A Class of Efficient Shrinkage Estimators for Modelling the Reliability of Burr XII Distribution

For the purpose of modelling the Reliability of Burr XII Distribution, a family of shrinkage estimators is proposed for any parameter of any distribution when a prior guess value ( 0 ) of is available from the past.In addition, two sub-models of the shrinkage type estimators for estimating the reliability and parameters of the Burr XII Distribution using two types of shrinkage weight functions with the preliminary test of the hypothesis 0 0 θ θ : H  against the alternative H 1 : θ ≠ θ 0 have been proposed and studied.The criteria for studying the properties of two sub-models of the reliability estimators which are the , Bias ratio, Mean Squared Error and Relative Efficiency were derived and computed numerically for each sub-model for the purpose of studying the behavior of the estimators for the Burr XII Distribution because they are complicated and contain many complex functions.The numerical results showed the usefulness of the proposed two sub-models of the reliability estimators of Burr XII Distribution relative to the classical estimators for both of the shrinkage functions when the value of the a priori guess value ( 0 ) is close to the true value of .In addition, the comparison between the proposed two sub-models of the shrinkage estimators and with classical estimators was made.