an:06661757
Zbl 1375.60051
Tian, Weizhong; Wang, Tonghui
Quadratic forms of refined skew normal models based on stochastic representation
EN
Random Oper. Stoch. Equ. 24, No. 4, 225-234 (2016).
00361202
2016
j
60E05 62H05
skew normal distribution; quadratic form; moment generating function
Summary: In [J. Multivariate Anal. 100, No. 3, 533--545 (2009; Zbl 1154.62342)], the second author et al. first introduced the skew chi-square distribution based on the multivariate skew normal distribution provided by \textit{A. Azzalini} [Scand. J. Stat. 12, 171--178 (1985; Zbl 0581.62014)], and \textit{R. Ye} et al. [J. Multivariate Anal. 131, 229--239 (2014; Zbl 1298.62086)] 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 \textit{A. K. Gupta} and \textit{J. T. Chen} [Ann. Inst. Stat. Math. 56, No. 2, 305--315 (2004; Zbl 1056.62064)], 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 \textit{W. Ning} [Random Oper. Stoch. Equ. 23, No. 1, 21--29 (2015; Zbl 1310.62065)]. In the end, we will study the probabilistic representation of multivariate skew elliptical models.
Zbl 1154.62342; Zbl 0581.62014; Zbl 1298.62086; Zbl 1056.62064; Zbl 1310.62065