Multivariate skew-normal/independent distributions: properties and inference

Abstract

Liu (1996) discussed a class of robust normal/independent distributions which contains a group of thick-tailed cases. In this article, we develop a skewed version of these distributions in the multivariate setting, and we call them multivariate skew normal/independent distributions. We derive several useful properties for them. The main virtue of the members of this family is that they are easy to simulate and lend themselves to an EM-type algorithm for maximum likelihood estimation. For two multivariate models of practical interest, the EM-type algorithm has been discussed with emphasis on the skew-t, the skew-slash, and the contaminated skew-normal distributions. Results obtained from simulated and two real data sets are also reported.