Quadratic forms of refined skew normal models based on stochastic representation

Weizhong Tian 1  and Tonghui Wang 2
  • 1 Department of Mathematical Sciences, Eastern New Mexico University, United States of America
  • 2 Department of Mathematical Sciences, New Mexico State University, United States of America
Weizhong Tian and Tonghui Wang

Abstract

Wang, Li and Gupta [] first introduced the skew chi-square distribution based on the multivariate skew normal distribution provided by Azzalini [], and Ye, Wang and Gupta [] extended this results into the skew Wishart distribution. Motivated by these results, we first study a new type of multivariate skew normal distribution introduced by Gupta and Chen [], the moment generating function, independence and quadratic form are discussed, and also a new type of skew chi-square distribution was introduced. Later on, we defined a new type of skew Wishart distribution based on the matrix skew normal models introduced by Ning []. In the end, we will study the probabilistic representation of multivariate skew elliptical models.

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