Testing Hypotheses about the Shape Parameter of a Gamma Distribution

The purpose of this expository article is to provide greater access to critical values for testing hypotheses about the shape parameter of a gamma distribution. Among the possible tests, we consider tests of exponentiality against gamma increasing failure rate and/or decreasing failure rate alternatives. Extensive tables of critical values are given for individual sample sizes from 2 to 30, and values of the shape parameter in half-integer increments from i to 10. Median unbiased estimators are also given for the shape parameter to avoid small-sample complications with maximum likelihood methods. Power curves are given for testing exponentiality against gamma alternatives. These curves illustrate certain advantages of this parametric test over nonparametric alternatives.