Statistical inference of Burr-XII distribution under progressive Type-II censored competing risks data with binomial removals

Abstract

In this paper, we consider the analysis of Burr XII distribution based on the competing risks model under progressive Type-II censoring, where the amount of units withdrawn at each stage is assumed to be random and subject to a binomial distribution. The maximum likelihood estimations of unknown parameters are derived and their existence and uniqueness are proved as well. Furthermore, approximate confidence intervals are also constructed by using the observed Fisher information matrix and delta method. Moreover, Bayes estimators and associated credible intervals under different loss functions are obtained based on MCMC method. In addition, simulation study used to evaluate the performance of all estimators proposed is included. Finally, a practical data example is given to illustrate all the inferential processes developed here.