Fiducial inference for gamma distributions: two-sample problems

Abstract

This article derives the fiducial inferences for two-sample gamma distributions. Confidence intervals (CIs) are constructed for the difference between the shape, scale parameters and means of two populations. Fiducial based hypothesis tests are also derived. We evaluated the performance of fiducial CIs and tests by Monte Carlo simulation and compared with published methods such as the parametric bootstrap (PB), Shiue-Bain-Engelhardt (SBE) and the signed-likelihood ratio tests (SLRT). Our fiducial approaches are not only more accurate than other methods for small samples, but also much faster than existing methods. And our methods outperform others in real-life applications too.