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Manual Reference Pages  - skekurx (3)

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NAME

skekurx(3f) - [M_math:statistics] Compute unbiased estimator of the population SKEWNESS and KURTOSIS

CONTENTS

Synopsis
Description
Options
Returns
Examples
Author

SYNOPSIS

SUBROUTINE SKEKURX(Y,N,YSKEW,YKURT)

      integer,intent(in) :: n
      real,intent(in)    :: y(*)
      real,intent(out)   :: yskew
      real,intent(out)   :: ykurt

DESCRIPTION

This routine calculates the unbiased estimator of the population kurtosis and skewness from a subset of samples

      kurt = {n*(n+1)/((n-1)*(n-2)*(n-3))*SUM[((x(i)-xbar)/stddev)**4]} -
                3*(n-1)**2/((n-2)*(n-3))

      skew =  ( n / ((n-1)*(n-2)) *SUM{((X(i) - xbar)/stddev)**3}

where xbar and stddev are the sample mean and standard deviation

Note that this is apparently the skewness and kurtosis calculated by the MicroSoft Excel product. I checked the Excel help and Excel uses the above formulas. No references are given in the Excel documentation. Note that this converges on the standard expression for excess kurtosis and skewness as N becomes large.

OPTIONS

RETURNS

EXAMPLES

AUTHOR

John S. Urban

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skekurx (3)

March 11, 2021

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