Bayesian Estimation and Prediction for Zero-Inflated Discrete Weibull Distribution - Duangsaphon, Monthira; Budsaba, Kamon; Nidsunkid, Sudarat; Chaiprasithikul, Dusit (Thailand Statistician, 2025)
This paper proposes the Bayesian estimation of the zero-inflated discrete Weibull distribution assuming three prior distributions, namely Beta-Uniform-Uniform prior, Beta-Jeffreys’ rule prior, and Beta-Beta-Gamma prior. It is commonly known that there is no compact form for the Bayes estimators. The Bayesian estimate of the model parameters has been performed through the random walk Metropolis algorithm. The Bayes estimates of the unknown parameters and the credible interval construction are established based on the generated samples. Moreover, the maximum likelihood estimation is considered, as well as the confidence interval estimation for the model parameters has been performed through normal approximation. The performance of the Bayes estimators has also been compared with the classical estimators through the Monte Carlo simulation study. Further, the Bayesian prediction of a future observation is proposed under the three prior distributions. The posterior predictive distribution of a future observation cannot be evaluated analytically. To obtain the estimate of future sample, the Metropolis-Hastings algorithm is used. Two datasets have been analyzed to show how the proposed model and the method work in practice.