Product Convolution of Generalized Subexponential Distributions

Abstract

Assume that ξ and η are two independent random variables with distribution functions Fξ and Fη, respectively. The distribution of a random variable ξη, denoted by Fξ⊗Fη, is called the product-convolution of Fξ and Fη. It is proved that Fξ⊗Fη is a generalized subexponential distribution if Fξ belongs to the class of generalized subexponential distributions and η is nonnegative and not degenerated at zero.