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Sains Malaysiana 37(1) : 95-99 (2008)
Two Stage Ranked Set Sampling for Estimating the Population Median (Pensampelan Set Terpangkat Dua Tahap untuk Penganggaran Median Populasi)
Abdul Aziz Jemain, Amer Al-Omari & Kamarulzaman Ibrahim School of Mathematical Sciences Faculty of Science and Technology, University Kebangsaan Malaysia 43600 UKM Bangi, Selangor D.E., Malaysia
Received: 12 April 2007 / Accepted: 29 June 2007
ABSTRACT
McIntyre was the first to suggest ranked set sampling (RSS) method for estimating the population mean. In this paper, we modify RSS to come up with new sampling method, namely, two stage ranked set sampling (TSRSS) for samples of size
Keywords: Ranked set sampling; simple random sampling; two stage ranked set sampling.
ABSTRAK
McIntyre mula memperkenalkan kaedah pensampelan set terpangkat (RSS) untuk menganggar min populasi. Dalam kertas ini, kami mengubahsuai kaedah RSS supaya mendapat kaedah yang baru iaitu pensampelan set terpangkat dua tahap untuk sampel bersaiz
Kata kunci: Pensampelan set terpangkat; pensampelan rawak ringkas; pensampelan set terpangkat dua tahap
RUJUKAN/REFERENCES
Al-Saleh, M.F. & Al-Kadiri, M.A. 2000. Double ranked set sampling. Statistics and Probability Letters 48(2): 205-212. Al-Saleh, M.F. & Al-Omari, A. I. 2002. Multistage ranked set sampling. Journal of Statistical Planning and Inference 102(2): 273-286. Jemain, A.A. & Al-Omari, A.I. 2006a. Double percentile ranked set samples for estimating the population mean. Advances and Applications in Statistics 6(3): 261-276. Jemain, A. A. & Al-Omari, A. I. 2006b. Multistage median ranked set samples for estimating the population mean. Pakistan Journal of Statistics 22(3): 195-207. Jemain, A.A., Al-Omari, A.I. & Ibrahim, K. 2007. Multistage median ranked set sampling for estimating the population median. Journal of Mathematics and Statistics 3(2): 58-64. McIntyre, G. A. 1952. A method for unbiased selective sampling using ranked sets. Australian Journal. Agricultural Research 3: 385-390. Mode, N., Consequest, L. & Marker, D. 1999. Ranked set sampling for ecological research: accounting for the total costs of sampling. Environmetrics 10: 179-194. Muttlak, H.A., 1997. Median ranked set sampling. Journal of Applied Statistical Sciences 6(4): 245-255. Muttlak, H. A. 2003a. Investigating the use of quartile ranked set samples for estimating the population mean. Journal of Applied Mathematics and Computation 146: 437- 443. Muttlak, H. A. 2003b. Modified ranked set sampling methods. Pakistan Journal of Statistics 315-323. Samawi, H. Abu-Dayyeh, W. & Ahmed, S. 1996. Extreme ranked set sampling, The Biometrical Journal 30: 577-586. 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.
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. The TSRSS is suggested for estimating the population median in order to increase the efficiency of the estimators. The TSRSS was compared to the simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS), median ranked set sampling (MRSS) and balance groups ranked set sampling (BGRSS) methods. It is found that, TSRSS gives an unbiased estimator of the population median of symmetric distributions and it is more efficient than SRS. Also, it is more efficient than RSS, ERSS, MRSS and BGRSS based on the same number of measured units. For asymmetric distributions considered in this study, TSRSS has a small bias and smaller variance than SRS, RSS, ERSS, MRSS and BGRSS methods.
