Indices of Skewness and Kurtosis - Indices of Multivariate Kurtosis

Mardia's multivariate kurtosis. This index is defined as

(179)

where xi is the ith vector of observations, is a vector of sample means, p is the number of observed variables, and S is the sample covariance matrix.

Relative multivariate kurtosis. This index is defined as

(180)

Normalized multivariate kurtosis. This index is defined as

(181)

Mardia-based kappa. This index is defined as

(182)

Mean scaled univariate kurtosis. This index is defined as

(183)

Adjusted mean scaled univariate kurtosis. This index is defined as

(184)

with

(185)