On Representations of the Doubly Non-Central F Distribution

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.