Please use this identifier to cite or link to this item: http://repositorio.ufla.br/jspui/handle/1/15329
Title: A normal approximation to the F distribution
Other Titles: Aproximação normal da distribuição F
Keywords: F distribution
Normal distribution
Distribuição F
Distribuição normal
Issue Date: Apr-2011
Publisher: Universidade Estadual Paulista
Citation: FERREIRA, D. C. A normal approximation to the F distribution. Revista Brasileira de Biometria, São Paulo, v. 29, n. 2, p. 222-228, abr./jun. 2011.
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.
URI: http://jaguar.fcav.unesp.br/RME/fasciculos/v29/v29_n2/Daniel.pdf
repositorio.ufla.br/jspui/handle/1/15329
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