The multivariate extended skew normal distribution and its quadratic forms

Abstract

In this paper, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, and independence are discussed. Based on this class of distributions, the extended noncentral skew chi-square distribution is defined and its properties are investigated. Also the necessary and sufficient conditions, under which a quadratic form of the model has an extended noncentral skew chi-square distribution, are obtained. For illustration of our main results, several examples are given.