Bayesian Shrinkage Estimator of Burr XII Distribution

Abstract

In this paper, we derive the generalized Bayesian shrinkage estimator of parameter of Burr XII distribution under three loss functions: squared error, LINEX, and weighted balance loss functions. Therefore, we obtain three generalized Bayesian shrinkage estimators (GBSEs). In this approach, we find the posterior risk function (PRF) of the generalized Bayesian shrinkage estimator (GBSE) with respect to each loss function. The constant formula of GBSE is computed by minimizing the PRF. In special cases, we derive two new GBSEs under the weighted loss function. Finally, we give our conclusion.