Modified Goodness-of-Fit Tests for Gamma Distributions with Unknown Location and Scale Parameters

Abstract

The common Kolmogorov-Smirnov, Anderson-Darling, and Cramer-von Mises goodness-of-fit tests require continuous underlying distributions with known parameters. This paper gives tables of critical values for these tests for gamma distributions with unknown location and scale parameters and known shape parameters. The powers of these tests are given for a number of alternative distributions. A relation between the critical values and the inverse square of the shape parameter is presented. For larger sample sizes, the modified CvM test is usually the most powerful of the three tests. One exception is for the alternative of a lognormal distribution where the modified AD test is most powerful. The equation, C = ao + a1(1/ß2) describes the relation between critical value and shape parameter quite well.