Goodness-of-Fit Tests for Bivariate and Multivariate Skew-Normal Distributions

Goodness-of-fit tests are proposed for the skew-normal law in arbitrary dimension. In the bivariate case the proposed tests utilize the fact that the moment-generating function of the skew-normal variable is quite simple and satisfies a partial differential equation of the first order. This differential equation is estimated from the sample and the test statistic is constructed as an L-2-type distance measure incorporating this estimate. Extension of the procedure to dimension greater than two is suggested whereas an effective bootstrap procedure is used to study the behaviour of the new method with real and simulated data.