Omnibus tests of multinormality based on skewness and kurtosis

Measures of univariate skewness and kurtosis have long been used as a test of univariate normality, several omnibus test procedures based on a combination of the measures having been proposed, see Pearson, D'Agestino and Bowman (1977) and Mardia (1979). Mardia (1970) proposed measures of multivariate skewness and kurtosis, and constructed a test of multinormality based on these measures. we obtain the correlation between these measures and propose several omnibus tests using the two measures. The performances of these tests are compared by means of a Monte Carlo study.