A Modified Kolmogorov-Smirnov Test for Weibull Distributions with Unknown Location and Scale Parameters

When the parameters in a continuous distribution are unknown and must be estimated, the standard Kolmogorov-Smirnov (K-S) goodness-of-fit tables do not represent the true distribution of the test statistics. This paper uses Monte Carlo techniques to create tables of critical values for a K-S type test for Weibull distributions with unknown location and scale parameters, but known shape parameter. The power of the proposed test is investigated, as is the relationship between critical values and the shape parameters. The results indicate that the modified K-S test appears to be a reasonable goodness-of-fit test for the Weibull family with unknown scale and location parameters.