A General Class of Multivariate Skew-Elliptical Distributions

Abstract

This paper proposes a general class of multivariate skew-elliptical distributions. We extend earlier results on the so-called multivariate skew-normal distribution. This family of distributions contains the multivariate normal, Student's t, exponential power, and Pearson type II, but with an extra parameter to regulate skewness. We also obtain the moment generating functions and study some distributional properties. Several examples are provided.elliptical distributions exponential power family mixture of normals Pearson type II skewness