Comparison of some interval estimation methods for the parameters of the gamma distribution

Abstract

Several methods of finding interval estimators of the parameters of the gamma distribution are considered in the literature. In this work we compare the following methods: Wald confidence intervals; profile likelihood intervals; Bayesian intervals using the Jeffreys prior, the reference prior when α is the parameter of interest and β the nuisance parameter, the reference prior when β is the parameter of interest and α the nuisance parameter; and three fiducial methods. The comparison is done using Montecarlo simulations, in terms of the coverage probabilities and the expected lengths of the intervals, considering small, medium and large sample sizes. As an important result of the simulations we found that the fiducial methods are the best when the sample size is very small, and as the sample size increases all the methods, except the Wald confidence intervals, have a similar behavior. An example of application is shown considering earthquake data of Mexico.