On the Distribution of the Kolmogorov-Smirnov D-Statistic

Abstract

Gnedenko and Korolyuk [1] have pointed out that the exact distribution of the Kolmogorov-Smirnov $D$-statistic can be obtained explicitly by solving a certain double-boundary random walk problem, which, in turn, is solved by the principle of reflection. This principle is employed here in what is believed to be a new way to derive Gnedenko's and Korolyuk's result.