Indices of Skewness and Kurtosis - Indices of Multivariate Kurtosis

Mardia's multivariate kurtosis

This index is defined as

(179)

where x_i 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)

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