Abstract
The chi-square distribution is one of the most widely used probability distributions; thus many functions have been advanced as approximations to the chi-square cumulative distribution function. One measure of the quality of an approximation is the maximum absolute error of the associated error function. This paper investigates the error functions for three normal approximations to the chi-square cumulative distribution function, those offered by Fisher, Wilson-Hilferty, and Kelley. In particular, a technique is developed for each approximation to find the maximum absolute error for fixed degrees of freedom. The maximum absolute error for each approximation and certain degrees of freedom is tabled.
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