An Approximation to the Wilcoxon-Mann-Whitney Distribution

Abstract

An approximation, based on the sum of independent uniform random variables, to the Wilcoxon-Mann-Whitney null-distribution, is proposed. Numerical comparisons with the normal approximation show that this uniform approximation is appreciably more accurate even when the smaller sample size is large. A table of percentiles of the distributions of the sum of independent uniform random variables is given for the uniform approximation. An extension of existing tables of percentiles of the exact distribution is also given.