Minimax Estimation of the Parameter of the Burr Type Xii Distribution

In this paper the classical estimators of the shape parameter 0 for the Burr Type XII distribution, such as, the Maximum Likelihood Estimator (MLE), the Uniformly Minimum Variance Unbiased Estimator (UMVUE), and the Minimum Mean Squared Error (MinMSE) estimator are obtained. Then the problem of finding the minimax estimators of this parameter under the squared log error, precautionary, and weighted balanced squared error loss functions by applying the theorem of Lehmann [1950] is concerned. The obtained results have been interpreted in the light of two-person zero sum game. All these estimators are compared empirically using Monte Carlo simulation.