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Characterization of beta distribution on symmetric cones

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  • Kołodziejek, Bartosz

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=1−XU are independent if and only if there exist positive numbers pi, i=1,2,3, such that X and Y follow beta distributions with parameters (p1+p3,p2) and (p3,p1), respectively.

Suggested Citation

  • Kołodziejek, Bartosz, 2016. "Characterization of beta distribution on symmetric cones," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 414-423.
    • Handle: RePEc:eee:jmvana:v:143:y:2016:i:c:p:414-423
    DOI: 10.1016/j.jmva.2015.10.004
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    References listed on IDEAS

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    1. Nagar, Daya K. & Roldán-Correa, Alejandro & Gupta, Arjun K., 2013. "Extended matrix variate gamma and beta functions," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 53-69.
    2. Hassairi, A. & Regaig, O., 2009. "Characterizations of the beta distribution on symmetric matrices," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1682-1690, September.
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