A Refinement of Ratio Estimation in Ranked Set Sampling and Stratified Ranked Set Sampling Approaches

Authors

DOI:

https://doi.org/10.21015/vtm.v12i1.1619

Abstract

Estimation of population mean is a persistent subject issue in sampling surveys and many discrete efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this an improved version of ratio estimator are presented in this paper under the ranked set sampling scheme and stratified ranked set sampling scheme. Comparison amongst estimators is made in terms of Mean Square Errors ( ) and Percentage Relative Efficiencies ( ). The expression for  of the proposed estimator is pinned-down to first order of approximations. It turns out from both simulation studies as well as real data set that the proposed estimator dominates its existing counterpart estimators.

References

Ali, A., Butt, M. M., & Zubair, M. (2022). Generalized chain regression-cum-chain ratio estimator for population mean under stratified extreme-cum-median ranked set sampling. Mathematical Problems in Engineering, 2022, 1–13.

Amiri, S., Jafari Jozani, M., & Modarres, R. (2018). Randomly selected order statistics in ranked set sampling: A less expensive comparable alternative to simple random sampling. Environmental and Ecological Statistics, 25, 237–256.

Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (2008). A first course in order statistics. SIAM.

Audu, A., Ishaq, O., & James, T. (2017). Ratio and product estimators: New strategies with unknown weight for finite population. Edited Proceedings of Nigeria Statistical Society, 1, 83–86.

Bhushan, S., Kumar, A., Shahab, S., Lone, S. A., Akhtar, M. T., et al. (2022). On efficient estimation of the population mean under stratified ranked set sampling. Journal of Mathematics, 2022.

Kadilar, C., & Cingi, H. (2003). Ratio estimators in stratified random sampling. Biometrical Journal, 45(2), 218–225.

Kadilar, C., Unyazici, Y., & Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50, 301–309.

Khan, L., & Shabbir, J. (2016). Improved ratio-type estimators of population mean in ranked set sampling using two concomitant variables. Pakistan Journal of Statistics and Operation Research, pp. 507–518.

Khan, L., Shabbir, J., & Khalil, A. (2019). A new class of regression cum ratio estimators of population mean in ranked set sampling. Life Cycle Reliability and Safety Engineering, 8, 201–204.

Koçyiğit, E. G., & Rather, K. U. I. (2023). The new sub-regression type estimator in ranked set sampling. Journal of Statistical Theory and Practice, 17(2), 27.

Lakhkar, K., & Shabbir, J. (2016). A class of hartley-ross type unbiased estimators for population mean using ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 45(3), 917–928.

Lakhkar, K., Shabbir, J., & Gupta, S. (2016). Unbiased ratio estimators of the mean in stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 46(6), 1151–1158.

Lynne Stokes, S. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods, 6(12), 1207–1211.

Mandowara, V., & Mehta, N. (2014). Modified ratio estimators using stratified ranked set sampling. Hacettepe Journal of Mathematics and Statistics, 43(3), 461–471.

McIntyre, G. (1952). A method for unbiased selective sampling, using ranked sets. Australian journal of agricultural research, 3(4), 385–390.

Patil, G. (2006). Ranked set sampling. Encyclopedia of environmetrics.

Samawi, H. M., & Muttlak, H. A. (1996). Estimation of ratio using rank set sampling. Biometrical Journal, 38(6), 753–764.

Singh, S. (2003). Advanced Sampling Theory With Applications: How Michael"" Selected"" Amy, Vol. 2, Springer Science & Business Media.

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), 1–31.

Valliant, R., Dorfman, A. H., & Royall, R. M. (2000). Finite population sampling and inference: a prediction approach, number 04; QA276. 6, V3., John Wiley New York.

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Published

2024-03-06

How to Cite

khan, lakhkar, javid shabbir, Qazi Ubaid, & Taj Farin Khan. (2024). A Refinement of Ratio Estimation in Ranked Set Sampling and Stratified Ranked Set Sampling Approaches. VFAST Transactions on Mathematics, 12(1), 30–45. https://doi.org/10.21015/vtm.v12i1.1619