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Embrechts, Frey and McNeil (2005) proposed a test based on Kolmogorov-Smirnov test using concepts from Gnanadesikan and Kettenring (1972) that it is possible to obtain beta samples from normal samples using a transformation in the Mahalanobis quadratic distance. However, this test is influenced by the sample dependence present in the quadratic distance. Liang, Pan and Yang (2004) presented a way to obtain univariate beta samples, each independent and identically distributed, through transformations
in a p-variate normal sample. This work aimed to propose two tests for multivariate normality: a goodness- of-fit test based on Kolmogorov-Smirnov test and an intensive test based on parametric bootstrap. Monte Carlo simulations were used in order to estimate type I error rates and the power of the tests. Comparisons were conducted between the proposed tests and the multivariate normality test that was presented in the literature. Although the proposed tests have obtained good control of the type I error rates, the use of these tests was not recommended due to the poor performance of power presented by them.
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