An asymptotic expansion for the non-central F-distribution

Abstract EN

A new asymptotic expansion is derived for the non-central F-distribution F (F′ \ m1, m2, λ), which is suitable for large m1 / 2, small m2 \ 2, r ∈ N and 0 < q < 1, where Q (m2 \ 2, -klog q) = Γ (m2 \ 2, -klog q) / Γ (m2 \ 2) is the incomplete Gamma function ratio and k = ((m1 \ 2) + r) + ((m2 \ 2)-1) \ 2.

This form has some advantages over previous asymptotic expansions in this region of the parameter space in which Hn depends on all three parameters m1 \ 2, m2 \ 2 and q.

The advantage of this new expansion is that an algorithm based on it can be more easily tuned for particular accuracy requirements and for particular parameter ranges.