On the long tail property of product convolution

Zhaolei Cui; Guancheng Jiang; Yuebao Wang

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arXiv · 1901.01399

On the long tail property of product convolution

Zhaolei Cui·Guancheng Jiang·Yuebao Wang

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Abstract

Let $X$ and $Y$ be two independent random variables with corresponding distributions $F$ and $G$ supported on $[0,\infty)$. The distribution of the product $XY$, which is called the product convolution of $F$ and $G$, is denoted by $H$. In this paper, some suitable conditions about $F $ and $G $ are given, under which the distribution $H$ belongs to the long-tailed distribution class. Here, $F$ is a generalized long-tailed distribution and is not necessarily an exponential distribution. Finally, a series of examples are given to show that the above conditions are satisfied by many distributions and one of them is necessary in some sense.

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Zhaolei Cui, Guancheng Jiang, Yuebao Wang. 2019-01-05. On the long tail property of product convolution. https://arxiv.org/abs/1901.01399

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