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

Abstract

In this paper, the prob lem o f estimating the scale parameter of log gamma distribution under Bayesian and maximu m 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 simulat ion study has been carried out to illustrate the numerical applicat ions 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 maximu m likelihood framewo rks. The performance of different Bayes estimators has also been compared using five d ifferent loss functions. The study indicated that for estimation of the said parameter, the Bayesian estimation can be preferred over maximu m likelihood estimation. While in case of the Bayesian estimation, the entropy loss function under Jeffreys can effectively be emp loyed.