On the long tail property of product convolution

2019/01/05 by Zhaolei Cui, Cui, Zhaolei, Jiang Guancheng +3
Decision Sciences · Mathematics · Economics, Econometrics and Finance · #Probability and Risk Models #Statistical Distribution Estimation and Applications #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1901.01399

Abstract

Let X and Y be two independent random variables with corresponding distributions F and G supported on [0,∞). 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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