Estimation of the Population Mean Using Paired Ranked Set Sampling
Affiliation(s)
1 Department of Studies in Statistics, University of Mysore, Mysore, India. 2 All India Institute of Speech and Hearing, Mysore, India.
1 Department of Studies in Statistics, University of Mysore, Mysore, India. 2 All India Institute of Speech and Hearing, Mysore, India.
ABSTRACT
In the situation where the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to SRS. In this paper we propose an estimator of the population mean using paired ranked set sampling (RSS) method. The proposed estimator is an unbiased estimator of the population mean when the set size is even. In case of odd set size the estimator is unbiased when the underlying distribution is symmetric. It is shown that the proposed estimator is more efficient than its counterpart SRS method for all distributions considered in this study.
In the situation where the sampling units in a study can be easily ranked than quantified, the ranked set sampling methods are found to be more efficient and cost effective as compared to SRS. In this paper we propose an estimator of the population mean using paired ranked set sampling (RSS) method. The proposed estimator is an unbiased estimator of the population mean when the set size is even. In case of odd set size the estimator is unbiased when the underlying distribution is symmetric. It is shown that the proposed estimator is more efficient than its counterpart SRS method for all distributions considered in this study.
KEYWORDS
Ranked Set Sampling, Paired Ranked Set Sampling, Population Mean, Relative Efficiency, Errors in Ranking
Ranked Set Sampling, Paired Ranked Set Sampling, Population Mean, Relative Efficiency, Errors in Ranking
Cite this paper
Biradar, B. and Santosha, C. (2015) Estimation of the Population Mean Using Paired Ranked Set Sampling. Open Journal of Statistics, 5, 97-103. doi: 10.4236/ojs.2015.52012.
Biradar, B. and Santosha, C. (2015) Estimation of the Population Mean Using Paired Ranked Set Sampling. Open Journal of Statistics, 5, 97-103. doi: 10.4236/ojs.2015.52012.
References
[1] McIntyre, G.A. (1952) A Method for Unbiased Selective Sampling Using Ranked Sets. Australian Journal of Agricultural Research, 3,385-390.
http://dx.doi.org/10.1071/AR9520385 [2] McIntyre, G.A. (2005) A Method for Unbiased Selective Sampling, Using Ranked Sets. The American Statistician, 59, 230-232. Originally Appeared in Australian Journal of Agricultural Research, 3, 385-390.
http://dx.doi.org/10.1198/000313005X54180
http://dx.doi.org/10.1071/AR9520385 [3] Dell, T.R. and Clutter, J.L. (1972) Ranked Set Sampling Theory with Order Statistics Background. Biometrics, 28, 545-555.
http://dx.doi.org/10.2307/2556166 [4] 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 [5] Samwi, H., Ahmad, M. and Abu-Dayyeh, W. (1996) Estimating the Population Mean Using Extreme Ranked Set Sampling. Biometrical Journal, 38, 577-586.
http://dx.doi.org/10.1002/bimj.4710380506 [6] Muttlak, H.A. (1997) Median Ranked Set Sampling. Journal of Applied Statistical Sciences, 6, 245-255. [7] Muttlak, H.A. (2003) Investigating the Use of Quartile Ranked Set Samples for Estimating the Population Mean. Journal of Applied Mathematics and Computation, 146, 437-443.
http://dx.doi.org/10.1016/S0096-3003(02)00595-7 [8] Jemain, A.A., Al-Omari, A. and Ibrahim, K. (2008) Some Variations of Ranked Set Sampling. Electronic Journal of Applied Statistical Analysis, 1, 1-15. [9] Biradar, B.S. and Santosha, C.D. (2015) Estimation of the Population Mean Based on Extrmemes Ranked Set Sampling. American Journal of Mathematics and Statistics, 5, 32-36. [10] Wolfe, D.A. (2004) Ranked Set Sampling: An Approach to More Efficient Data Collection. Statistical Science, 19, 636-643.
http://dx.doi.org/10.1214/088342304000000369 [11] Wolfe, D.A. (2010) Ranked Set Sampling. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 460-466.
http://dx.doi.org/10.1002/wics.92 [12] Chen, Z.H., Bai, Z.D. and Sinha, B.K. (2004) Ranked Set Sampling: Theory and Applications. Springer, New York.
http://dx.doi.org/10.1007/978-0-387-21664-5 [13] Balci, S., Akkaya, A.D. and Ulgen, B.E. (2013) Modified Maximum Likelihood Estimators Using Ranked Set Sampling. Journal of Computational and Applied Mathematics, 238,171-179.
http://dx.doi.org/10.1016/j.cam.2012.08.030 [14] Arnold, B.C., Balkrishna, N. and Nagaraj, H.N. (1992) A First Course in Order Statistics. John Wiley and Sons, New York. [15] David, H.A. and Levine, D.N. (1972) Ranked Set Sampling in the Presence of Judgment Ranking Error. Biometrics, 28, 553-555.
[1] McIntyre, G.A. (1952) A Method for Unbiased Selective Sampling Using Ranked Sets. Australian Journal of Agricultural Research, 3,385-390.
http://dx.doi.org/10.1071/AR9520385 [2] McIntyre, G.A. (2005) A Method for Unbiased Selective Sampling, Using Ranked Sets. The American Statistician, 59, 230-232. Originally Appeared in Australian Journal of Agricultural Research, 3, 385-390.
http://dx.doi.org/10.1198/000313005X54180
http://dx.doi.org/10.1071/AR9520385 [3] Dell, T.R. and Clutter, J.L. (1972) Ranked Set Sampling Theory with Order Statistics Background. Biometrics, 28, 545-555.
http://dx.doi.org/10.2307/2556166 [4] 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 [5] Samwi, H., Ahmad, M. and Abu-Dayyeh, W. (1996) Estimating the Population Mean Using Extreme Ranked Set Sampling. Biometrical Journal, 38, 577-586.
http://dx.doi.org/10.1002/bimj.4710380506 [6] Muttlak, H.A. (1997) Median Ranked Set Sampling. Journal of Applied Statistical Sciences, 6, 245-255. [7] Muttlak, H.A. (2003) Investigating the Use of Quartile Ranked Set Samples for Estimating the Population Mean. Journal of Applied Mathematics and Computation, 146, 437-443.
http://dx.doi.org/10.1016/S0096-3003(02)00595-7 [8] Jemain, A.A., Al-Omari, A. and Ibrahim, K. (2008) Some Variations of Ranked Set Sampling. Electronic Journal of Applied Statistical Analysis, 1, 1-15. [9] Biradar, B.S. and Santosha, C.D. (2015) Estimation of the Population Mean Based on Extrmemes Ranked Set Sampling. American Journal of Mathematics and Statistics, 5, 32-36. [10] Wolfe, D.A. (2004) Ranked Set Sampling: An Approach to More Efficient Data Collection. Statistical Science, 19, 636-643.
http://dx.doi.org/10.1214/088342304000000369 [11] Wolfe, D.A. (2010) Ranked Set Sampling. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 460-466.
http://dx.doi.org/10.1002/wics.92 [12] Chen, Z.H., Bai, Z.D. and Sinha, B.K. (2004) Ranked Set Sampling: Theory and Applications. Springer, New York.
http://dx.doi.org/10.1007/978-0-387-21664-5 [13] Balci, S., Akkaya, A.D. and Ulgen, B.E. (2013) Modified Maximum Likelihood Estimators Using Ranked Set Sampling. Journal of Computational and Applied Mathematics, 238,171-179.
http://dx.doi.org/10.1016/j.cam.2012.08.030 [14] Arnold, B.C., Balkrishna, N. and Nagaraj, H.N. (1992) A First Course in Order Statistics. John Wiley and Sons, New York. [15] David, H.A. and Levine, D.N. (1972) Ranked Set Sampling in the Presence of Judgment Ranking Error. Biometrics, 28, 553-555.