Bayesian estimation of the mixture of Burr Type-XII distributions using doubly censored data

Abstract This study discusses the Bayesian and maximum likelihood estimation methods for analyzing the data from a 3-component mixture of Burr Type-XII probability distributions. The maximum likelihood estimators with their variances cannot be obtained in an explicit form and thus an iterative procedure is used to calculate them numerically. Contrary to this, elegant closed form algebraic expressions of Bayes estimators and their posterior risks are derived. Using the informative and noninformative priors, the posterior predictive distributions along with predictive intervals are also discussed. A method of eliciting hyperparameters using prior predictive distribution is also a part of this study. Some interesting properties (including, posterior risks and Bayesian predictive intervals) of Bayes estimators and their behavior across different sample sizes, left and right test termination times, informative prior versus Jeffreys noninformative prior, are provided via a detailed Monte Carlo simulation study. To assess the suitability and application of the proposed model, a real life data example is also discussed in this article. Based on the simulated results and real data application, it is concluded that the IP paired with DLF (SELF) is a more suitable for estimating mixing component.