Higher moments (skewness and kurtosis)
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gsl_stats_skew(data)
This function computes the skewness of data, a dataset of length
n. The skewness is defined as,
\[skew = {1 \over N} \sum
{\left( x_i - {\hat{\mu}} \over {\hat{\sigma}} \right)}^3\]
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().
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gsl_stats_skew_m_sd(data, mean, sd)
This function computes the skewness of the dataset data using the
given values of the mean mean and standard deviation sd,
\[skew = {1 \over N} \sum {\left( x_i - mean \over sd \right)}^3\]
where \(x_i\) are the elements of the dataset data. The skewness
measures the asymmetry of the tails of a distribution.
These functions are useful if you have already computed the mean and
standard deviation of data and want to avoid recomputing them.
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gsl_stats_kurtosis(data)
This function computes the kurtosis of data. The kurtosis is defined as,
\[kurtosis = {1 \over N} \left( \sum
{\left(x_i - {\hat{\mu}} \over {\hat{\sigma}} \right)}^4
\right) - 3\]
The kurtosis measures how sharply peaked a distribution is, relative to
its width. The kurtosis is normalized to zero for a Gaussian
distribution.
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gsl_stats_kurtosis_m_sd(data, mean, sd)
This function computes the kurtosis of the dataset data using the
given values of the mean mean and standard deviation sd,
\[kurtosis = {1 \over N}
\left( \sum {\left(x_i - mean \over sd \right)}^4 \right) - 3\]
This function is useful if you have already computed the mean and
standard deviation of data and want to avoid recomputing them.