Infinite divisibility of products and quotients of i.i.d. random variables

F.W. Steutel, V.K. Rohatgi, G.J. Székely

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Abstract

Given independent and identically distributed (i.i.d) random variables X and Y, we consider the infinite divisibility of XY and X/Y when X is (is not) infinitely divisible.For example, we prove that the product and quotient of two i.i.d. standard Cauchy randomvariables are infinitely divisible, and that the product of two i.i.d. Poisson random variables as well as the quotient of two i.i.d. Pareto random variables are not infinitely divisible. We also consider the possible infinite divisibility of 1/X.
Original languageEnglish
Pages (from-to)53-59
JournalThe Mathematical Scientist
Volume15
Publication statusPublished - 1990

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    Steutel, F. W., Rohatgi, V. K., & Székely, G. J. (1990). Infinite divisibility of products and quotients of i.i.d. random variables. The Mathematical Scientist, 15, 53-59.