Likelihood ratio tests for comparing several gamma distributions

Likelihood ratio tests (LRTs) for comparing several independent gamma distributions with respect to shape parameters, scale parameters, and means are derived. The LRT for testing homogeneity of several gamma distributions is also derived. Extensive simulation studies indicate that the null distributions of the LRT statistics for all four problems depend on the parameters only weakly, and for practical purposes, they are independent of the parameters. Furthermore, our simulation studies suggest that the null distribution of the LRT statistic for testing the equality of shape parameters and that of the LRT statistic for testing the equality of scale parameters are essentially the same. Numerical algorithms to compute the maximum likelihood estimates and p-values are given. Percentiles of the null distributions are tabulated for some selected sample sizes to compare three and five gamma distributions. The methods are illustrated using two practical examples. Copyright (C) 2015 John Wiley & Sons, Ltd.