Characterization of beta distribution on symmetric cones

Abstract

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.

12 pages. arXiv admin note: text overlap with arXiv:1403.0236, arXiv:1501.02575, arXiv:1307.3988

References in corpus (1)

• Kshirsagar--Tan independence property of beta matrices and related characterizations

Cited by in corpus (3)

• Beta distributions and Sonine integrals for Bessel functions on symmetric cones
• A Matsumoto-Yor characterization for Kummer and Wishart random matrices
• The generalized fundamental equation of information on symmetric cones