Miller S.H. Table of Percentage Points of Kolmogorov Statistics

Research paper. — American Statistical Association Journal. — 1956 (March). — Vol. 51, No. 273. — pp. 111—121.A simple method for testing the probability that a set of numbers is a sample from a known distribution consists of comparing the empirical cumulative distribution function of the sample, S_n(x), with the known cumulative distribution function F(x). Both D_n=maximum{S_n(x)-F(x)} and D_n* = maximum|Sn(x)- F(x)| are random variables, independent of the special form of F(x), if F(x) is continuous. This paper contains more extensive tables of the percentage points in the distributions of D_n and D_n* than have been published previously. These values are obtained by empirical modification of a known asymptotic formula.