Confidence interval estimation for the difference and ratio of the means of two gamma distributions

Gamma distribution is widely used in applied fields due to its flexibility of accommodating right-skewed data. This article explores statistical methods for constructing confidence intervals for both the difference and ratio of two gamma means. We propose several methods based on the concepts of generalized inference, variance estimates recovery (MOVER) and parametric bootstrapping. The performances of proposed methods are evaluated and compared via a comprehensive simulation study. Simulation results show that the hybrid method that combines MOVER with parametric bootstrapping can provide confidence intervals with reasonable coverage probabilities and interval lengths even for parameter settings with small shape parameters. Finally, two real data examples from environmental and engineering studies are analyzed using the proposed methods.