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An Efficient Class of Estimators for the Finite Population Mean in Ranked Set Sampling
Department of Statistics Government College Toru, Khyber Pukhtunkhwa, Pakistan
Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
- 1 Department of Statistics Government College Toru, Khyber Pukhtunkhwa, Pakistan
- 2 Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
Open Journal of Statistics·Volume 06 (2016)·Pages 426–435·Published 8 June 2016·DOI10.4236/ojs.2016.63038
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Abstract
In this paper, we propose a class of estimators for estimating the finite population mean of the study variable under Ranked Set Sampling (RSS) when population mean of the auxiliary variable is known. The bias and Mean Squared Error (MSE) of the proposed class of estimators are obtained to first degree of approximation. It is identified that the proposed class of estimators is more efficient as compared to [1] estimator and several other estimators. A simulation study is carried out to judge the performances of the estimators.
KeywordsRanked Set SamplingAuxiliary VariableBiasMean Squared ErrorRelative Efficiency
- Singh, H.P., Tailor, R. and Singh, S. (2014) General Procedure for Estimating the Population Mean Using Ranked Set Sampling. Journal of Statistical Computation and Simulation, 84, 931-945. http://dx.doi.org/10.1080/00949655.2012.733395
- Mclntyre, G. (1952) A Method for Unbiased Selective Sampling, Using Ranked Sets. Crop and Pasture Science, 3, 385-390. http://dx.doi.org/10.1071/AR9520385
- Takahasi, K. and Wakimoto, K. (1968) On Unbiased Estimates of the Population Mean Based on the Sample Stratified by Means of Ordering. Annals of the Institute of Statistical Mathematics, 20, 1-31. http://dx.doi.org/10.1007/BF02911622
- Samawi, H.M. and Muttlak, M.A. (1996) Estimation of Ratio Using Ranked Set Sampling. Biometrical Journal, 38, 753-764. http://dx.doi.org/10.1002/bimj.4710380616
- Dell, T. and Clutter, J. (1972) Ranked Set Sampling Theory with Order Statistics Background. Biometrics, 545-555. http://dx.doi.org/10.2307/2556166
- Stokes, S.L. (1977) Ranked Set Sampling with Concomitant Variables. Communication in Statistics: Theory and Methods, 6, 1207-1211. http://dx.doi.org/10.1080/03610927708827563
- Khan, L. and Shabbir, J. (2015) A Class of Hartley-Ross Type Unbiased Estimators for Population Mean Using Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics. http://dx.doi.org/10.15672/HJMS.20156210579
- Khan, L. and Shabbir, J. (2016) Hartley-Ross Type Unbiased Estimators Using Ranked Set Sampling and Stratified Ranked Set Sampling. North Carolina Journal of Mathematics and Statistics, 2, 10-22.
- Kadilar, C., Unyazici, Y. and Cingi, H. (2009) Ratio Estimator for the Population Mean Using Ranked Set Sampling. Statistical Papers, 50, 301-309. http://dx.doi.org/10.1007/s00362-007-0079-y
- Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (2012) A First Course in Order Statistics. Vol. 54, Siam.
- Searls, D.T. (1964) The Utilization of a Known Coefficient of Variation in the Estimation Procedure. Journal of the American Statistical Association, 59, 1225-1226. http://dx.doi.org/10.1080/01621459.1964.10480765
- Khoshnevisan, M., Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. (2007) A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s). Far East Journal of Theoretical Statistics, 22, 181-191.
- Lohr, S. (1999) Sampling: Design and Analysis. Duxbury Press, Boston.