Percentage points of a weighted Kolmogorov-Smirnov statistic

Abstract

Let F and G be the cumulative distribution functions corresponding to two independent random variables. Define the shift function, Δ(x), by F(x)=G(x+Δ(x)). Doksum and Sievers (1976) compared two confidence bands for Δ(x). The confidence band they found to be best requires the percentage points of a weighted form of the Kolmogorov-Smirnov statistic. The goal in this paper is to supply a table of some of the exact percentage points.