MVT (version 0.3)

kurtosis: Mardia's multivariate kurtosis coefficient

Description

This function computes the kurtosis of a multivariate distribution and estimates the kurtosis parameter for the t-distribution using the method of moments.

Usage

kurtosis(x, center, cov)

Arguments

x

vector or matrix of data with, say, p columns.

center

mean vector of the distribution or second data vector of length p.

cov

covariance matrix (p x p) of the distribution.

Value

A list with the following components :

kurtosis

returns the value of Mardia's multivariate kurtosis.

kappa

returns the excess kurtosis related to a multivariate t-distribution.

eta

estimated shape (kurtosis) parameter using the methods of moments, only valid if $0 \le \eta < 1/4$.

References

Mardia, K.V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.

Osorio, F., and Galea, M. (2015). Statistical inference in multivariate analysis using the t-distribution. Unpublished manuscript.

Examples

data(companies)
S <- cov(companies)
kurtosis(companies, colMeans(companies), S)