Improved of Stein-Type Estimator of the Variance of Normal Distribution via Shrinkage Estimation
Abbas Najim Salman1, Bayda Atiya Khalaf2, Haydar Sabeeh Kalash3
1Abbas N. Salman is a Professor in the Department of Mathematics, College of Education for pure Sciences / Ibn Al-Haithm -Baghdad University -Baghdad – Iraq.
2Bayda Atiya Khalaf is Lecturer in the Department of Mathematics, College of Education for Pure Sciences / Ibn Al-Haithm – Baghdad University – Baghdad – Iraq.
3Haydar Sabeeh Kalash is a Master of Electrical – Communication Engineer from University Technology Malaysia.
Manuscript received on May 09, 2014. | Revised Manuscript Received on May 20, 2014. | Manuscript published on May 20, 2014. | PP: 14-17 | Volume-2, Issue-6, May 2014. | Retrieval Number: F0470052614/2014©BEIESP
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© The Authors. Published By: Blue Eyes Intelligence Engineering & Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: This paper concerned with pre- test single stage shrinkage estimator for estimating the variance (σ2 ) of normal distribution N(μσ2), when a prior estimate (σo2 ) about (σ2 ) is available from the past experiences or similar cases as well as the mean is known (say μo) , by using Stein-type estimator , shrinkage weight factor ψ(.) and pre-test region R. Expressions for Bias , Mean Squared Error and Relative Efficiency of the proposed estimator are derived. Conclusions and numerical results are presented for Relative Efficiency and Bias Ratio. Comparisons were made with the existing estimators.
Keywords: Normal Distribution, Stein-Type Estimator, Single Stage Shrinkage Estimator, Prior Estimate, Bias Ratio, Mean Squared Error and Relative Efficiency.