A new multivariate kurtosis and its asymptotic distribution

In this paper, we propose a new definition for multivariate kurtosis based on the two measures of multivariate kurtosis defined by Mardia (1970) and Srivastava (1984), respectively. Under normality, the exact values of the expectation and the variance for the new multivariate sample measure of kurtosis are given. We also give the third moments for the sample measure of new multivariate kurtosis. After that standardized statistics and normalizing transformation statistic for the sample measure of a new multivariate kurtosis are derived by using these results. Finally, in order to evaluate accuracy of these statistics, we present the numerical results by Monte Carlo simulation for some selected values of parameters.