Single Stage Shrinkage Estimator for the Shape Parameter of the Pareto Distribution

Abbas Najim Salman; Adel Abdulkadhim Hussein

doi:https://doi.org/10.14445/22315373/IJMTT-V35P521

International Journal of Mathematics Trends and Technology

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Volume 35 | Number 3 | Year 2016 | Article Id. IJMTT-V35P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V35P521

Single Stage Shrinkage Estimator for the Shape Parameter of the Pareto Distribution

Abbas Najim Salman, Adel Abdulkadhim Hussein

Abstract

In this paper, we employee single stage shrinkage estimator for estimate the shape parameter of the Pareto distribution when the scale parameter is known. The proposed estimator is shown to have a smaller mean squared error in a region around when comparison with the usual and existing estimators.

Keywords

Pareto Distribution, Shrinkage Estimation, Prior Guess, Pre Test Region, Bias, Mean Squared Error and Relative Efficiency.

References

[1] Al-Hemyari,Z.A., Khurshid, A and Al-Joboori, A. N.,(2009), On Thompson Type Estimators for the Mean of Normal Distribution, REVISTA INVESTIGACION OPERACIONAL J. Vol. 30, No.2,109-116.
[2] Al-Joboori, A.N., et al (2014), Single and Double Stage Shrinkage Estimators for the normal Mean with the Variance Cases, International Journal of statistic, Vol.(38),2,PP, 1127-1134.
[3] Al-Joboori, A.N., Khalef, B.A. and Hayder S.K., (2014), Improved of Stein-Type Estimator of the Variance of Normal Distribution via Shrinkage Estimation Technique, International Journal of Inventive Engineering and Science (IJIES), Vol.(2),6, PP.14-17.
[4] Al-Joboori, A.N. ,A.A. Hussein and M.A.Mohammd, (2011),On Significance Testimator in Pareto Distribution Via Shrinkage Technique, Journal of College of Enginnering.
[5] Casella, G., (2002), Shrinkage , In: Encyclopedia of Envirnmetrics, 4, 1992-1994 (Eds.A.H.EL.Shaarawi and w.w.Piegorsch), John Wiley :New York.
[6] Cirillo R., "The Economics of Vilfredo Pareto", Frank Case and Company Limited, London, (1979).
[7] Malik, H.J., (1970), Estimation of the Parameter of the Pareto Distribution, Metrika, Vol.15, pp. 126-132.
[8] Ord, J.K., (1975), Statistical Models for Personal income Distributions in Statistical 158, Dordrecht, Reidel.
[9] Mehta,J.S. and Srinivasan,R., (1971), "Estimation of the Mean by Shrinkage to a Point", J. Amer. Statist. Assoc., 66, p.86-90.
[10] Saleh, A.K.E., (2006), Theory of Preliminary Test and Stein-Type Estimators with Application, Wiley and Sons, NewYork.
[11] Rytgaard, M., (1990), Estimation in the Pareto Distribution, Astin Bulletin, Vol.20, No.2, pp.201-216.
[12] Rashid, H. A. and Al-Gazi, N. A. A., (2014), Bayes Estimators for the Shape Parameter of Pareto Distribution under Generalized Square Errors Loss Function, Mathematical Theory and Modeling, Vol. 4,No. 11. pp 20-32.
[13] Thompson, J.R., (1968), Some Shrinkage Techniques for Estimating the Mean, J. Amer. Statist. Assoc, Vol.63, pp.113-122.
[14] Prakash, G., Singh, D.C. and Singh, R.D., (2006), Some Test Estimator for the Scale Parameter of Classical Pareto Distribution., Journal of Statistical Research, Vol.40(2), pp.41-54.
[15] Singh, D.C., Prakash, G. and Singh, P., (2007), Shrinkage Testimators of the Shape Parameter of Pareto Distribution Using LINEX Loss Function, Communication in Statistics-Theory and Methods, Vol.36(4), pp.741-753.
[16] Singh, D.C., Singh, P. and Singh, P.R., (1996), Shrunken Estimators for the Scale Parameter of Classical Pareto Distribution, Microelectron Reliability, Vol.36(3), pp.435-439.

Citation :

Abbas Najim Salman, Adel Abdulkadhim Hussein, "Single Stage Shrinkage Estimator for the Shape Parameter of the Pareto Distribution," International Journal of Mathematics Trends and Technology (IJMTT), vol. 35, no. 3, pp. 156-162, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V35P521