On Representations of the Doubly Non-Central <i>F</i> Distribution

Abstract

Abstract The cumulative doubly non-central F-distribution associated with the random variable F″ = mS1/nS2 is considered where S1 and S2 are two independent non-central chi-square varites with degrees of freedom n and m and non-centrality parameters λ1 and λ2, respectively. Representations in terms of series are presented together with efficient computational procedures for the special functions used in numerical evaluation.