Abstract
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.
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Research supported by the National Science Foundation of China (No. 11071182).
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Cui, Z., Wang, Y. On the long tail property of product convolution. Lith Math J 60, 315–329 (2020). https://doi.org/10.1007/s10986-020-09482-w
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DOI: https://doi.org/10.1007/s10986-020-09482-w