Product and Quotient of Inverse Paralogistic Distribution Generated Based on Farlie-Gumbel-Morgenstern (FGM) Copula

Abstract

In this article, Inverse Paralogistic distribution based on Farlie-Gumbel-Morgenstern (FGM) copula is introduced. Derivations of exact distribution V = XY ,W = X/Y , and Z = X/(X + Y ) are obtained in closed form. Corresponding moment properties of these distributions are also derived. The expressions turn out to involve known special functions.

On the Distribution of the Product of Inverse Pareto and Exponential Random Variables

“…These include the beta family (Tang & Gupta, 1984), student's t family (Wallgren, 1980), uniform family (Sakamoto, 1943), gamma family (Stuart, 1962), exponential family (Malik & Trudel, 1986), Inverse Burr distribution (Pizon & Arcede, 2018), and Lomax distribution (Arcede & Macalos, 2016). This article investigated the distribution of the product of independent random variable XY following Inverse Pareto (X) and Exponential respectively, positive values of y and θ.…”