A normal approximation to the F distribution

Abstract

A new normal approximation, Φ(z) , for the cumulative distribution function (c.d.f.) of the F distribution, F(x, ν1 , ν2 ), with associated degrees of freedom, ν1 and ν2 , is proposed for large ν2 and fixed ν1. The proposed approximation is compared to several others approximations such as a normal, ordinary chi-square, Scheffé-Tukey and Li and Martin approximations. The employed numerical analysis indicates that, for ν2/ν1 ≥ 3, the accuracy of the proposed normal approximation is to at least the third decimal place for most small values of ν1 . This is a comparable accuracy that is achievable using Li and Martin (2002) approximation with shrinking factor approximation (SFA) using a chi-square c.d.f. with degrees of freedom ν1. The advantage of the proposed normal approximation over SFA is that normal c.d.f. is easily obtained than that of chi-square.