Probabilistic representations of matrix variate skew normal models

Abstract

AbstractAzzalini [Scand. J. Stat. 12 (1985), 171–178] first introduced the skew normal distribution family with a shape parameter λ, and then extended this family by adding an additional shape parameters ξ. Basic properties of these two families were studied. Henze [Scand. J. Stat. 13 (1986), 271–275] gave the probabilistic representations for these two families by interpreting it as the linear combination of a normal random variable with another normal random variable truncated at the origin and several properties were illustrated. Chen and Gupta [Statistics 39 (2005), no. 3, 247–253] extended the skew normal distribution family to the matrix variate and proposed the moment generating function and the quadratic form of the matrix variate skew normal models. Motivated by these results, we first study the probabilistic representation for the matrix variate skew normal models and several properties. Then we define the extended skew normal model of the matrix variate, and give the probabilistic representation for this family and its extension.