Bayesian Estimation and Prediction for Discrete Zubair Weibull Distribution under Type-II Censoring Scheme

Abstract

This paper discussed the Bayesian estimation for the unknown parameters, survival, hazard rate, and alternative hazard rate functions of the discrete Zubair Weibull distribution. Informative priors (gamma and beta) for the parameters of the distribution are assumed. The Bayes estimators are derived under the squared error and linear-exponential loss functions based on Type-II censored sample. Credible intervals for the parameters, survival, hazard rate, and alternative hazard rate functions are obtained. The Bayes predictors (point and interval) for the future observation are obtained considering two-sample prediction. A simulation study is performed using the Markov Chain Monte Carlo algorithm for different sample sizes, and censoring rates to assess the performance of the estimators. Moreover, three real data sets were applied to investigate the flexibility and applicability of the distribution.