Stratified Unified Ranked Set Sampling with Perfect Ranking
Abstract
In this paper, a new modified ranked set sampling method is suggested, which is called stratified unified ranked set sampling (SURSS), for estimating the population mean. Then, we compare the efficiency of the empirical mean estimator based on the proposed sampling method with simple random sampling (SRS), stratified simple random sampling (SSRS) and stratified ranked set sampling (SRSS) via a simulation under three symmetric distributions: standard normal, uniform, and Student’s t. The simulation results indicate that the estimator based on SURSS with perfect ranking is unbiased and more efficient than competitors based on SRS, SSRS, and SRSS for symmetric distributions. Keywords : simple random sampling ; ranked set sampling ; unified ranked set sampling ; stratified unified ranked set samplingReferences
Al-Omari, A.I., & Bouza, C.N. (2014). Review of Ranked Set Sampling: Modifications and Applications. Revista Investigacion Operacional, 35(3), 215-235.
Dell, T.R., & Clutter, J.L. (1972). Ranked Set Sampling Theory with Order Statistics Background. Biometrics, 28, 545–555.
Matthews, M.J. & Wolfe, D.A. (2017). Unified Ranked Sampling. Statistics & Probability Letters, 112(C), 173–178.
McIntype, G.A. (1952). A Method of Unbiased Selective Sampling Using Ranked Sets. Australian Journal of Agricultural Research, 3(4), 385-390.
Samawi, H. M. (1996). Stratified ranked set sample, Pakistan Journal of Statistics, 12(1), 9-16.
Takahasi, K., & 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.
Zamanzade, E. (2014). Unified Ranked Set Sampling. Retrieved August 1,2019, from https://arxiv.org/vc/arxiv/papers/1411/1411.1351v1.pdf
Dell, T.R., & Clutter, J.L. (1972). Ranked Set Sampling Theory with Order Statistics Background. Biometrics, 28, 545–555.
Matthews, M.J. & Wolfe, D.A. (2017). Unified Ranked Sampling. Statistics & Probability Letters, 112(C), 173–178.
McIntype, G.A. (1952). A Method of Unbiased Selective Sampling Using Ranked Sets. Australian Journal of Agricultural Research, 3(4), 385-390.
Samawi, H. M. (1996). Stratified ranked set sample, Pakistan Journal of Statistics, 12(1), 9-16.
Takahasi, K., & 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.
Zamanzade, E. (2014). Unified Ranked Set Sampling. Retrieved August 1,2019, from https://arxiv.org/vc/arxiv/papers/1411/1411.1351v1.pdf
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Published
2020-09-01
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Research Article
