The subexponential product convolution of two Weibull-type distributions

Abstract

Let X1 and X2 be two independent and nonnegative random variables with distributions F1 and F2, respectively. This paper proves that if both F1 and F2 are of Weibull type and fulfill certain easily verifiable conditions, then the distribution of the product X1X2, called the product convolution of F1 and F2, belongs to the class S* and, hence, is subexponential. © 2010 Australian Mathematical Publishing Association Inc.