Improved Goodness-Of-Fit Tests

Two statistics for testing goodness of fit for small sample sizes are provided. The first statistic, Sn, 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 Snand 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