Product of independent inverted hypergeometric function type I variables

Abstract

ABSTRACT: The inverted hypergeometric function type I distribution has the probability density function proportional to xν−1(1 + x)−(ν+γ)2F1(α, β; γ; (1 + x)−1), x > 0 , where 2F1 is the Gauss hypergeometric function. In this article, we derive the probability density function of the product of two independent random variables having inverted hypergeometric function type I distribution. We also consider several other products involving inverted hypergeometric function type I, beta type I, beta type II, beta type III, Kummer–beta and hypergeometric function type I variables.