Improved maximum likelihood estimation of the parameters of the Gamma-Uniform distribution with bias-corrections

Abstract

A two-parameter Gamma-Uniform distribution was recently introduced as a prominent alternative in modeling bounded phenomena. Unfortunately, however, its maximum likelihood estimators (MLEs) are found to be highly biased in finite samples, a limitation that might effect this model’s application in data modeling. In this article, we construct nearly unbiased estimators for the unknown parameters of this distribution by deriving analytical bias-corrected maximum likelihood estimators applying the Cox and Snell methodology, the Firth’s method and also via the parametric Bootstrap bias correction approach. Our extensive simulation clearly revealed that the three bias reduction methods yield very good estimates which are nearly unbiased and exhibit comparable efficiency. Finally, we consider a real data set where the variable under enquiry is the proportion of unemployed labor force reported across some 158 nations in 2018 to show case the positive gain of incorporating the bias correction in the model fitting.

Keywords:

• Bootstrap bias-correction
• Cox-Snell bias-correction
• Firth’s method
• Gamma-Uniform distribution
• Maximum likelihood estimators
• Monte Carlo simulation

Acknowledgments

The authors are thankful to the referees for many valuable suggestions.

Additional information

Funding

Josmar Mazucheli gratefully acknowledge the partial financial support from Fundação Araucária (Grant 064/2019 - UEM/Fundação Araucária).