Likelihood Ratio Tests for Comparing Several Gamma Distributions

• Activity Number: 613
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Meesook Lee* and Kalimuthu Krishnamoorthy and Wang Xiao
• Companies: South Louisiana Community College and University of Louisiana and University of Louisiana
• Keywords: Constrained MLEs ; Exact test ; Large sample test ; Power ; Rainfall distribution ; Type I error

Abstract

Likelihood ratio tests (LRTs) for comparing several independent gamma distributions with respect to shape parameters, scale parameters and means are derived. Extensive simulation study indicates that the null distributions of the LRT statistics for all three problems are free of parameters, and so the LRTs are exact. Furthermore, our simulation studies suggest that the null distribution of the LRT for testing equality of shape parameters and that of the LRT for testing equality of scale parameters are 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 populations. The methods are illustrated using two examples.