Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data

With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.