11.2.3 Higher moments (skewness and kurtosis)

(`skew``data`)-
Compute the skewness of
`data`. The skewness is defined as(11.7)

where 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`mean`and`sd`.

(`skew_m_sd``data, mean, sd`)-
Compute the skewness of the dataset
`data`using the given values of the mean`mean`and standard deviation varsd(11.8)

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

(`kurtosis``data`)-
Compute the kurtosis of
`data`. The kurtosis is defined as(11.9)

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

(`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`(11.10)

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