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Exponential and related probability distributions on symmetric matrices
Statistics & Probability Letters ( IF 0.9 ) Pub Date : 2022-04-11 , DOI: 10.1016/j.spl.2022.109499
Abdelhamid Hassairi 1 , Amel Roula 1
Affiliation  

Pursuing the study initiated in Hassairi and Roula (2019), we show in the present paper that the reliability function of a probability distribution on the cone Ω of positive definite symmetric matrices characterizes the distribution without any invariance condition. We also show that the characterization of the exponential probability distribution on Ω by a memoryless property holds without assuming an invariance condition. We then study the connection between the exponential distribution on Ω and the uniform distribution on a bounded interval of Ω. A notion of matrix Pareto distribution is introduced, and it is shown that this distribution possesses the long tail property.



中文翻译:

对称矩阵上的指数和相关概率分布

根据 Hassairi 和 Roula (2019) 发起的研究,我们在本文中展示了圆锥上概率分布的可靠性函数Ω正定对称矩阵的特征描述了没有任何不变性条件的分布。我们还表明,指数概率分布的表征Ω在不假设不变条件的情况下,无记忆属性成立。然后我们研究指数分布之间的联系Ω和有界区间上的均匀分布Ω. 引入矩阵Pareto分布的概念,证明该分布具有长尾性质。

更新日期:2022-04-11
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