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Abstract
In this study, we introduce a novel approach for estimating the mean of a finite population using Ranked Set Sampling (RSS), termed the generalized exponential ratio estimator. We derive expressions for the bias and mean squared error (MSE) of the proposed estimator up to the first order of approximation. To assess its performance, we conduct a thorough theoretical and numerical analysis using simulated and real data. Our results demonstrate that the generalized exponential ratio estimator outperforms both the classical ratio estimator and the estimator proposed by Kadilar et al. (2009) under RSS, highlighting its superior efficiency.
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References
-
Bahl, S., & Tuteja, R. K. (1991). Ratio and product type exponential estimator. Journal of Information and Optimization Sciences, 12:159–163. https://doi.org/10.1080/02522667.1991.10699058
Bouza, C. N. 2013. Ranked set sampling for the product estimator. Investigación Operacional 29(3):201-206.
Bhushan, S., & Kumar, A. (2022). Novel log type class of estimators under ranked set sampling. Sankhya B 84(1):421–447.
Dell, T. R., & Clutter, J. L. (1972). Ranked set sampling theory with order statistics background. Biometrics, 28:545–555. https://doi.org/10.2307/2556166
Kadilar, C., & Cingi, H. (2003). Ratio estimators in stratified random sampling. Biometrical Journal, 45:218–225. https://doi.org/10.1002/bimj.200390007
Kadilar, C., & Cingi, H. (2005). A new ratio estimator in stratified random sampling. Communications in Statistics: Theory and Methods, 34: 597–602. https://doi.org/10.1081/STA-200052156
Kadilar, C., Unyazici, Y., & Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50: 301–309. https://doi.org/10.1007/s00362-007-0079-y
Kadilar, G. O. (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15:207–214. DOI: 10.22237/jmasm/1478002380
Mahdizadeh, M., & Zamanzade. E. (2022). On interval estimation of the population mean in ranked set
sampling. Commun Stat Simul Comput 51(5):2747–2768.
McIntyre, G. A. (1952). A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research, 3: 385–390. http://dx.doi.org/10.1071/AR9520385
Muttlak, H. A., & Mc Donald, L. L. (1990). Ranked set sampling with respect to concomitant variables and with size biased probability of selection. Communications in Statistics-Theory and Methods, 19(1), 205–219.
Ozturk, O. (2011). Sampling from partially rank-ordered sets. Environmental and Ecological Statistics 18(4):757–779.
Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics-Theory and Methods, 18:379–392. https://doi.org/10.1080/03610928908829905
Rather, K. U. I., & Kadilar, C. (2021). Exponential type estimator for The population mean under Ranked set sampling. Journal of Statistics: Advances in Theory and Applications, 25(1):1–12.
Rather, K. U. I., Kocyigit, E. G., Unal, C., & Jeelani, M. I. (2022). New exponential ratio estimator in Ranked set sampling. Pakistan Journal of Statistics and operation research, 18(2):403–409. https://doi.org/10.18187/pjsor.v18i2.3921
Samawi, H. M., & Muttlak, H. A., (1996). Estimation of ratio using rank set sampling. Biometrical Journal, 38:753–764. https://doi.org/10.1002/bimj.4710380616
Samawi, H. M., & Siam, M. I. (2003). Ratio estimation using stratified ranked set sample. Metron, 61:75–90.
Singh, R., Chauhan, P., Sawan, N., & Smarandache, F. (2007). Improvement in estimating the population mean using exponential estimator in simple random sampling. International Journal of Statistics and Economics, 3(A09):13–18.
Singh, H.P., Tailor, R., & Singh, S. (2014). General procedure for estimating the population mean using ranked set sampling. Journal of Statistical Computation and Simulation 84(5): 931–945.
Yadav, S. K. (2015). Improved exponential ratio cum dual to ratio type estimator of population mean. International Journal of Applied and Computational Mathematics, 1(4): 89–598.
Yadav, S. K., & Shukla, A. K. (2014). Improved product cum dual to product estimator of population mean in stratified random sampling. Journal of Statistics Applications & Probability, 3(3): 363.