Testing for multinormality with goodness-of-fit tests based on phi divergence measures

In this paper, a beta transform of multivariate normal datasets is obtained. The phi divergence measure, DΦ(F,G) between two distributions F and G is used to obtain a goodnessof-fit test to multivariate normality (MVN) based on the theoretical density function of the beta transformed random variable and a window-size-spacing-based sample density function. Three versions of the statistic are derived from three known phi divergence measures that are based on a sum of squares. The empirical critical values of the statistics are obtained and the empirical type-one-error rates as well as powers of the statistics in comparison with those of other well-known competing statistics are computed through extensive simulation study. The study shows that the new statistics have good control over type-one-error and are highly competitive with the existing well-known ones in terms of power performance. The applicability of the new statistics is also carried out in comparison with three other efficient techniques using four different datasets, and all the competing statistics agreed perfectly in their decisions of rejection or otherwise of the multivariate normality of the datasets. As a result, they can be regarded as appropriate statistics for assessing multinormality of datasets especially, in large samples.