Multivariate normality test using Srivastava’s skewness and kurtosis

Abstract

In this paper, we consider the multivariate normality test based on the sample measures of multivariate skewness and kurtosis defined by Srivastava [11]. Koizumi et al. [4] proposed test statistics $M_1$ and $M_2$ using Srivastava’s sample skewness and kurtosis, which are asymptotically distributed as ${\chi }^2$-distribution. We propose a new test statistic $M_3$ by taking account of the variance of $M_2$ under the normality. In order to evaluate the accuracy of the proposed test statistic, the numerical results by a Monte Carlo simulation for some selected values of parameters are presented.