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Biometrika 1979 66(3):577-584; doi:10.1093/biomet/66.3.577
© 1979 by Biometrika Trust
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An F approximation and its application

C. HIROTSU

Faculty of Engineering, University of Tokyo

Formulae for upper probabilities and for upper percentiles of statistics which follow approximately an F distribution are developed. Their accuracies are compared numerically with the usual ones adjusting only the first two cumulants, when applied to the noncentral F distribution, the statistic of a particular cumulative sum method and the studentized range. Furthermore, it is pointed out that the {chi}2 approximation of the squared range from identically and independently distributed normal variables is more accurate than the well-known {chi} approximation by Patnaik (1950) so far as upper 1 and 5% points are concerned.

Key Words: Cumulative sum method • Chi approximation • Chi-squared approximation • F approximation • Noncentral F distribution • Studentized range • Unbalanced data


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