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### 21.3 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.

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