Classical and Bayesian Inference for the Burr Type XII Distribution Under Generalized Progressive Type I Hybrid Censored Sample

Abstract

This paper describes the classical and Bayesian estimation for the parameters of the Burr Type XII distribution based on generalized progressive Type I hybrid censored sample. We first discuss the maximum likelihood estimators of unknown parameters using the expectation-maximization (EM) algorithm and associated interval estimates using Fisher information matrix. We then derive the Bayes estimators with respect to different symmetric and asymmetric loss functions. In this regard, we use Lindley's approximation and importance sampling methods. Highest posterior density (HPD) intervals of unknown parameters are constructed as well. The results of simulation studies and real data analysis are conducted to compare the performance of the proposed point and interval estimators.

Keywords

• Burr Type XII distribution
• Confidence intervals
• EM algorithm
• Generalized progressive hybrid censoring
• Markov chain Monte Carlo technique