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Abstract 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 | S n (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.
Leslie H. Miller (Thu,) studied this question.