Bayesian Inference on the Burr type-XII Model Parameters Based on Progressive type-II Fuzzy Order Statistics

Abstract

Abstract In statistical inference, the experimental results are usually considered precise information. However, these results cannot always be recorded or measured precisely, which is called Fuzzy data, which can be considered an imprecise type of data with a source of uncertainty. This paper presents a Fuzzy Bayesian estimation for Burr type-XII distribution parameters based on progressive type-II fuzzy order statistics. The Bayesian estimators have been derived by Tierney-Kadane and Monte Carlo integration approximations and compared with the exact Bayesian estimators, via Monte Carlo simulations. The simulation results indicated that the exact Bayes results provide better estimators and outperform the other approximation methods. Finally, a numerical example is given to demonstrate the efficiency of the proposed methods.