Computing the Distribution of a Linear Combination of Inverted Gamma Variables

Abstract

A formula for evaluation of the distribution of a linear combination of independent inverted gamrra random variables by one-dimensional numerical integration is presented. The formula is direct application of the inversion formula given by Gil-Pelaez [4]. This method is applied to computation of the generalized p-values used for exact significance testing and interval estimation of the parameter of interest in the Behrens-Fisher problem and for variance components in balanced mixed linear model. 1.