Simultaneous Confidence Intervals for the Ratios of the Means of Zero-Inflated Gamma Distributions and Its Application

Abstract

Heavy rain in September (the middle of the rainy season in Thailand) can cause unexpected events and natural disasters such as flooding in many areas of the country. Rainfall series that contain both zero and positive values belong to the zero-inflated gamma distribution, which combines the binomial and gamma distributions. Precipitation in various areas of a country can be estimated by using simultaneous confidence intervals (CIs) for the ratios of the means of multiple zero-inflated gamma populations. Herein, we propose six simultaneous CIs constructed using the fiducial generalized CI method, Bayesian and highest posterior density (HPD) interval methods based on the Jeffreys’rule or uniform prior, and method of variance estimates recovery (MOVER). The performances of the proposed simultaneous CI methods were evaluated using a Monte Carlo simulation in terms of the coverage probabilities and expected lengths. The results from a comparative simulation study show that the HPD interval based on the Jeffreys’rule prior performed the best in most cases, while in some situations, the fiducial generalized CI performed well. All of the methods were applied to estimate the simultaneous CIs for the ratios of the means of natural rainfall data from six regions in Thailand.

Keywords

• zero-inflated gamma distribution
• simultaneous confidence intervals
• Bayesian estimation
• fiducial approach