stats::kurtosis
-- kurtosis
(excess)stats::kurtosis
(data)
returns the kurtosis
(the coefficient of excess) of the data.
stats::kurtosis(x1, x2, ..)
stats::kurtosis([x1, x2, ..])
stats::kurtosis(s <, c>)
x1, x2, .. |
- | the statistical data: arithmetical expressions. |
s |
- | a sample of domain type stats::sample . |
c |
- | an integer representing a column index of the sample
s . This column provides the data x1 ,
x2 etc. |
an arithmetical expression. FAIL
is returned, if the
kurtosis does not exist.
(1/n*((x[1] - X)^4 + .. +(x[n] - X)^4)) / (1/n*((x[1] - X)^2 + .. +(x[n] - X)^2))^2 - 3 ,where X is the mean value of the x[i]. The kurtosis measures whether a distribution is ``flat'' or ``peaked''. For normally distributed data the kurtosis is zero. If the distribution function of the data has a flatter top than the normal distribution, then the kurtosis is negative. The kurtosis is positive, if the distribution function has a high peak, compared to the normal distribution.
c
is optional, if the data are given
by a stats::sample
object containing only one non-string column. Cf. example 3.We calculate the kurtosis of some values:
>> stats::kurtosis(0, 7, 7, 6, 6, 6, 5, 5, 4, 1)
-74146/271441
Alternatively, the data may be passed as a list:
>> stats::kurtosis([2, 2, 4, 6, 8, 10, 10])
-85/54
We create a sample:
>> stats::sample([[a, 5, 8], [b, 3, 7], [c, d, 0]])
a 5 8 b 3 7 c d 0
The kurtosis of the second column is:
>> stats::kurtosis(%, 2)
/ d \4 / d \4 / 2 d \4 3 | 1/3 - - | + 3 | 7/3 - - | + 3 | --- - 8/3 | \ 3 / \ 3 / \ 3 / -------------------------------------------------- - 3 / / d \2 / d \2 / 2 d \2 \2 | | 1/3 - - | + | 7/3 - - | + | --- - 8/3 | | \ \ 3 / \ 3 / \ 3 / /
We create a sample consisting of one string column and one non-string column:
>> stats::sample([["1996", 1242], ["1997", 1353], ["1998", 1142]])
"1996" 1242 "1997" 1353 "1998" 1142
We compute the kurtosis of the second column. In this case this column does not have to be specified, since it is the only non-string column:
>> stats::kurtosis(%)
-3/2