Measures of Multivariate Skewness and Kurtosis with Applications

1 December 1970

journal article
Published by JSTOR in Biometrika

Vol. 57 (3) , 519-530
https://doi.org/10.2307/2334770

Abstract

SUMMARY Measures of multivariate skewness and kurtosis are developed by extending certain studies on robustness of the t statistic. These measures are shown to possess desirable properties. The asymptotic distributions of the measures for samples from a multivariate normal population are derived and a test of multivariate normality is proposed. The effect of nonnormality on the size of the one-sample Hotelling's T² test is studied empirically with the help of these measures, and it is found that Hotelling's T² test is more sensitive to the measure of skewness than to the measure of kurtosis.

Keywords

MULTIVARIATE SKEWNESS
HOTELLING'S T2 TEST
STATISTIC
SKEWNESS AND KURTOSIS
APPLICATIONS MEASURES
MEASURES OF MULTIVARIATE

This publication has 0 references indexed in Scilit: