Bayesian confidence intervals for the ratio of the means of zero-inflated gamma distributions with application to rainfall data

Abstract

Herein, we propose eight Bayesian methods (credible and highest posterior density intervals using the Jeffreys rule, independence Jeffreys, uniform, or normal-gamma priors) and one based on the fiducial quantity for constructing confidence intervals for the ratio of the means of zero-inflated gamma distributions. Simulation studies were conducted to evaluate the efficacies of the confidence intervals and compare their performances in terms of coverage probabilities and expected lengths, in which the Bayesian highest posterior density interval using the Jeffreys rule prior performed the best. We also applied the methods to rainfall datasets from northern Thailand to demonstrate their efficacies with real data.