Authors

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

Journal title

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.