The delta-corrected Kolmogorov-Smirnov test for the two-parameter Weibull distribution

Abstract

Summary Monte Carlo simulation techniques are used to create tables of critical values for the delta-corrected Kolmogorov-Smirnov statistic-a modification of the classical Kolmogorov-Smirnov statistic-for the Weibull distribution with known location parameter and unknown shape and scale parameters. The power of the proposed test is investigated relative to values of delta in the unit interval and relative to a wide variety of alternative distributions. The results indicate that using the delta-correction can lead to as many as 8.4 percentage points more power than can be achieved with the classical Kolmogorov-Smirnov test, with no change in the size of the test. Furthermore, carrying out the delta-corrected test involves no more steps or calculations than for the classical Kolmogorov-Smirnov test. In general, it is shown that a slight modification-or correction-in the definition of the empirical distribution function of the Kolmogorov-Smirnov test can lead to power enhancement without changing the type I error rate of the test. Two examples clearly show the effectiveness of the delta-corrected test. The delta-corrected Kolmogorov-Smirnov test is recommended for testing the goodness of fit to the twoparameter Weibull distribution.