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.
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References
Bobecka, K., Wesolowski, J.: The Lukacs-Olkin-Rubin theorem without invariance of the “quotient”. Studia Math. 152, 147–160 (2002)
Casalis, M., Letac, G.: The Lukacs-Olkin-Rubin characterization of the Wishart distributions on symmetric cone. Ann. Stat. 24, 763–786 (1996)
Hassairi, A., Lajmi, S.: Riesz exponential families on symmetric cones. J. Theor. Probab. 14, 927–948 (2001)
Hassairi, A., Lajmi, S., Zine, R.: Beta-Riesz distributions on symmetric cones. J. Stat. Plann. Inf. 133, 387–404 (2005)
Lukacs, E.: A characterization of the gamma distribution. Ann. Math. Stat. 26, 319–324 (1955)
Olkin, I., Rubin, H.: A characterization of the Wishart distribution. Ann. Math. Stat. 33, 1272–1280 (1962)
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Hassairi, A., Lajmi, S. & Zine, R. A Characterization of the Riesz Probability Distribution. J Theor Probab 21, 773–790 (2008). https://doi.org/10.1007/s10959-008-0142-1
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DOI: https://doi.org/10.1007/s10959-008-0142-1