Bayesian estimation of finite3-component mixture of Burr Type-XII distributions assuming Type-I right censoring scheme

Abstract

As compared to simple models, the mixture models of underlying lifetime distributions are intuitively more appropriate and appealing to model the heterogeneous nature of process. This study focuses on the problem of estimating the parameters of a newly developed 3-component mixture of Burr Type-XII distributions using Type-I right censored data. Firstly, considering a Bayesian structure, some mathematical properties of a 3-component mixture of Burr Type-XII distributions are discussed. These mathematical properties include Bayes estimators and posterior risks for the unknown component and proportion parameters using the non-informative and the informative priors under squared error loss function, precautionary loss function and DeGroot loss function. Secondly, in case when no or little prior information is available, elicitation of hyperparameters is given. Also, the posterior predictive distribution for a future observation and the Bayesian predictive interval are constructed. Moreover, the limiting expressions for the Bayes estimators and posterior risks are derived. In addition, the performance of the Bayes estimators for different sample sizes, test termination times and parametric values under different loss functions is investigated. Finally, simulated datasets are designed for the different comparisons and the model is illustrated using the real data.