Biometrika

Biometrika 1970 57(3):519-530; doi:10.1093/biomet/57.3.519
© 1970 by Biometrika Trust

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Measures of multivariate skewness and kurtosis with applications

K. V. MARDIA

University of Hull

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.

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