Small sample inference for gamma parameters: one-sample and two-sample problems

Signed-likelihood ratio tests (SLRTs) are derived for testing the shape and scale parameters and the mean of a gamma distribution. The properties of the proposed tests are evaluated by Monte Carlo simulation and compared with the other tests available in the literature. SLRTs are also developed for two-sample problems of comparing two shape parameters, two scale parameters and two means, and their merits are evaluated by Monte Carlo simulation. Evaluation studies indicate that the SLRTs are accurate even for small samples and are comparable with or better than other tests. Furthermore, simple parametric bootstrap (PB) methods based on the maximum likelihood estimates are proposed for interval estimation. The PB confidence intervals are satisfactory even for small samples. The methods are illustrated and compared using two examples. Copyright (c) 2014 John Wiley & Sons, Ltd.