The Convolution of Generialized-F Distributions

Abstract

**Please note that the full text is embargoed** 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 hypergeometric 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.