Combined probability tests for multivariate skew normality

A probability distribution that has gained importance in recent years is the multivariate skew normal (MSN) distribution, which extends the multivariate normal distribution by incorporating a shape parameter, providing probability models for data sets that exhibit moderate degrees of skewness. Three statistical tests for multivariate skew normality are proposed here based on combined probability tests, like Fisher’s method, and some data transformations. The results of intensive Monte Carlo simulation studies show that the proposed tests have good size and power properties and are competitive against a existing test for the same problem. Two real data sets are analyzed in order to illustrate the usefulness of the tests. R scripts to implement the tests are available at a public GitHub repository.