A Test for the Scale Parameters of Two Gamma Distributions using the Generalized Likelihood Ratio

Abstract The method of maximum likelihood is used to develop a statistical test for the scale parameters of two gamma distributions with common shape factors. A simple method of determining the power of the test using the non-central chi square distribution is also presented. The results of applying the test to gamma-scale parameters are compared with results obtained by applying the “t” test to normal and log-normal means. The likelihood ratio test for differences in gamma-scale parameters is more powerful than the “t” test applied to log-normal means. The power is nearly equal for the likelihood test of gamma-scale parameters and the “t” test for non-transformed means, although the latter test may not be as robust as is the likelihood ratio test. Since many meteorological variables are known to be gamma distributed, this test should have several applications in meteorology.