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An approximation to the F distribution using the chi-square distribution

Lookup NU author(s): Dr Baibing Li, Professor Elaine Martin


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For the cumulative distribution function (c.d.f.) of the F distribution, F(x; k, n), with associated degrees of freedom, k and n, a shrinking factor approximation (SFA), G(λkx; k), is proposed for large n and any fixed k, where G(x; k) is the chi-square c.d.f. with degrees of freedom, k, and λ=λ (kx; n) is the shrinking factor. Numerical analysis indicates that for n/k ≥ 3, approximation accuracy of the SFA is to the fourth decimal place for most small values of k. This is a substantial improvement on the accuracy that is achievable using the normal, ordinary chi-square, and Scheffé-Tukey approximations. In addition, it is shown that the theoretical approximation error of the SFA, F(x;k, n) - G(λkx; k), is O(1/n2) uniformly over x. © 2002 Elsevier Science B.V. All rights reserved.

Publication metadata

Author(s): Li B, Martin EB

Publication type: Article

Publication status: Published

Journal: Computational Statistics and Data Analysis

Year: 2002

Volume: 40

Issue: 1

Pages: 21-26

ISSN (print): 0167-9473

ISSN (electronic): 1872-7352

Publisher: Elsevier BV


DOI: 10.1016/S0167-9473(01)00097-4


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