The product of two dependent random variables with regularly varying or rapidly varying tails |
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Authors: | Jun Jiang Qihe Tang |
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Institution: | a China Zheshang Bank, Hangzhou 310006, PR Chinab Department of Statistics and Actuarial Science, The University of Iowa, 241 Schaeffer Hall, Iowa City, IA 52242, USA |
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Abstract: | Let X and Y be two nonnegative and dependent random variables following a generalized Farlie-Gumbel-Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY. We quantify the impact as the limit, as x→∞, of the quotient of Pr(XY>x) and Pr(X∗Y∗>x), where X∗ and Y∗ are independent random variables identically distributed as X and Y, respectively. We obtain an explicit expression for this limit when X is regularly varying or rapidly varying tailed. |
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Keywords: | primary 60E05 secondary 62H20 62E20 |
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