Pretest Single Stage Shrinkage Estimator for the Shape Parameter of the Power Function Distribution

Prof.Abbas Najim Salman; Alaa M. Hamad; Ahmed I.Abdul-Nabi

doi:https://doi.org/10.14445/22315373/IJMTT-V36P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 36 | Number 1 | Year 2016 | Article Id. IJMTT-V36P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V36P506

Pretest Single Stage Shrinkage Estimator for the Shape Parameter of the Power Function Distribution

Prof.Abbas Najim Salman, Alaa M. Hamad, Ahmed I.Abdul-Nabi

Citation :

Prof.Abbas Najim Salman, Alaa M. Hamad, Ahmed I.Abdul-Nabi, "Pretest Single Stage Shrinkage Estimator for the Shape Parameter of the Power Function Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 36, no. 1, pp. 56-59, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V36P506

Abstract

This paper focuses on the estimation the shape parameter (∞) of power function distribution if a prior knowledge (∞0) is available about the shape parameter as the initial value and when the scale parameter is known (θ=1) via pretest single stage shrinkage estimator (SSSE) andproposed an optimal acceptable Region (R) for testing this prior knowledge. Expressions of the Bias, Mean Squared Error [MSE(.)] and Relative Efficiency [R.EFF(.)]for the proposed estimator were derived. Numerical results about behavior performance of considered estimator are discussed via study the mentioned expressions. These numerical results displayed in annexed tables. Comparisons between the proposed estimator and the classical estimator as well as with some earlier studies were made to show the effectiveness and usefulness of the considered estimator.

Keywords

Power Function Distribution, Single Stage Shrinkage Estimator, Prior Knolwledge, pre test region, Bias Ratio, Mean Squared Error and Relative Efficiency.

References

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