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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. Rossi
Paperback (6"x9"), 592 pages, 60 figures
ISBN 0954612078
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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 0954612078GNU Scientific Library Reference Manual - Third Edition (v1.12)See the print edition