Published

2023-07-12

Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling

Algunos estimadores combinados mejorados de la media de la población en el muestreo de conjuntos clasificados estratificados

DOI:

https://doi.org/10.15446/rce.v46n2.104591

Keywords:

Auxiliary variable, Bias, Ranked set sampling, Study variable, Mean square error (en)
Error cuadrático medio, Inclinación, Muestreo de conjuntos clasificados, Variable de estudio, Variable auxiliar (es)

Downloads

Authors

This paper presents improved population mean estimators using auxiliary variables in Stratified Ranked Set Sampling. We have derived the expressions for bias and mean square errors up to the first order of approximation and shown that the proposed estimators under optimum conditions are more efficient than other estimators taken in this paper. In an attempt to verify the efficiencies of proposed estimators, theoretical results are supported by numerical illustrations and simulation study for which we have considered two populations.

Este artículo presenta estimadores mejorados de la media de la población utilizando variables auxiliares en el muestreo de conjuntos ordenados estratificados. Hemos derivado las expresiones para el sesgo y los errores cuadráticos medios hasta el primer orden de aproximación y hemos demostrado que los estimadores propuestos en condiciones óptimas son más eficientes que otros estimadores tomados en este artículo. En un intento por verificar las eficiencias de los estimadores propuestos, los resultados teóricos están respaldados por ilustraciones numéricas y estudios de simulación para los cuales hemos considerado dos poblaciones.

References

Al-Omari, Ibrahim, A. & Bouza, C. (2014), ‘Review of ranked set sampling: modifications and applications’, Investigación Operacional 35(3), 215-235.

Bhushan, S., Gupta, R., Singh, S. & Kumar, A. (2020), ‘A new efficient log type class of estimators using auxiliary variable’, International Journal of Statistics and Systems 15(1), 19-28.

Bouza, C., Singh, P. & Singh, R. (2018), ‘Ranked set sampling and optional scrambling randomized response modeling’, Investigación Operacional 39(1), 100-107.

Chaudhary, M., Singh, R., Shukla, R., Kumar, M. & Smarandache, F. (2009), ‘A family of estimators for estimating population mean in stratified sampling under non-response’, Pakistan Journal of Statistics and Operation Research pp. 47-54. DOI: https://doi.org/10.18187/pjsor.v5i1.153

Cochran, W. (1977), ‘Sampling techniques’, Wiley eastern limited’, New Delhi.

Ganeslingam, S. & Ganesh, S. (2006), ‘Ranked set sampling versus simple random sampling in the estimation of the mean and the ratio’, Journal of Statistics and Management Systems 9(2), 459-472. DOI: https://doi.org/10.1080/09720510.2006.10701217

Haq, A. & Shabbir, J. (2013), ‘Improved family of ratio estimators in simple and stratified random sampling’, Communications in Statistics-Theory and Methods 42(5), 782-799. DOI: https://doi.org/10.1080/03610926.2011.579377

Kadilar, C. & Cingi, H. (2003), ‘Ratio estimators in stratified random sampling’, Biometrical Journal: Journal of Mathematical Methods in Biosciences 45(2), 218-225. DOI: https://doi.org/10.1002/bimj.200390007

Koyuncu, N. & Kadilar, C. (2009), ‘Family of estimators of population mean using two auxiliary variables in strati-ed random sampling’, Communications in Statistics-Theory and Methods 38(14), 2398-2417. DOI: https://doi.org/10.1080/03610920802562723

McIntyre, G. (1952), ‘A method for unbiased selective sampling, using ranked sets’, Australian journal of agricultural research 3(4), 385-390. DOI: https://doi.org/10.1071/AR9520385

Muneer, S., Shabbir, J. & Khalil, A. (2017), ‘Estimation of finite population mean in simple random sampling and strati-ed random sampling using two auxiliary variables’, Communications in Statistics-Theory and Methods 46(5), 2181-2192. DOI: https://doi.org/10.1080/03610926.2015.1035394

Samawi, H. & Muttlak, H. (1996), ‘Estimation of ratio using rank set sampling’, Biometrical Journal 38(6), 753-764. DOI: https://doi.org/10.1002/bimj.4710380616

Samawi, H. & Siam, M. (2003), ‘Ratio estimation using stratified ranked set sample’, Metron 61(1), 75-90.

Shabbir, J. & Gupta, S. (2006), ‘A new estimator of population mean in stratified sampling’, Communications in Statistics-Theory and Methods 35(7), 1201-1209. DOI: https://doi.org/10.1080/03610920600629112

Shabbir, J. & Gupta, S. (2007), ‘On estimating the finite population mean with known population proportion of an auxiliary variable’, Pakistan Journal of Statistics 23(1), 1.

Singh, H., 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. DOI: https://doi.org/10.1080/00949655.2012.733395

Singh, R. & Kumar, M. (2012), ‘Improved estimators of population mean using two auxiliary variables in strati-ed random sampling’, Pakistan Journal of Statistics and Operation Research pp. 65-72. DOI: https://doi.org/10.18187/pjsor.v8i1.161

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. DOI: https://doi.org/10.1007/BF02911622

How to Cite

APA

Singh, R. and Kumari, A. (2023). Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling. Revista Colombiana de Estadística, 46(2), 1–18. https://doi.org/10.15446/rce.v46n2.104591

ACM

[1]
Singh, R. and Kumari, A. 2023. Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling. Revista Colombiana de Estadística. 46, 2 (Jul. 2023), 1–18. DOI:https://doi.org/10.15446/rce.v46n2.104591.

ACS

(1)
Singh, R.; Kumari, A. Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling. Rev. colomb. estad. 2023, 46, 1-18.

ABNT

SINGH, R.; KUMARI, A. Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling. Revista Colombiana de Estadística, [S. l.], v. 46, n. 2, p. 1–18, 2023. DOI: 10.15446/rce.v46n2.104591. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/104591. Acesso em: 28 mar. 2025.

Chicago

Singh, Rajesh, and Anamika Kumari. 2023. “Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling”. Revista Colombiana De Estadística 46 (2):1-18. https://doi.org/10.15446/rce.v46n2.104591.

Harvard

Singh, R. and Kumari, A. (2023) “Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling”, Revista Colombiana de Estadística, 46(2), pp. 1–18. doi: 10.15446/rce.v46n2.104591.

IEEE

[1]
R. Singh and A. Kumari, “Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling”, Rev. colomb. estad., vol. 46, no. 2, pp. 1–18, Jul. 2023.

MLA

Singh, R., and A. Kumari. “Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling”. Revista Colombiana de Estadística, vol. 46, no. 2, July 2023, pp. 1-18, doi:10.15446/rce.v46n2.104591.

Turabian

Singh, Rajesh, and Anamika Kumari. “Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling”. Revista Colombiana de Estadística 46, no. 2 (July 12, 2023): 1–18. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/104591.

Vancouver

1.
Singh R, Kumari A. Some Improved Combined Estimators of Population Mean in Stratified Ranked Set Sampling. Rev. colomb. estad. [Internet]. 2023 Jul. 12 [cited 2025 Mar. 28];46(2):1-18. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/104591

Download Citation

CrossRef Cited-by

CrossRef citations1

1. Rajesh Singh, Chitra Saroj, Anamika Kumari. (2024). Understanding stunting and its determinant among children in the most populous state of India using estimation of population mean under ranked set sampling in the presence of missing data. Mathematical Population Studies, 31(3), p.204. https://doi.org/10.1080/08898480.2024.2402011.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Captures
  • Mendeley - Readers: 1
-
see details

Article abstract page views

259

Downloads

License

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).