On the long tail property of product convolution

Let X and Y be two independent random variables with corresponding distributions F and G 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, we give some suitable conditions on F and G , under which the distribution H...

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Published in:Lithuanian mathematical journal 2020-07, Vol.60 (3), p.315-329
Main Authors: Cui, Zhaolei, Wang, Yuebao
Format: Article
Language:English
Subjects:
Actuarial Sciences
Convolution
Independent variables
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability distribution functions
Probability Theory and Stochastic Processes
Random variables
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description Let X and Y be two independent random variables with corresponding distributions F and G 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, we give some suitable conditions on F and G , under which the distribution H belongs to the long-tailed distribution class. Here F is a generalized long-tailed distribution, not necessarily an exponential distribution. Finally, we give a series ofexamples to show that our conditions are satisfied by many distributions, and one of them is necessary in some sense.
doi_str_mv 10.1007/s10986-020-09482-w
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subjects Actuarial Sciences
Convolution
Independent variables
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability distribution functions
Probability Theory and Stochastic Processes
Random variables
title On the long tail property of product convolution
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