Computing the population mean on the use of auxiliary information under ranked set sampling

Document Type : Article


Department of Mathematics & Computing, Indian Institute of Technology Dhanbad, Dhanbad-826004, India


In this manuscript, a generalized class of estimators has been developed for estimating a finite population means in ranked set sampling scheme. The expressions for bias and mean square error (MSE) of the proposed class of estimators have been derived up to the first order of approximation. Some estimators are shown to be a member of the proposed class. The proposed class of estimators has been compared through the MSE criterion over the other existing member estimators of the proposed class of estimators. The theoretical conditions are obtained under which the proposed class of estimators has performed better. Efficiency comparisons, empirical study, and simulation study also delineate the soundness of our proposed generalized class of the estimators under ranked set sampling (RSS).


Main Subjects

1. Cochran, G. "Some properties of estimators based on sampling scheme with varying probabilities", Austrian Journal of Statistics, 17, pp. 22-28 (1940).
2. Robson, D.S. "Application of multivariate polykays to the theory of unbiased ratio-type estimation", Journal of the American Statistical Association, 52, pp. 511- 522 (1957).
3. Murthy, M.N. "Product method of estimation", Sankhya A, 26, pp. 69-74 (1964).
4. McIntyre, G.A. "A method for unbiased selective sampling using ranked sets", Crop and Pasture Science, 3, pp. 385-390 (1952).
5. Takahasi, K. and Wakimoto, K. "On unbiased estimates of the population mean based on the sample stratified by means of ordering", Annals of the Institute of Statistical Mathematics, 20, pp. 1-31 (1968).
6. Dell, T.R. and Clutter, J.L. "Ranked set sampling theory with order statistics background", Biometrics, 28, pp. 545-555 (1972).
7. Stokes, L. "Ranked set sampling with concomitant variables", Communications in Statistics-Theory and Methods, 6, pp. 1207-1211 (1977).
8. Samawi, H.M. and Muttlak, H.A. "Estimation of ratio using rank set sampling", Biometrical Journal, 38, pp. 753-764 (1996).
9. Al-Saleh, M.F. and Al-Omari, A.I. "Multistage ranked set sampling", Journal of Statistical Planning and Inference, 102(2), pp. 273-286 (2002).
10. Bouza, C.N. "Ranked set sub sampling the nonresponse strata for estimating the difference of means", Biometrical Journal: Journal of Mathematical Methods in Biosciences, 44(7), pp. 903-915 (2002).
11. Wolfe, D.A. "Ranked set sampling: an approach to more efficient data collection", Statistical Science, 19, pp. 636-643 (2004).
12. Al-Omari, A.I., Jaber, K., and Al-Omari, A. "Modified ratio-type estimators of the mean using extreme ranked set sampling", Journal of Mathematics and Statistics, 4(3), pp. 150-155 (2008).
13. Al-Omari, A.I. "Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling", Statistics & Probability Letters, 82(11), pp. 1883-1890 (2012).
14. Mandowara, V.L. and Mehta, N. "Efficient generalized ratio-product type estimators for finite population mean with ranked set sampling", Austrian Journal of Statistics, 42, pp. 137-148 (2013).
15. Al-Omari, A.I. and Gupta, S. "Double quartile ranked set sampling for estimating population ratio using auxiliary information", Pakistan Journal of Statistics, 30(4), pp. 513-535 (2014).
16. Pal, S.K. and Singh, H.P. "Estimation of finite population mean using auxiliary information in systematic sampling", International Journal of System Assurance Engineering and Management, 8(2), pp. 1392-1398 (2017).
17. Vishwakarma, G.K., Zeeshan, S.M., and Bouza- Herrera, C.N. "Ratio and product type exponential estimators for population mean using ranked set sampling", Revista Investigacion Operacional, 38(3), pp. 266-271 (2017).
18. Jeelani, M.I., Bouza, C.N., and Sharma, M. "Modified ratio estimator under rank set sampling", Investigaci on Operacional, 38(1), pp. 101-104 (2017).
19. Noor Ul Amin, M., Arif, F., and Hanif, M. "A new scheme using the ranked sets", Journal of Statistics and Management Systems, 21(8), pp. 1565-1573 (2018).
20. Al-Omari, A.I. and Haq, A. "A new sampling method for estimating the population mean", Journal of Statistical Computation and Simulation, 89(11), pp. 1973- 1985 (2019).
21. Saini, M. and Kumar, A. "Ratio estimators using stratified random sampling and stratified ranked set sampling", Life Cycle Reliability and Safety Engineering, 8(1), pp. 85-89 (2019).
22. Singh, A. and Vishwakarma, G.K. "Improved predictive estimation for mean using the Searls technique under ranked set sampling", Communications in Statistics-Theory and Methods, 50(9), pp. 2015-2038 (2021).
23. Ahmed, S., Shabbir, J., and Gupta, S. "Predictive estimation of population mean in ranked set sampling", Revstat Statistical Journal, 17(4), pp. 551-562 (2019).
24. Mehta, V., Singh, H.P., and Pal, S.K. "A general procedure for estimating finite population mean using ranked set sampling", Investigacion Operacional, 41(1), pp. 80-93 (2020).
25. Koyuncu, N. and Al-Omari, A.I. "Generalized  robustregression- type estimators under different ranked set sampling", Mathematical Sciences, 15(1), pp. 29-40 (2021).
26. Vishwakarma, G.K. and Singh, A. "Generalized estimator for computation of population mean under neutrosophic ranked set technique: An application to solar energy data", Computational and Applied Mathematics, 41(144), 01820 (2022).
27. Vishwakarma, G.K. and Singh, A. "Computing the effect of measurement errors on ranked set sampling estimators of the population mean", Concurrency and Computation: Practice and Experience, 34(27), e7333 (2022).
28. Bouza, C.N. "Ranked set sampling for the product estimator", Revista Investigacion Operacional, 29(3), pp. 201-206 (2008).
29. Upadhyaya, L.N. and Singh, H.P. "Use of transformed auxiliary variable in estimating the finite population mean", Biometrical Journal, 41, pp. 627-636 (1999).
30. Sisodia, B.V.S. and Dwivedi, V.K. "A modified ratio estimator using coefficient of variation of auxiliary variable", Journal of Indian Society Agricultural Statistics, 33, pp. 13-18 (1981).
31. Singh, S., Advanced Sampling Theory with Applications, Volume II, Kluwer Academic Publishers (2003).
32. R Studio: RSSampling/RSSampling.pdf, (2022).
Volume 30, Issue 6
Transactions on Computer Science & Engineering and Electrical Engineering (D)
November and December 2023
Pages 2083-2097