Kshirsagar–Tan independence property of beta matrices and related characterizations

Bobecka, Konstancja; Wesołowski, Jacek

doi:10.3150/07-bej118

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2016

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“…Similar characterization of beta distribution for random matrices was proved under numerous additional assumptions in [6]. The characterization of 2 × 2 matrix-variate beta distribution was also given by [2], but the characterization condition was of a different nature.…”

Section: Introductionmentioning

confidence: 71%

Characterization of beta distribution on symmetric cones

Kołodziejek

2016

Journal of Multivariate Analysis

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In the paper we generalize the following characterization of beta distribution to the symmetric cone setting: let $X$ and $Y$ be independent, non-degenerate random variables with values in $(0,1)$, then $U=1-XY$ and $V=\frac{1-X}{U}$ are independent if and only if there exist positive numbers $p_i$, $i=1,2,3$, such that $X$ and $Y$ follow beta distributions with parameters $(p_1+p_3,p_2)$ and $(p_3,p_1)$, respectively.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1403.0236, arXiv:1501.02575, arXiv:1307.398

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Section: Introductionmentioning

confidence: 71%