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 GNU Scientific Library Reference Manual - Third Edition (v1.12) by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. RossiPaperback (6"x9"), 592 pages, 60 figuresISBN 0954612078RRP £24.95 (\$39.95)

## 20.3 Higher moments (skewness and kurtosis)

Function: double gsl_stats_skew (const double data[], size_t stride, size_t n)
This function computes the skewness of data, a dataset of length n with stride stride. The skewness is defined as,
skew = (1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^3

where x_i are the elements of the dataset data. The skewness measures the asymmetry of the tails of a distribution.

The function computes the mean and estimated standard deviation of data via calls to gsl_stats_mean and gsl_stats_sd.

Function: double gsl_stats_skew_m_sd (const double data[], size_t stride, size_t n, double mean, double sd)
This function computes the skewness of the dataset data using the given values of the mean mean and standard deviation sd,
skew = (1/N) \sum ((x_i - mean)/sd)^3

These functions are useful if you have already computed the mean and standard deviation of data and want to avoid recomputing them.

Function: double gsl_stats_kurtosis (const double data[], size_t stride, size_t n)
This function computes the kurtosis of data, a dataset of length n with stride stride. The kurtosis is defined as,
kurtosis = ((1/N) \sum ((x_i - \Hat\mu)/\Hat\sigma)^4)  - 3

The kurtosis measures how sharply peaked a distribution is, relative to its width. The kurtosis is normalized to zero for a gaussian distribution.

Function: double gsl_stats_kurtosis_m_sd (const double data[], size_t stride, size_t n, double mean, double sd)
This function computes the kurtosis of the dataset data using the given values of the mean mean and standard deviation sd,
kurtosis = ((1/N) \sum ((x_i - mean)/sd)^4) - 3

This function is useful if you have already computed the mean and standard deviation of data and want to avoid recomputing them.

 ISBN 0954612078 GNU Scientific Library Reference Manual - Third Edition (v1.12) See the print edition