The difference between two distribution functions

Abstract

There are many methods for measuring the difference between two location parameters. In this paper, statistics are proposed in order to estimate the difference of two location parameters. The statistics are designed not using the means, variances, signs and ranks, but with the cumulative distribution functions. Hence these are measured as the differences in the area between two univariate cumulative distribution functions. It is found that the difference in the area between two empirical cumulative distribution functions is the difference of two sample means, and its integral is also the difference of two population means.