                 errors, biases, duplicates, number rounding, and
                 omissions. The focus will be the detection of fraud,
                 intentional errors, and unintentional errors using data
                 analytics. Despite the quantitative and computing bias,
                 the book will still be interesting to read with
                 interesting vignettes and illustrations. Most chapters
                 will be understandable by accountants and auditors that
                 usually are lacking in the rigors of mathematics and
                 statistics. The data interrogation methods are based on
                 (a) known statistical techniques, and (b) the author's
                 own published research in the field.",
  acknowledgement = ack-nhfb,
  subject =      "Forensic accounting; Fraud; Misleading financial
                 statements; LAW / Forensic Science",
  tableofcontents = "Front Matter \\
                 Using Access in Forensic Investigations \\
                 Using Excel in Forensic Investigations \\
                 Using PowerPoint in Forensic Presentations \\
                 High-Level Data Overview Tests \\
                 Benford's Law: The Basics \\
                 Benford's Law: Assessing Conformity \\
                 Benford's Law: The Second-Order and Summation Tests \\
                 Benford's Law: The Number Duplication and Last-Two
                 Digits Tests \\
                 Testing the Internal Diagnostics of Current Period and
                 Prior Period Data \\
                 Identifying Fraud Using the Largest Subsets and Largest
                 Growth Tests \\
                 Identifying Anomalies Using the Relative Size Factor
                 Test \\
                 Identifying Fraud Using Abnormal Duplications within
                 Subsets \\
                 Identifying Fraud Using Correlation \\
                 Identifying Fraud Using Time-Series Analysis \\
                 Fraud Risk Assessments of Forensic Units \\
                 Examples of Risk Scoring with Access Queries \\
                 The Detection of Financial Statement Fraud \\
                 Using Analytics on Purchasing Card Transactions \\
                 References \\
                 Index",
}

@Book{Zenil:2011:RTC,
  editor =       "Hector Zenil",
  booktitle =    "Randomness through computation: some answers, more
                 questions",
  title =        "Randomness through computation: some answers, more
                 questions",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xviii + 419",
  year =         "2011",
  ISBN =         "981-4327-74-3",
  ISBN-13 =      "978-981-4327-74-9",
  LCCN =         "QA274 .R363 2011",
  bibdate =      "Mon Feb 18 18:30:30 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  subject =      "Stochastic processes; Computational complexity; Random
                 polynomials",
  tableofcontents = "Is randomness necessary? / R. Graham \\
                 Probability is a lot of logic at once: if you don't
                 know which one to pick, take 'em all / T. Toffoli \\
                 Statistical testing of randomness: new and old
                 procedures / A. L. Rukhin \\
                 Scatter and regularity imply Benford's law\ldots{} and
                 more / N. Gauvrit, J.-P. Delahaye \\
                 Some bridging results and challenges in classical,
                 quantum and computational randomness / G. Longo, C.
                 Palamidessi, T. Paul \\
                 Metaphysics, metamathematics and metabiology / G.
                 Chaitin \\
                 Uncertainty in physics and computation / M. A. Stay \\
                 Indeterminism and randomness through physics / K.
                 Svozil \\
                 The Martin-L{\"o}f--Chaitin thesis: the identification
                 by recursion theory of the mathematical notion of
                 random sequence / J.-P. Delahaye \\
                 The road to intrinsic randomness / S. Wolfram \\
                 Algorithmic probability its discovery, it's properties
                 and application to strong AI / R. J. Solomonoff \\
                 Algorithmic randomness as foundation of inductive
                 reasoning and artificial intelligence / M. Hutter \\
                 Randomness, Occam's razor, AI, creativity and digital
                 physics / J. Schmidhuber \\
                 Randomness everywhere: my path to algorithmic
                 information theory / C. S. Calude \\
                 The impact of algorithmic information theory on our
                 current views on complexity, randomness, information
                 and prediction / P. G\'acs \\
                 Randomness, computability and information / J. S.
                 Miller \\
                 Studying randomness through computation / A. Nies \\
                 Computability, algorithmic randomness and complexity /
                 R. G. Downey \\
                 Is randomness native to computer science? Ten years
                 after / M. Ferbus-Zanda, S. Grigorieff \\
                 Randomness as circuit complexity (and the connection to
                 pseudorandomness) / E. Allender \\
                 Randomness: a tool for constructing and analyzing
                 computer programs / A. Ku{\v{c}}era \\
                 Connecting randomness to computation / M. Li \\
                 From error-correcting codes to algorithmic
                 informational theory / L. Staiger \\
                 Randomness in algorithms / O. Watanabe \\
                 Is the universe random? / C. S. Calude, J. L. Casti, G.
                 J. Chaitin, P. C. W. Davies, K. Svozil, S. Wolfram \\
                 What is computation? (How) Does nature computer? / C.
                 S. Calude, G. J. Chaitin, E. Fredkin, A. J. Leggett, R.
                 de Ruyter, T. Toffoli, S. Wolfram",
}

@Book{Gorroochurn:2012:CPP,
  author =       "Prakash Gorroochurn",
  booktitle =    "Classic Problems of Probability",
  title =        "Classic Problems of Probability",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xi + 314",
  year =         "2012",
  DOI =          "https://doi.org/10.1002/9781118314340",
  ISBN =         "1-118-06325-2 (paperback), 1-118-31432-8,
                 1-118-31433-6 (e-book), 1-118-31434-4 (e-book),
                 1-118-31431-X (e-book)",
  ISBN-13 =      "978-1-118-06325-5 (paperback), 978-1-118-31432-6,
                 978-1-118-31433-3 (e-book), 978-1-118-31434-0 (e-book),
                 978-1-118-31431-9 (e-book)",
  LCCN =         "QA273.A4",
  bibdate =      "Mon Feb 25 05:50:42 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter / i?-xi \\
                 Chapter 1: Cardano and Games of Chance (1564) / 1--8
                 \\
                 Chapter 2: Galileo and a Discovery Concerning Dice
                 (1620) / 9--12 \\
                 Chapter 3: The Chevalier de M{\'e}r{\'e} Problem I: The
                 Problem of Dice (1654) / 13--19 \\
                 Chapter 4: The Chevalier de M{\'e}r{\'e} Problem II:
                 The Problem of Points (1654) / 20--38 \\
                 Chapter 5: Huygens and the Gambler's Ruin (1657) /
                 39--48 \\
                 Chapter 6: The Pepys--Newton Connection (1693) / 49--53
                 \\
                 Chapter 7: Rencontres with Montmort (1708) / 54--61 \\
                 Chapter 8: Jacob Bernoulli and his Golden Theorem
                 (1713) / 62--80 \\
                 Chapter 9: De Moivre's Problem (1730) / 81--88 \\
                 Chapter 10: De Moivre, Gauss, and the Normal Curve
                 (1730, 1809) / 89--107 \\
                 Chapter 11: Daniel Bernoulli and the St. Petersburg
                 Problem (1738) / 108--118 \\
                 Chapter 12: d'Alembert and the ?Croix ou Pile? Article
                 (1754) / 119--123 \\
                 Chapter 13: d'Alembert and the Gambler's Fallacy (1761)
                 / 124--128 \\
                 Chapter 14: Bayes, Laplace, and Philosophies of
                 Probability (1764, 1774) / 129--155 \\
                 Chapter 15: Leibniz's Error (1768) / 156--158 \\
                 Chapter 16: The Buffon Needle Problem (1777) / 159--168
                 \\
                 Chapter 17: Bertrand's Ballot Problem (1887) / 169--174
                 \\
                 Chapter 18: Bertrand's Strange Three Boxes (1889) /
                 175--178 \\
                 Chapter 19: Bertrand's Chords (1889) / 179--185 \\
                 Chapter 20: Three Coins and a Puzzle from Galton (1894)
                 / 186--188 \\
                 Chapter 21: Lewis Carroll's Pillow Problem No. 72
                 (1894) / 189--193 \\
                 Chapter 22: Borel and a Different Kind of Normality
                 (1909) / 194--198 \\
                 Chapter 23: Borel's Paradox and Kolmogorov's Axioms
                 (1909, 1933) / 199--207 \\
                 Chapter 24: Of Borel, Monkeys, and the New Creationism
                 (1913) / 208--214 \\
                 Chapter 25: Kraitchik's Neckties and Newcomb's Problem
                 (1930, 1960) / 215--223 \\
                 Chapter 26: Fisher and the Lady Tasting Tea (1935) /
                 224--232 \\
                 Chapter 27: Benford and the Peculiar Behavior of the
                 First Significant Digit (1938) / 233--239 \\
                 Chapter 28: Coinciding Birthdays (1939) / 240--246 \\
                 Chapter 29: L{\'e}vy and the Arc Sine Law (1939) /
                 247--252 \\
                 Chapter 30: Simpson's Paradox (1951) / 253--259 \\
                 Chapter 31: Gamow, Stern, and Elevators (1958) /
                 260--263 \\
                 Chapter 32: Monty Hall, Cars, and Goats (1975) /
                 264--270 \\
                 Chapter 33: Parrondo's Perplexing Paradox (1996) /
                 271--276 \\
                 Bibliography / 277--295 \\
                 Photo Credits / 296--298 \\
                 Index / 299--314",
}

@Proceedings{Niola:2012:RRA,
  editor =       "Vincenzo Niola and Michel Kadoch and Alexander
                 Zemliak",
  booktitle =    "{Recent researches in automatic control and
                 electronics: proceedings of the 14th International
                 conference on automatic control, modelling and
                 simulation (ACMOS '12): proceedings of the 11th
                 International conference on microelectronics,
                 nanoelectronics, optoelectronics (MINO '12): Saint Malo
                 and Mont Saint-Michel, France, April 2--4, 2012}",
  title =        "{Recent researches in automatic control and
                 electronics: proceedings of the 14th International
                 conference on automatic control, modelling and
                 simulation (ACMOS '12): proceedings of the 11th
                 International conference on microelectronics,
                 nanoelectronics, optoelectronics (MINO '12): Saint Malo
                 and Mont Saint-Michel, France, April 2--4, 2012}",
  publisher =    "WSEAS",
  address =      "???, Greece",
  pages =        "209",
  year =         "2012",
  ISBN =         "1-61804-080-4 (paperback)",
  ISBN-13 =      "978-1-61804-080-0 (paperback)",
  LCCN =         "????",
  bibdate =      "Tue Feb 19 06:02:11 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
}

@Book{Tijms:2012:UPC,
  author =       "Henk C. Tijms",
  booktitle =    "Understanding probability: chance rules in everyday
                 life",
  title =        "Understanding probability: chance rules in everyday
                 life",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Third",
  pages =        "x + 562",
  year =         "2012",
  ISBN =         "1-107-65856-X",
  ISBN-13 =      "978-1-107-65856-1",
  LCCN =         "QA273",
  bibdate =      "Mon Feb 18 06:48:08 MST 2013",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  acknowledgement = ack-nhfb,
  tableofcontents = "Preface \\
                 Introduction \\
                 Part I. Probability in Action \\
                 1. Probability questions \\
                 2. The law of large numbers and simulation \\
                 3. Probabilities in everyday life \\
                 4. Rare events and lotteries \\
                 5. Probability and statistics \\
                 6. Chance trees and Bayes' rule \\
                 Part II. Essentials of Probability \\
                 7. Foundations of probability theory \\
                 8. Conditional probability and Bayes \\
                 9. Basic rules for discrete random variables \\
                 10. Continuous random variables \\
                 11. Jointly distributed random variables \\
                 12. Multivariate normal distribution \\
                 13. Conditioning by random variables \\
                 14. Generating functions \\
                 15. Discrete-time Markov chains \\
                 16. Continuous-time Markov chains \\
                 Appendix \\
                 Counting methods and ex \\
                 Recommended reading \\
                 Answers to odd-numbered problems \\
                 Bibliography \\
                 Index",
}

@Book{Abergel:2013:ESR,
  editor =       "Fr{\'e}d{\'e}ric Abergel and Bikas K. Chakrabarti and
                 Anirban Chakraborti and Asim Ghosh",
  booktitle =    "Econophysics of systemic risk and network dynamics",
  title =        "Econophysics of systemic risk and network dynamics",
  publisher =    "Springer Italia",
  address =      "Milan, Italy",
  bookpages =    "????",
  pages =        "119--129",
  year =         "2013",
  DOI =          "https://doi.org/10.1007/978-88-470-2553-0",
  ISBN =         "88-470-2553-2, 88-470-2552-4",
  ISBN-13 =      "978-88-470-2553-0, 978-88-470-2552-3",
  bibdate =      "Mon Feb 18 16:48:12 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/benfords-law.bib",
  series =       "New Econ. Windows",
  acknowledgement = ack-nhfb,
  tableofcontents = "Part 1. Systemic risk, network dynamics and other
                 empirical studies \\
                 Diffusion of Defaults Among Financial Institutions /
                 Gabrielle Demange \\
                 Systemic Risk and Complex Systems: A Graph-Theory
                 Analysis / Delphine Lautier and Franck Raynaud \\
                 Omori Law After Exogenous Shocks on Supplier-Customer
                 Network / Yoshi Fujiwara \\
                 Aftershock Prediction for High-Frequency Financial
                 Markets' Dynamics / Fulvio Baldovin, Francesco Camana,
                 Michele Caraglio, Attilio L. Stella and Marco Zamparo
                 \\
                 How Unstable Are Complex Financial Systems? Analyzing
                 an Inter-bank Network of Credit Relations / Sitabhra
                 Sinha, Maximilian Thess and Sheri Markose \\
                 Study of Statistical Correlations in Intraday and Daily
                 Financial Return Time Series / Gayatri Tilak, Tam{\'a}s
                 Sz{\'e}ll, R{\'e}my Chicheportiche and Anirban
                 Chakraborti \\
                 A Robust Measure of Investor Contrarian Behaviour /
                 Damien Challet and David Morton de Lachapelle \\
                 Evolution of Zipf's Law for Indian Urban Agglomerations
                 Vis-{\`a}-Vis Chinese Urban Agglomerations / Kausik
                 Gangopadhyay and Banasri Basu \\
                 Part 2. Model-based studies \\
                 Reaction to Extreme Events in a Minimal Agent Based
                 Model / Andrea Zaccaria, Matthieu Cristelli and Luciano
                 Pietronero \\
                 Predatory Trading and Risk Minimisation: How to (B)Eat
                 the Competition / Anita Mehta \\
                 Statistical Mechanics of Labor Markets / He Chen and
                 Jun-ichi Inoue \\
                 Kolkata Paise Restaurant Problem: An Introduction /
                 Asim Ghosh, Soumyajyoti Biswas, Arnab Chatterjee,
                 Anindya Sundar Chakrabarti and Tapan Naskar, et al. \\
                 Kolkata Paise Restaurant Problem and the Cyclically
                 Fair Norm / Priyodorshi Banerjee, Manipushpak Mitra and
                 Conan Mukherjee \\
                 An Introduction to Multi-player, Multi-choice Quantum
                 Games: Quantum Minority Games and Kolkata Restaurant
                 Problems / Puya Sharif and Hoshang Heydari \\
                 Part 3. Miscellaneous reports \\
                 Cluster Analysis and Gaussian Mixture Estimation of
                 Correlated Time-Series by Means of Multi-dimensional
                 Scaling / Takero Ibuki, Sei Suzuki and Jun-ichi Inoue
                 \\
                 Analyzing Crisis in Global Financial Indices / Sunil
                 Kumar and Nivedita Deo \\
                 Study of Systemic Risk Involved in Mutual Funds /
                 Kishore C. Dash and Monika Dash \\
                 Characterizing Price Index Behavior Through Fluctuation
                 Dynamics / Prasanta K. Panigrahi, Sayantan Ghosh, Arjun
                 Banerjee, Jainendra Bahadur and P. Manimaran",
}

@Book{Miller:2015:BLT,
  editor =       "Steven J. Miller",
  booktitle =    "{Benford's Law}: theory and applications",
  title =        "{Benford's Law}: theory and applications",
  publisher =    pub-PRINCETON,
  address =      pub-PRINCETON:adr,
  pages =        "xxvi + 438",
  year =         "2015",
  DOI =          "https://doi.org/10.1515/9781400866595",
  ISBN =         "0-691-14761-2 (hardcover), 1-4008-6659-6 (e-book)",
  ISBN-13 =      "978-0-691-14761-1 (hardcover), 978-1-4008-6659-5
                 (e-book)",
  LCCN =         "QA273.6 .B46 2015",
  MRclass =      "60-06 (62-06)",
  MRnumber =     "3408774",
  bibdate =      "Tue Nov 17 09:41:52 MST 2015",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/statpapers.bib",
  URL =          "http://press.princeton.edu/titles/10527.html",
  acknowledgement = ack-nhfb,
  subject =      "Distribution (Probability theory); Probability
                 measures; MATHEMATICS / Applied; MATHEMATICS /
                 Probability and Statistics / General; Distribution
                 (Probability theory); Probability measures.",
  tableofcontents = "Foreword / xiii \\
                 Preface / xvii \\
                 Notation / xxiii \\
                 Part I. General Theory I: Basis of Benford's Law / 1
                 \\
                 Chapter 1. A Quick Introduction to Benford's Law / 3
                 \\
                 Chapter 2. A Short Introduction to the Mathematical
                 Theory of Benford's Law / 23 \\
                 Chapter 3. Fourier Analysis and Benford's Law / 68 \\
                 Part II. General Theory II: Distributions and Rates of
                 Convergence / 107 \\
                 Chapter 4. Benford's Law Geometry / 109 \\
                 Chapter 5. Explicit Error Bounds via Total Variation /
                 119 \\
                 Chapter 6. L{\'e}vy Processes and Benford's Law / 135
                 \\
                 Part III. Applications I: Accounting and Vote Fraud /
                 175 \\
                 Chapter 7. Benford's Law as a Bridge between Statistics
                 and Accounting / 177 \\
                 Chapter 8. Detecting Fraud and Errors Using Benford's
                 Law / 191 \\
                 Chapter 9. Can Vote Counts Digits and Benford's Law
                 Diagnose Elections? Chapter 10. Complementing Benford's
                 Law for Small N: A Local Bootstrap Bootstrap Model /
                 227 \\
                 Part IV. Applications II: Economics / 233 \\
                 Chapter 11. Measuring the Quality of European
                 Statistics / 235 \\
                 Chapter 12. Benford's Law and Fraud in Economic
                 Research / 244 \\
                 Chapter 13. Testing for Strategic Manipulation of
                 Economic and Financial Data / 257 \\
                 Part V. Applications III: Sciences / 265 \\
                 Chapter 14. Psychology and Benford's Law / 267 \\
                 Chapter 15. Managing Risk in Numbers Games: Benford's
                 Law and the Small-Number Phenomenon / 276 \\
                 Chapter 16. Benford's Law in the Natural Sciences / 290
                 \\
                 Chapter 17. Generalizing Benford's Law: A Reexamination
                 of Falsified Clinical Data / 304 \\
                 Part VI. Applications IV: Images / 317 \\
                 Chapter 18. Partial Volume Modeling of Medical Imaging
                 Systems Using the Benford Distribution / 319 \\
                 Chapter 19. Application of Benford's Law to Images /
                 338 \\
                 Part VII. Exercises / 371 \\
                 Chapter 20. Exercises / 373 \\
                 Phenomenon / 399 \\
                 Distribution / 401 \\
                 Bibliography / 402 \\
                 Index / 433",
}

@Proceedings{Cornea:2020:ISC,
  editor =       "Marius Cornea and Weiqiang Liu and Arnaud Tisserand",
  booktitle =    "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  title =        "{2020 27th IEEE Symposium on Computer Arithmetic:
                 ARITH 2020: proceedings: Portland, Oregon, USA, 7--10
                 June 2020}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2020",
  DOI =          "https://doi.org/10.1109/ARITH48897.2020",
  ISBN =         "1-72817-120-2, 1-72817-121-0",
  ISBN-13 =      "978-1-72817-120-3, 978-1-72817-121-0",
  LCCN =         "????",
  bibdate =      "Wed Jul 7 06:24:52 2021",
  bibdate =      "Wed Jul 7 06:23:45 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/benfords-law.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeexplore.ieee.org/servlet/opac?punumber=9146973",
  acknowledgement = ack-nhfb,
}

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