Likelihood Ratio Tests in Two Gamma Populations for Equality of Shape Parameters

• Activity Number: 425
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Ram Tripathi*+ and Jerome P. Keating
• Companies: Univ of Texas At San Antonio and The University of Texas at San Antonio
• Keywords: gamma distribution ; shape parameter ; likelihood ratio test ; simulation ; cubuc-spline smoothing

Abstract

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 Weibul 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 of shape parameters across a collection of independent populations. In this paper, we develop a likelihood ratio test regarding the shape parameters and numerically investigate the properties of this test with respect to control of Type I error rate for small samples. We also develop critical values of the test statistic via simulation, and compare these with the corresponding critical values of the asymptotic chi-square distribution of the likelihood ratio statistic. These tests are motivated by the need to have simple, easy to use tests and accurate procedures for small samples.