Performance analysis of powers of skewness and kurtosis based multivariate normality tests and use of extended Monte Carlo simulation for proposed novelty algorithm

An ample study of the comparative powers of a number of omnibus multivariate normality tests is main object in this paper. Since testing for multivariate normality tests is considerably more challenging process than for testing of univariate one and therefore, study of testing for multivariate normality tests has its increasing demand. Through this paper, we have explored several techniques for assessing multivariate normality (MVN) and as well as comparative analysis for their competence have also been demonstrated. The results of extensive Monte Carlo simulation study of the size corrected power of various tests of multivariate normality for drawn samples from contaminated normal distributions have been explored as well. Moreover, a novel algorithm has been proposed in order to evaluate the size corrected powers for testing multivariate normality. The algorithm proposed herein is a fast easily implementable algorithm and it can be applied for both types of univariate and multivariate normality tests. Using Different omnibus tests for sample size 50 and 200, graphs for empirical powers of multivariate normal data with lower and upper contamination have been presented. Finally, some significant conclusions of our present study have been drawn.