On Kolmogorov-Smirnov type one-sample statistics

Abstract

SUMMARY Asymptotic expansions with a term in n −½ of the distributions of Pyke's modified one-sample Kolmogorov-Smirnov statistics, C + n , C − n and C n are derived. From these expansions and the already known ones for D + n , D − n , D n , V n = D + n + D − n and K n = C + n + C − n are deduced expansions for the percentage points. The approximate percentage points determined by these expansions are sufficiently accurate to be used in applications.