On beta-product convolutions
On beta-product convolutions
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DOI：
10.1080/03461238.2011.555939
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发表时间：
2010-01
影响因子：
1.8
通讯作者：
E. Hashorva
中科院分区：
文献类型：
--
作者：
E. Hashorva
设R是独立于S的贝塔分布的正随机变量。在本文中，我们对R和RS之间的关系感兴趣。对于这个模型，我们首先得到了一些分布性质，然后研究了当R正则在0时RS的尾下渐近性，反之亦然。我们的第一个应用涉及与椭圆分布有关的分量样本极小值的渐近行为。进一步，我们得到了二元极分布的聚集风险的下尾渐近性。
Let R be a positive random variable independent of S which is beta distributed. In this paper we are interested on the relation between R and RS. For this model we derive first some distributional properties, and then investigate the lower tail asymptotics of RS when R is regularly varying at 0, and vice-versa. Our first application concerns the asymptotic behaviour of the componentwise sample minima related to elliptical distributions. Further, we derive the lower tail asymptotics of the aggregated risk for bivariate polar distributions.