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.