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

Citation
Rw. Abernathy et Rp. Smith, APPLYING SERIES EXPANSION TO THE INVERSE BETA-DISTRIBUTION TO FIND PERCENTILES OF THE F-DISTRIBUTION, ACM transactions on mathematical software, 19(4), 1993, pp. 474-480
Citations number
4
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Computer Sciences",Mathematics
ISSN journal
0098-3500
Volume
19
Issue
4
Year of publication
1993
Pages
474 - 480
Database
ISI
SICI code
0098-3500(1993)19:4<474:ASETTI>2.0.ZU;2-J
Abstract
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.