Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data

Abstract

The Burr Type XII distribution has been widely applied in the real data analysis. In the censored data modeling, adopting the efficient parameter estimation methods and then predicting the censored observation are very important. In this paper, the parameters estimation and prediction of the Burr Type XII distribution under the doubly censoring scheme are studied. The maximum likelihood estimates of the unknown parameters are earned through the Expectation–Maximization (EM) algorithm. Since the Bayes estimators cannot be evaluated in explicit form, we propose to apply the Tierney and Kadane’s and Markov Chain Monte Carlo procedure to approximate them. The asymptotic and the highest posterior density credible confidence intervals for the unknown parameters are introduced. Based on the Monte Carlo simulations, different proposed estimators are compared. The predictive intervals of the future observation are also constructed. Finally, the proposed methods have been studied using the two real microfluidics data.