Theoretical aspects for adaptive progressive Type-II censored competing risks and its applications in climatic data

Abstract

An adaptive progressively Type-II censoring scheme for competing risks data is studied, where the causes of failures may occur at times that follow three-parameter Burr XII distribution. Furthermore, some causes of failures are assumed to be unknown. The maximum likelihood and Bayes estimates are obtained as point estimations for the unknown parameters. The approximate confidence intervals and credible intervals of the estimators are also computed. The results of Bayes estimators are computed against different symmetric and asymmetric loss functions such as squared error, LINEX and general entropy based on Markov chain Monte Carlo approach. Gibbs within the Metropolis’Hasting algorithm is applied to generate Markov chain Monte Carlo samples from the posterior density functions. Two real data sets are analyzed for illustration. Simulation results are carried out to explicate the precision of the estimators.