A Study of the Accuracy of Some Approximations fort, χ², andFTail Probabilities

This article summarizes an empirical study on the numerical accuracy of some computational formulas for the tail probabilities of t, χ2, and F distributions, in terms of the maximum absolute error for all p, 0 < p ≤ 1. The results are intended to fill a conspicuous gap in the statistical literature concerning the empirical quality of the approximations, and they are useful for designing efficient and accurate computing algorithms for such probabilities.