Densities and distribution functions of the ratio of two linear functions and the product of Gamma variates: A saddlepoint approach

Abstract

© 2017 Taylor & Francis Group, LLC. Saddlepoint approximations for the densities and the distribution functions of the ratio of two linear functions of gamma random variables and the product of gamma random variables are derived. Ratios of linear functions with positive and negative weights and non identical gamma variables are considered. The saddlepoint approximations are very accurate in the tails as in the center of the distribution. Extensive simulation studies are used to evaluate the accuracy of the proposed methods.