Generalized Class of Some Novel Estimators under Ranked Set Sampling
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Keywords:
: Study variable; Auxiliary variable; Bias, Mean square error; Ranked set samplingAbstract
In this paper, mean estimators under ranked set sampling are reviewed. In this paper, we have also presented some improved novel classes of estimators for estimating the population mean using auxiliary variable under ranked set sampling. We have derived the expressions for bias and mean squared error of the proposed estimators up to the first order of approximation and the proposed classes of estimators are found to be more efficient than the other estimators in this study. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by empirical study.
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References
Al-Hadhrami, S.A. (2009). Ratio type estimators of the population mean based on ranked set sampling. Int. J. Math. Comput. Phys. Electr. Comput. Eng., 3(11), 896-900.
Al-Omari, A.I., Jemain, A.A. and Ibrahim, K. (2009). New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Revista Investig. Oper., 30(2), 97-108.
Bhushan, S. and Kumar, A. (2020a). On optimal classes of estimators under ranked set sampling. Commun. Stat. Theory Methods, 51(8), 2610-2639.
Bhushan, S. and Kumar, A. (2020b). Log type estimators of population mean under ranked set sampling. Predictive Analyt. Statist. Big Data: Concepts Model., 28, 47-74.
Bhushan, S. and Kumar, A. (2021). Novel log type class of estimators under ranked set sampling. Sankhya B. https://doi.org/10.1007/s13571-021-00265-y
Bhushan, S., Kumar, A. and Lone, S.A. (2022). On some novel classes of estimators using RSS. Alexandria Engineering Journal, 61, 5465-5474.
Brar, S.S. and Malik, S.C. (2014). Generalized ratio type estimator of population mean under ranked set sampling. Int. J. Stat. Reliab. Eng., 1(2), 179-193.
Bouza, C.N. and Al-Omari, A.B. (2014). Review of Ranked Set Sampling: Modifications and Applications. Revista Investigacion Operacional, 35(3), 215-240.
Bouza, C.N., Singh, P., and Singh, R. (2018). Ranked set sampling and optional scrambling randomized response modeling. Revista Investigacion Operacional, 39(1), 100-107.
Dell, T.R. and Clutter, J.L. (1972). Ranked set sampling theory with order statistics background. Biometrics, 28, 545-555.
[Missing author?] (Year not specified). Simple random sampling in the estimation of the mean and the ratio. Journal of Statistics and Management Systems, 9(2), 459-472.
Jeelani, M.I., Mir, S.A. and Pukhta, M.S. (2014). A class of modified ratio estimators using linear combination of quartile deviation and median of auxiliary variable under ranked set sampling. Univ. J. Appl. Math., 2(6), 245-249.
Jeelani, M.I., Bouza, C.N. and Sharma, M. (2017). Modified ratio estimator under ranked set sampling. Revista Investig. Oper., 38(1), 103-106.
Kadilar, C., Unyazici, Y. and Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Stat. Pap., 50, 301-309.
Khan, L. and Shabbir, J. (2016). An efficient class of estimators of finite population mean under ranked set sampling. Open J. Stat., 6, 426-435.
Khan, Z. and Ismail, M. (2019). Ratio-type estimator of population mean based on ranked set sampling. Pakistan J. Stat. Oper. Res., 15(2), 445-449.
McIntyre, G.A. (1952). A method of unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3, 385-390.
Mandowara, V.L. and Mehta, N. (2013). Efficient generalized ratio-product type estimators for finite population mean with ranked set sampling. Austr. J. Stat., 42(3), 137-148.
Mehta, N. and Mandowara, V.L. (2016). A modified ratio-cum-product estimator of finite population mean using ranked set sampling. Commun. Stat. Theory Methods, 45(2), 267-276.
Mehta, V., Singh, H.P. and Pal, S.K. (2020). A general procedure for estimating finite population mean using ranked set sampling. Revista Investig. Oper., 41(1), 80-92.
Saini, M. and Kumar, A. (2016). Ratio estimators for the finite population mean under simple random sampling and ranked set sampling. Int. J. Syst. Assur. Eng. Manage., 8(2), 488-492.
Samawi, H.M. and Muttlak, H.A. (1996). Estimation of ratio using ranked set sampling. Biometr. J., 38, 753–764.
Singh, H.P., Tailor, R. and Singh, S. (2014). General procedure for estimating the population mean using ranked set sampling. J. Stat. Comput. Simul., 84(5), 931-945.
Takahasi, K. and Wakimoto, K. (1968). On unbiased estimates of the population mean based on the sample stratified using ordering. Annals of Institute of Statistical Mathematics, 20, 1-31.
Yu, L.H. and Lam, K. (1997). Regression estimator in ranked set sampling. Biometrics, 53, 1070-1080.