A Note on Bayesian and Maximum Likelihood Estimation of Scale Parameter of Log Gamma Distribution

Abstract

In this paper, the problem of estimating the scale parameter of log gamma distribution under Bayesian and maximum likelihood framework has been addressed. The uniform and Jeffreys priors have been assumed for posterior analysis. The Bayes estimators and associated risks have been derived under five different loss functions. The credible intervals and highest posterior density intervals have been constructed under each prior. A simulation study has been carried out to illustrate the numerical applications of the results and to compare the performance of different estimators. The purpose is to compare the performance of the estimators based on Bayesian and maximum likelihood frameworks. The performance of different Bayes estimators has also been compared using five different loss functions. The study indicated that for estimation of the said parameter, the Bayesian estimation can be preferred over maximum likelihood estimation. While in case of the Bayesian estimation, the entropy loss function under Jeffreys can effectively be employed.