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The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”

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  • Bartosz Kołodziejek

    (Warsaw University of Technology)

Abstract

We prove the Lukacs–Olkin–Rubin theorem without invariance of the distribution of the “quotient,” which was the key assumption in the original proof of (Olkin–Rubin in Ann Math Stat 33:1272–1280, 1962). Instead, we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) “quotient” for any division algorithm satisfying some natural conditions. For that purpose, a new proof of the Olkin–Baker functional equation on symmetric cones is given.

Suggested Citation

  • Bartosz Kołodziejek, 2016. "The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”," Journal of Theoretical Probability, Springer, vol. 29(2), pages 550-568, June.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:2:d:10.1007_s10959-014-0587-3
    DOI: 10.1007/s10959-014-0587-3
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    References listed on IDEAS

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    1. A. Hassairi & S. Lajmi & R. Zine, 2008. "A Characterization of the Riesz Probability Distribution," Journal of Theoretical Probability, Springer, vol. 21(4), pages 773-790, December.
    2. A. Hassairi & S. Lajmi, 2001. "Riesz Exponential Families on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 14(4), pages 927-948, October.
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