Multivariate normality test using Srivastava’s skewness and kurtosis

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 M1 and M2 using Srivastava’s sample skewness and kurtosis, which are asymptotically distributed as χ2-distribution. We propose a new test statistic M3 by taking account of the variance of M2 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.