On the Canonical-Based Goodness-of-fit Tests for Multivariate Skew-Normality

Abstract

It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace transform and empirical characteristic function, respectively, using the canonical form of the MSN distribution. Applications with Monte Carlo simulations and real-life data examples are reported to illustrate the usefulness of the new tests.