Statistical inference of the Burr Type III distribution under joint progressively Type-II censoring

Abstract

The joint censoring technique is essential when the study's objective is to assess the relative benefits of products in relation to their service times. To reduce the cost and duration of the experiment, progressive censoring has gained a lot of attention in recent years. This article examines the statistical inference for the Burr Type III distribution using a joint progressive Type II censoring method on two samples. For model parameters, both the maximum likelihood and Bayesian methods are considered. Next, approximate confidence intervals are obtained based on the observed information matrix. Confidence intervals are also obtained using the procedures of Bootstrap-P and Bootstrap-T. Bayesian estimators are provided for symmetric and asymmetric loss functions. The Bayesian estimators cannot be produced in closed forms; hence, we compute the Bayesian estimators and the related credible intervals using the Markov chain Monte Carlo method. To evaluate the performance of the estimators, we conduct comprehensive simulation experiments. Finally, for purposes of illustration, we analyze two real data sets.

Keywords

• Burr Type III distribution
• Maximum likelihood estimation
• Bootstrap methods
• Bayesian estimation
• Minimum expected loss function