GNU Scientific Library – Reference Manual: Higher moments (skewness and kurtosis)

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