Improved goodness-of-fit tests

Abstract

SUMMARY Two statistics for testing goodness of fit for small sample sizes are provided. The first statistic, S n , can be used to test the fit to any completely specified continuous distribution function and is more powerful than the Kolmogorov-Smirnov statistic in the cases tested. The second statistic, S * n , tests the fit to an exponential distribution with mean unknown. It is more powerful than a Kolmogorov-Smirnov type statistic suggested by Lilliefors (1969) for the cases tested. Critical values for S n and S * n are given for sample size n=1 (1)20(5)30 and α=0.20, 0.15, 0.10, 0.05 and 0.01. The critical values and power analyses were obtained by Monte Carlo techniques. These new statistics are closely related to the Kolmogorov-Smirnov statistic and are computationally equival