Estimating the Shape Parameter for the Power Function Distribution through Shrinkage Technique

Abbas Najim Salman, Alaa M. Hamad

Abstract: In this paper a recommended method based on shrinkage estimation technique has been implemented to estimate the shape parameter () of the power function distribution. The proposed approach will be involving the optimal region of prior estimation with new constant weight factor as well as including all the required statistical process. The statistical analyzing of the pattern behavior of the proposed estimator, equations of bias, mean squared error in addition to the relative efficiency expressions of the mentioned estimator were derived. The obtained outcomes were depending on the suggested data and including all of the analytical expressions.

Keywords: Power Function Distribution, Single Stage Shrinkage Estimator, Prior Knowledge, Pretest region, Bias Ratio, Mean Squared Error, Relative Efficiency