Comparing Several Gamma Means: An Improved Log-Likelihood Ratio Test

The two-parameter gamma distribution is one of the most commonly used distributions in analyzing environmental, meteorological, medical, and survival data. It has a two-dimensional minimal sufficient statistic, and the two parameters can be taken to be the mean and shape parameters. This makes it closely comparable to the normal model, but it differs substantially in that the exact distribution for the minimal sufficient statistic is not available. A Bartlett-type correction of the log-likelihood ratio statistic is proposed for the one-sample gamma mean problem and extended to testing for homogeneity of k≥2 independent gamma means. The exact correction factor, in general, does not exist in closed form. In this paper, a simulation algorithm is proposed to obtain the correction factor numerically. Real-life examples and simulation studies are used to illustrate the application and the accuracy of the proposed method