KOLMOGOROV-SMIRNOV TESTS OF FIT BASED ON SOME GENERAL BOUNDS.

This note gives a systematic method of computing the probability P[sub n](beta) of the event [Multiple line equation(s) cannot be represented in ASCII], where F[sub n] and F are the empirical and theoretical cumulative distribution functions and beta is a function on the interval (0, 1). The result is used to determine not only the significance level but also the exact power for an appropriate testing situation. When beta is a linear function, P[sub n](beta) may represent the probability distribution of the one-sided Kolmogorov-Smirnov statistic D[sup +, sub n]=sup[sub -Infinity < x < Infinity] [F[sub n(x) - F(x)]. Numerical examples are given in section 2, and they show that the method is extensively useful for practical applications. [ABSTRACT FROM AUTHOR]