Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T20:17:49.653Z Has data issue: false hasContentIssue false
  • English
  • Français

RATIO ESTIMATION OF THE POPULATION MEAN USING AUXILIARY INFORMATION UNDER THE OPTIMAL SAMPLING DESIGN

Published online by Cambridge University Press:  11 December 2020

Chunxian Long ,
Wangxue Chen Open the ORCID record for Wangxue Chen [Opens in a new window] ,
Rui Yang  and
Dongsen Yao
Chunxian Long
Affiliation:
Department of Mathematics and Statistics, Jishou University, Jishou416000, China E-mail: chenwangxue2015@163.com
Wangxue Chen
Affiliation:
Department of Mathematics and Statistics, Jishou University, Jishou416000, China E-mail: chenwangxue2015@163.com
Rui Yang
Affiliation:
Department of Mathematics and Statistics, Jishou University, Jishou416000, China E-mail: chenwangxue2015@163.com
Dongsen Yao
Affiliation:
Department of Mathematics and Statistics, Jishou University, Jishou416000, China E-mail: chenwangxue2015@163.com
Get access Rights & Permissions [Opens in a new window]

Abstract

Cost-effective sampling design is a problem of major concern in some experiments especially when the measurement of the characteristic of interest is costly or painful or time-consuming. In this article, we investigate ratio-type estimators of the population mean of the study variable, involving either the first or the third quartile of the auxiliary variable, using ranked set sampling (RSS) and extreme ranked set sampling (ERSS) schemes. The properties of the estimators are obtained. The estimators in RSS and ERSS are compared to their counterparts in simple random sampling (SRS) for normal data. The numerical results show that the estimators in RSS and ERSS are significantly more efficient than their counterparts in SRS.

Keywords

auxiliary variableextreme ranked set samplingranked set samplingratio estimator
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 449 - 460
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Al-Omari, A.I. (2012). Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling. Statistics and Probability Letters 82(11): 1883–1890.CrossRefGoogle Scholar
Chen, Z.H., Bai, Z.D., & Sinha, B.K. (2003). Ranked set sampling: theorem and applications. New York: Springer.Google Scholar
Chen, W.X., Xie, M.Y., & Wu, M. (2013). Parametric estimation for the scale parameter for scale distributions using moving extremes ranked set sampling. Statistics and Probability Letters 83(9): 2060–2066.CrossRefGoogle Scholar
Chen, W.X., Xie, M.Y., & Wu, M. (2016). Modified maximum likelihood estimator of scale parameter using moving extremes ranked set sampling. Communications in Statistics – Simulation and Computation 45(6): 2232–2240.CrossRefGoogle Scholar
Chen, W.X., Tian, Y., & Xie, M.Y. (2018). The global minimum variance unbiased estimator of the parameter for a truncated parameter family under the optimal ranked set sampling. Journal of Statistical Computation and Simulation 88(17): 3399–3414.CrossRefGoogle Scholar
Chen, W.X., Yang, R., Yao, D.S., & Long, C.X. (2019). Pareto parameters estimation using moving extremes ranked set sampling. Statistical Papers. https://doi.org/10.1007/s00362-019-01132-9.CrossRefGoogle Scholar
Cochran, W.G. (1997). Sampling technique, 3rd ed. New York: Wiley and Sons.Google Scholar
Kadilar, C. & Cingi, H. (2004). Ratio estimators in simple random sampling. Applied Mathematics and Computation 151(3): 893–902.CrossRefGoogle Scholar
McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked sets. Australian Journal of Agricultural Research 3(4): 385–390.CrossRefGoogle Scholar
Qian, W.S., Chen, W.X., & He, X.F. (2019). Parameter estimation for the Pareto distribution based on ranked set sampling. Statistical Papers. doi:10.1007/s00362-019-01102-1.Google Scholar
Qiu, G.X & Eftekharian, A. (2020). Extropy information of maximum and minimum ranked set sampling with unequal samples. Communications in Statistics – Theory and Methods. doi:10.1080/03610926.2019.1678640.Google Scholar
Samawi, H.M. & Muttlak, H.A. (1996). Estimation of ratio using rank set sampling. The Biometrical Journal 38(6): 753–764.CrossRefGoogle Scholar
Samawi, H.M., Ahmed, M.S., & Abu-Dayyeh, W. (1996). Estimating the population mean using extreme ranked set sampling. Biometrical Journal 38(5): 577–586.CrossRefGoogle Scholar
Singh, H.P. & Tailor, R. (2003). Use of known correlation coefficient in estimating the finite population mean. Statistics in Transition 6:555–560.Google Scholar
Srivastava, K. & Jhajj, H.S. (1981). A class on estimators of the population mean in survey sampling using auxiliary information. Biometrika 68(1): 341–343.CrossRefGoogle Scholar
Stokes, L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics – Theory and Methods 6(12): 1207–1211.CrossRefGoogle Scholar
Stokes, L. (1995). Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics 47(3): 465–482.Google Scholar
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.CrossRefGoogle Scholar
Upadhyaya, L.N. & Singh, H.P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal 41(5): 627–636.3.0.CO;2-W>CrossRefGoogle Scholar
Yang, R., Chen, W.X., Yao, D.S., Long, C., Dong, Y., & Shen, B. (2020). The efficiency of ranked set sampling design for parameter estimation for the log-extended exponential-geometric distribution. Iranian Journal of Science and Technology, Transactions A: Science 44(2): 497–507.CrossRefGoogle Scholar