Expected Bayesian Estimator and Hierarchical Bayesian Estimator for the Parameter of a Rayleigh Distribution Reliability System Under the Progressive Type-II Data Sample

Han (2004) first proposed a new definition of Bayesian estimators called "Expected Bayesian Estimators". This new approach was the generalization of the "hierarchical" approach proposed by Lindley and Smith (1972). Therefore, our main goal in this study is to examine and compare the expected Bayesian estimator and the hierarchical Bayesian estimator for the parameter of a reliability system the result of the Rayleigh probability distribution is the progressive  Type-II censored data. To this end, we describe the expected Bayesian estimator and the hierarchical Bayesian estimator in most of the three theorems, in which we show that the expectations of Bayesian estimators and the hierarchical Bayesian estimator converge to zero in various previous distributions.