A Characterization of the Riesz Probability Distribution

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• 作者：A. Hassairi ; S. Lajmi and R. Zine
• 关键词：Division algorithm ; Wishart distribution ; Riesz distribution ; Beta ; Riesz distribution ; Functional equation
• 刊名：Journal of Theoretical Probability
• 出版年：2008
• 出版时间：December, 2008
• 年：2008
• 卷：21
• 期：4
• 页码：773-790
• 全文大小：367.9 KB

文摘

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.