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stats::kurtosis -- kurtosis (excess)

Introduction

stats::kurtosis(data) returns the kurtosis (the coefficient of excess) of the data.

Call(s)

stats::kurtosis(x1, x2, ..)
stats::kurtosis([x1, x2, ..])
stats::kurtosis(s <, c>)

Parameters

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.

Returns

an arithmetical expression. FAIL is returned, if the kurtosis does not exist.

Related Functions

stats::obliquity

Details

Example 1

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
      

Example 2

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        /  /
      

Example 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
      

Changes




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