APPLYING SERIES EXPANSION TO THE INVERSE BETA-DISTRIBUTION TO FIND PERCENTILES OF THE F-DISTRIBUTION

Let 0 less than or equal to p less than or equal to 1 and F be the cum ulative distribution function (cdf) of the F-Distribution. We wish to find x(p) such that F(x(p)/n(1), n(2)) = p, where n(1) and n(2) are th e degrees of freedom. Traditionally, x(p) is found using a numerical r oot-finding method, such as Newton's method. In this paper, a procedur e based on a series expansion for finding x(p) is given. The series ex pansion method has been applied to the normal, chi-square, and t distr ibutions, but because of computational difficulties, it has not been a pplied to the F-Distribution. These problems have been overcome by mak ing the standard transformation to the beta distribution. The procedur e 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.