文章基本信息

标题：An Alternative Matrix Skew-Normal Random Matrix and Some Properties
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作者：Phil D. Young ; Phil D. Young ; Joshua D. Patrick 等
期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2019
页码：1-22
DOI：10.1007/s13171-019-00165-4
出版社：Indian Statistical Institute
摘要：We propose an alternative skew-normal random matrix, which is an extension of the multivariate skew-normal vector parameterized in Vernic ( A Stiint Univ Ovidius Constanta . 13 , 83–96 2005 , Insur. Math. Econ. 38 , 413–426 2006 ). We define the density function and then derive and apply the corresponding moment generating function to determine the mean matrix, covariance matrix, and third and fourth moments of the new skew-normal random matrix. Additionally, we derive eight marginal and two conditional density functions and provide necessary and sufficient conditions such that two pairs of sub-matrices are independent. Finally, we derive the moment generating function for a skew-normal random matrix-based quadratic form and show its relationship to the moment generating function of the noncentral Wishart and central Wishart random matrices.
关键词：Moment generating function ; Conditional distributions ; Marginal distributions ; Matrix quadratic form.