Bayesian analysis of type-I right censored data using the 3-component mixture of Burr distributions

This study is concerned with the problem of estimating the parameters of a 3-component mixture of Burr distributions using type-I right censored data. The closed form expressions for the Bayes estimators and their posterior risks assuming the noninformative (uniform and Jeffreys ) priors under squared-error loss function, precautionary loss function, and DeGroot loss function are derived. Performance of the Bayes estimators for different sample sizes, test termination times (a point of time after which all other tests are terminated), and parametric values under different loss functions is investigated. The posterior predictive distribution for a future observation and the Bayesian predictive interval are constructed. In addition, the limiting expressions for the Bayes estimators and posterior risks are derived. Simulated data sets are designed for the comparisons and the model is finally illustrated using the real data.