Bayesian Estimation of the Two-Parameter Gamma Distribution

ABSTRACT

A Bayesian estimation of the two-parameter gamma distribution is considered under the non informative prior. The Bayesian estimator is obtained by Gibbs sampling. The generation of the shape parameter in the Gibbs sampler is implemented using the adaptive rejection sampling method of Gilks and Wild (1992). Finally, the results of our numerical studies show that the Bayesian estimator using Gibbs sampling along with adaptive rejection sampling outperforms the maximum likelihood and moment based estimators, as well as the other Bayesian estimator.

Keywords:

• Adaptive rejection sampling
• Gibbs sampling
• Maximum likelihood estimation
• Non informative prior
• Rejection sampling
• The method of moments estimation
• Two-parameter gamma distribution

Mathematics Subject Classification:

• 62F15
• 65C05

Acknowledgment

This study was financially supported by special research fund of Chonnam National University in 2004.