Approximating Tail Areas of Probability Distributions

Abstract

A general method for approximating tail areas is developed through an extension of the methodology of Andrews. This extension is applied to both continuous and discrete distributions. Examples of the approximations are given for the standard normal, $t$, and chi-square distributions in the continuous case and for the Poisson and binomial distributions in the discrete case. Errors of the approximations are considered. The generality of the method shown indicates that extension is possible to other distributions.