The Convolution of GeneralizedFDistributions

Abstract

The generalized F variate is the ratio of two independent gamma variates, and its distribution includes as special cases such distributions as the inverted beta, Lomax, and Snedecor's F , Based on convolution, the distribution function of the sum of two independent generalized F variates is derived in terms of a Lauricella-Saran hyper-geometric function of three variables. The results are applied, with numerical examples given, to (a) a Bayesian analysis of the availability of a two-component series system and (b) a test of hypothesis on the multinormal mean vector whenever the covariance matrix has the intraclass correlation pattern.