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A Characterization of the Riesz Probability Distribution

Author

Listed:
  • A. Hassairi

    (Université de Sfax)

  • S. Lajmi

    (Université de Sfax)

  • R. Zine

    (Université de Sfax)

Abstract

Bobecka and Wesolowski (Studia Math. 152:147–160, [2002]) have shown that, in the Olkin and Rubin characterization of the Wishart distribution (see Casalis and Letac in Ann. Stat. 24:763–786, [1996]), when we use the division algorithm defined by the quadratic representation and replace the property of invariance by the existence of twice differentiable densities, we still have a characterization of the Wishart distribution. In the present work, we show that when we use the division algorithm defined by the Cholesky decomposition, we get a characterization of the Riesz distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:4:d:10.1007_s10959-008-0142-1
    DOI: 10.1007/s10959-008-0142-1
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. 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.
    2. Hassairi, Abdelhamid & Roula, Amel, 2022. "Exponential and related probability distributions on symmetric matrices," Statistics & Probability Letters, Elsevier, vol. 187(C).

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