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.

Keywords:

• Fiducial inference
• Two-sample gamma distributions
• Confidence interval
• Coverage
• Hypothesis test

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Acknowledgments

The authors are grateful to the referees for their valuable comments which led to the improvement of this paper. This work has been supported by Grant 11871294 and 11501134 from the National Natural Science Foundation of China, and Grant ZR2014AM019 from the Shandong Provincial Natural Science Foundation of China.