Applying Series Expansion to the Inverse Beta Distribution to Find Percentiles of the F-Distribution

Abstract

Let 0 ≤ 1 and F be the cumulative distribution function 1993 of the F-Distribution. We wish to find xp such that F(xp|n1, n2) = p, where n1 and n2 are the degrees of freedom. Traditionally, xp is found using a numerical root-finding method, such as Newton's method. In this paper, a procedure based on a series expansion for finding xpis given. The series expansion method has been applied to the normal, chi-square, and t distributions, but because of computational difficulties, it has not been applied to the F-Distribution. These problems have been overcome by making the standard transformation to the beta distribution. The procedure is explained in Sections 3 and 4. Empirical results of a comparison of CPU times are given in Section 5. The series expansion is compared to some of the standard root-finding methods. A table is given for p =.90. © 1993, ACM. All rights reserved.