Double Stage Shrinkage Estimator in Pareto Distribution


This paper proposes using preliminary test double stage shrinkage estimator (PTDSSE) for estimating the shape parameter () of Pareto distribution when the scale parameter equal to the smallest loss in a region (R) around available prior knowledge (0) about the actual value () as initial estimator as well as to reduce the mean squared error and the cost of experimentations. In situation where the experimentation time consuming and sample cost are very costly and expensive a double stage procedure can be used to reduce the expected sample size which are needed to obtain the estimator which minimize these costs. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor () and for acceptance suitable region (R). Expressions for Bias B(), Mean Square Error (MSE), Relative Efficiency [R.Eff()], Expected sample size [E(n/,R)], Expected sample size proportion [E(n/,R)/n], probability for avoiding the second sample saved for the proposed estimator are derived. Numerical results and conclusions are established when the consider estimator (PTDSSE) are testimator of level of significance . Comparisons between the proposed estimator with the classical and the existing estimators were curried out to show the usefulness of the proposed estimator.