#### Abstract Details

 Activity Number: 255 - Contributed Poster Presentations: Section on Statistical Computing Type: Contributed Date/Time: Monday, July 29, 2019 : 2:00 PM to 3:50 PM Sponsor: Section on Statistical Computing Abstract #305190 Title: The Decomposition of Quadratic Forms Under Matrix Variate Skew Normal Distribution Author(s): Ziwei Ma* and Tonghui Wang Companies: New Mexico State University and New Mexico State University Keywords: Skew-normal distributions; noncentral skew Wishart distributions; Quadratic forms; Decomposition Abstract: In this paper, several properties of noncentral skew Wishart distribution are studied and two results of decomposition properties are established as well. In general, a random $p\times p$ non-negative definite matrix, which follows noncentral skew Wishart distribution with the degree of freedom $k>1$, can be decomposed into the sum of two independent random matrices, where one follows the noncentral skew Wishart distribution and another one follows the noncentral Wishart distribution. For an illustration of these results, the linear mixed model with skew normal error is considered as an application.

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