Likelihood ratio tests in two gamma populations for equality of shape parameters Likelihood ratio tests in two gamma populations for equality of shape parameters

The introduction of shape parameters into the statistical literature opened new areas of research and allowed statisticians to use models that produced better fits to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many gamma-populations, one may test equality (or homogeneity) of shape parameters across a collection of independent populations. In this paper we develop standard asymptotic tests for testing the equality of shape parameters of gamma distributions using the log-likelihood ratio (LRT) test statistic. Other tests are given that summarize test hypotheses on the shape parameter of a single gamma distribution. We numerically investigate the performances of these tests and find that in large sample sizes that the distribution of the log-likelihood ratio test statistic converges nicely to that of a chi-square distribution.