Bayesian Estimation and Prediction for Discrete Weibull Distribution

This article is devoted to the Bayesian estimation of the discrete Weibull distribution parameters. Bayesian procedure is performed with three prior distributions, namely Uniform-Gamma, Jeffreys' rule, and Beta-Gamma. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. Moreover, Bayesian predictive inference is proposed and compared among three prior distributions. A real data set has been analyzed to show how the proposed model and the method work in practice. The simulation and real application results of over-dispersed data show that Beta-Gamma prior presents the best performance, while, in case of under-dispersed data, the Uniform-Gamma prior performs the best.