F distribution is one of
the most frequently used distributions in statistics. For example, it is used
for testing: equality of variances of two independent normal distributions,
equality of means in the one-way ANOVA setting, overall significance of a normal
linear regression model, and so on. In this paper, a simple chi-square
approximation for the cumulative distribution of the F-distribution is obtained via an adjusted log-likelihood ratio
statistic. This new approximation exhibits remarkable accuracy even when the
degrees of freedom of the F distribution are small.
Li, B. and Martin, E.B. (2002) An Approximation to the F Distribution Using the Chi-Square Distribution. Computational Statistics and Data Analysis, 40, 21-26.
https://doi.org/10.1016/S0167-9473(01)00097-4
Wong, A. (2008) Approximating the F Distribution via a General Version of the Modified Signed Log-Likelihood Ratio Statistic. Computational Statistics and Data Analysis, 52, 3902-3912. https://doi.org/10.1016/j.csda.2008.01.007
Davison, A.C., Fraser, D.A.S., Reid, N. and Sartori, N. (2014) Accurate Directional Inference for Vector Parameters in Linear Exponential Families. Journal of the American Statistical Association, 109, 302-314.
https://doi.org/10.1080/01621459.2013.839451
Bartlett, M.S. (1937) Properties of Sufficiency and Statistical Test. Proceedings of the Royal Society A, 160, 268-282. https://doi.org/10.1098/rspa.1937.0109
Lawley, D.N. (1956) A General Method for Approximating to the Distribution of the Likelihood Ratio Criteria. Biometrika, 43, 295-303.
https://doi.org/10.1093/biomet/43.3-4.295
Barndorff-Nielsen, O.E. and Cox, D.R. (1979) Edgeworth and Saddlepoint Approximation with Statistical Applications (with Discussion). Journal of the Royal Statistical Society, Series B, 41, 279-312.
