An Alternative Matrix Skew-Normal Random Matrix and Some Properties

Phil D. Young, Joshua D. Patrick (), John A. Ramey and Dean M. Young
Additional contact information
Phil D. Young: Baylor University
Joshua D. Patrick: Baylor University
John A. Ramey: Novi Labs
Dean M. Young: Baylor University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 1, No 3, 28-49

Abstract: Abstract 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.

Keywords: Moment generating function; Conditional distributions; Marginal distributions; Matrix quadratic form.; Primary 62E15; Secondary 60E05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13171-019-00165-4

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