Wei Ning, Arjun K. Gupta
November 28, 2012
Abstract. It was Azzalini (1985) who introduced the univariate skew normal distribution family with a shape parameter , and then extended skew normal distribution family by adding an additional shape parameters . Azzalini and Dalla Valle (1996) extended the results to the multivariate case. Basic properties for the univariate and multivariate cases were summarized by Azzalini (2005). Chen and Gupta (2005) considered the matrix variate skew normal distribution family and proposed the moment generating function and demonstrated that the distribution of the quadratic form of the skew normal matrix variate follows a Wishart distribution. Their results were generalized by Harrar and Gupta (2008). In this paper, we generalize the univariate extended skew normal distribution family to the matrix variate case. The moment generating function, the distribution of the quadratic form and the linear form, and the marginal and conditional distributions of this family are studied.