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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Bibliographic Details
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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Summary: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.
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-020-09482-w