Published

2016-01-01

Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters

Mejoras a los estimadores de razón de medias con el fin de estimar la media poblacional usando parámetros de localización no convencionales

DOI:

https://doi.org/10.15446/rce.v39n1.55139

Keywords:

Bias, Correlation Coefficient, Coefficient of Variation, Hodges- Lehmann Estimator, Mean Square Error, Tri-Mean (en)
Coeficiente de correlación poblacional, Coeficiente de variación, Error cuadrático medio, Estimador de Hodges-Lehmann,, Sesgo, Trimean. (es)

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Authors

  • Muhammad Abid Zhejiang University, Hangzhou, China
  • Nasir Abbas Government College University, Faisalabad, Pakistan
  • Hafiz Zafar Nazir University of Sargodha, Sargodha, Pakistan
  • Zhengyan Lin Zhejiang University, Hangzhou, China

Conventional measures of location are commonly used to develop ratio estimators. However, in this article, we attempt to use some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, and mid-range of the auxiliary variable for this purpose. To enhance the efficiency of the proposed mean ratio estimators, population correlation coefficient, coefficient of variation and the linear combinations of auxiliary variable have also been exploited. The properties associated with the proposed estimators are evaluated through bias and mean square errors. We also provide an empirical study for illustration and verification.

Las medidas convencionales de localización son a menudo usadas con el fin de desarrollar estimatores de razón. Sin embargo, en este artículo, se hace un intento por usar algunas medidas de localización no convencionales. Se incorpora la trimean, el estimador de Hodges-Lehmann y el rango medio de la variable auxiliar con este propósito. Para mejorar la eficiencia de los estimadores de razón de medias propuestos, el coeficiente de correlación poblacional, el coeficiente de variación y combinaciones lineales de variables auxiliares también han sido explotados. Las propiedades asociadas con los estimadores propuestos son evaluadas a través del sesgo y el error cuadrático medio. Un estudio empírico es presentado con fines de ilustración y verificación.

Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters

Mejoras a los estimadores de razón de medias con el fin de estimar la media poblacional usando parámetros de localización no convencionales

MUHAMMAD ABID1, NASIR ABBAS2, HAFIZ ZAFAR NAZIR3, ZHENGYAN LIN4

1Institute of Statistics, Zhejiang University, Faculty of Basic and Applied Sciences, Department of Mathematics, Hangzhou, China. Government College University, Faculty of Science And Technology, Department of Statistics, Faisalabad, Pakistan. Lecturer. Email: mabid@gcuf.edu.pk
2Government College University, Faculty of Science And Technology, Department of Statistics, Faisalabad, Pakistan. Visiting Lecturer. Email: nasirbhatti9181@yahoo.com
3University of Sargodha, Faculty of Science, Department of Statistics, Sargodha, Pakistan. Assistant Professor. Email: hafizzafarnazir@yahoo.com
4Institute of Statistics, Zhejiang University, Faculty of Basic and Applied Sciences, Department of Mathematics, Hangzhou, China. Professor. Email: zlin@zju.edu.cn

Abstract

Conventional measures of location are commonly used to develop ratio estimators. However, in this article, we attempt to use some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, and mid-range of the auxiliary variable for this purpose. To enhance the efficiency of the proposed mean ratio estimators, population correlation coefficient, coefficient of variation and the linear combinations of auxiliary variable have also been exploited. The properties associated with the proposed estimators are evaluated through bias and mean square errors. We also provide an empirical study for illustration and verification.

Key words: Bias, Correlation Coefficient, Coefficient of Variation, Hodges-Lehmann Estimator, Mean Square Error, Tri-Mean.

Resumen

Las medidas convencionales de localización son a menudo usadas con el fin de desarrollar estimatores de raz ón. Sin embargo, en este artículo, se hace un intento por usar algunas medidas de localización no convencionales. Se incorpora la trimean, el estimador de Hodges-Lehmann y el rango medio de la variable auxiliar con este propósito. Para mejorar la eficiencia de los estimadores de razón de medias propuestos, el coeficiente de correlación poblacional, el coeficiente de variación y combinaciones lineales de variables auxiliares también han sido explotados. Las propiedades asociadas con los estimadores propuestos son evaluadas a través del sesgo y el error cuadrático medio. Un studio empírico es presentado con fines de ilustración y verificación.

Palabras clave: coeficiente de correlación poblacional, coeficiente de variación, error cuadrático medio, estimador de Hodges-Lehmann, sesgo, trimean.

Texto completo disponible en PDF

References

1. Cochran, W. G. (1940), Sampling Techniques, 3 edn, Wiley Eastern Limited, New York.

2. Ferrell, E. (1953), 'Control charts using midranges and medians', Industrial Quality Control 9(5), 30-34.

3. Hettmansperger, T. & McKean, J. W. (1988), Robust Nonparametric Statistical, 1 edn, Arnold, London.

4. Jeelani, M. I., Maqbool, S. & Mir, S. A. (2013), 'Modified ratio estimators of population mean using linear combination of coefficient of skewness and quartile deviation', International Journal of Modern Mathematical Sciences 6(3), 174-183.

5. Kadilar, C. & Cingi, H. (2004), 'Ratio estimators in simple random sampling', Applied Mathematics and Computation 151, 893-902.

6. Kadilar, C. & Cingi, H. (2006), 'An improvement in estimating the population mean by using the correlation coefficient', Hacettepe Journal of Mathematics and Statistics 35(1), 103-109.

7. Murthy, M. (1967), Sampling Theory and Methods, 1 edn, Statistical Publishing Society, India.

8. Nazir, H., Riaz, M., Ronald, J. D. & Abbas, N. (2013), 'Robust cusum control charting', Quality Engineering 25(3), 211-224.

9. Rao, T. J. (1991), 'On certain methods of improving ratio and regression estimators', Communications in Statistics-Theory and Methods 20(10), 3325-3340.

10. Singh, D. & Chaudhary, F. S. (1986), Theory and Analysis of Sample Survey Designs, 1 edn, New Age International Publisher, India.

11. Singh, H. P. & Tailor, R. (2003), 'Use of known correlation coefficient in estimating the finite population means', Statistics in Transition 6(4), 555-560.

12. Singh, H. P., Tailor, R., Tailor, R. & Kakran, M. (2004), 'An improved estimator of population mean using power transformation', Journal of the Indian Society of Agricultural Statistics 58(2), 223-230.

13. Sisodia, B. V. S. & Dwivedi, V. K. (2012), 'A modified ratio estimator using coefficient of variation of auxiliary variable', Journal of the Indian Society of Agricultural Statistics 33(1), 13-18.

14. Subramani, J. & Kumarapandiyan, G. (2012a), 'Modified ratio estimators using known median and co-efficient of kurtosis', American Journal of Mathematics and Statistics 2(4), 95-100.

15. Subramani, J. & Kumarapandiyan, G. (2012b), 'Estimation of population mean using known median and co-efficient of skewness', American Journal of Mathematics and Statistics 2(5), 101-107.

16. Subramani, J. & Kumarapandiyan, G. (2012b), 'Estimation of population mean using co-efficient of variation and median of an auxiliary variable', International Journal of Probability and Statistics 1(4), 111-118.

17. Upadhyaya, L. N. & Singh, H. (1999), 'Use of transformed auxiliary variable in estimating the finite population mean', Biometrical Journal 41(5), 627-636.

18. Wang, T., Li, Y. & Cui, H. (2007), 'On weighted randomly trimmed means', Journal of Systems Science and Complexity 20(1), 47-65.

19. Yan, Z. & Tian, B. (2010), 'Ratio method to the mean estimation using coefficient of skewness of auxiliary variable', Information Computing and Applications 106, 103-110.

[Recibido en junio de 2014. Aceptado en marzo de 2015]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv39n1a05,
    AUTHOR  = {Abid, Muhammad and Abbas, Nasir and Zafar Nazir, Hafiz and Lin, Zhengyan},
    TITLE   = {{Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2016},
    volume  = {39},
    number  = {1},
    pages   = {63-79}
}

References

Cochran, W. G. (1940), Sampling Techniques, 3 edn, Wiley Eastern Limited, New York.

Ferrell, E. (1953), ‘Control charts using midranges and medians’, Industrial Quality Control 9(5), 30–34.

Hettmansperger, T. & McKean, J. W. (1988), Robust Nonparametric Statistical, 1 edn, Arnold, London.

Jeelani, M. I., Maqbool, S. & Mir, S. A. (2013), ‘Modified ratio estimators of population mean using linear combination of coefficient of skewness and quartile deviation’, International Journal of Modern Mathematical Sciences 6(3), 174–183.

Kadilar, C. & Cingi, H. (2004), ‘Ratio estimators in simple random sampling’, Applied Mathematics and Computation 151, 893–902.

Kadilar, C. & Cingi, H. (2006), ‘An improvement in estimating the population mean by using the correlation coefficient’, Hacettepe Journal of Mathematics and Statistics 35(1), 103–109.

Murthy, M. (1967), Sampling Theory and Methods, 1 edn, Statistical Publishing Society, India.

Nazir, H., Riaz, M., Ronald, J. D. & Abbas, N. (2013), ‘Robust cusum control charting’, Quality Engineering 25(3), 211–224.

Rao, T. J. (1991), ‘On certain methods of improving ratio and regression estimators’, Communications in Statistics-Theory and Methods 20(10), 3325–3340.

Singh, D. & Chaudhary, F. S. (1986), Theory and Analysis of Sample Survey Designs, 1 edn, New Age International Publisher, India.

Singh, H. P. & Tailor, R. (2003), ‘Use of known correlation coefficient in estimating the finite population means’, Statistics in Transition 6(4), 555–560.

Singh, H. P., Tailor, R., Tailor, R. & Kakran, M. (2004), ‘An improved estimator of population mean using power transformation’, Journal of the Indian Society of Agricultural Statistics 58(2), 223–230.

Sisodia, B. V. S. & Dwivedi, V. K. (2012), ‘A modified ratio estimator using coefficient of variation of auxiliary variable’, Journal of the Indian Society of Agricultural Statistics 33(1), 13–18.

Subramani, J. & Kumarapandiyan, G. (2012a), ‘Estimation of population mean using co-efficient of variation and median of an auxiliary variable’, International Journal of Probability and Statistics 1(4), 111–118.

Subramani, J. & Kumarapandiyan, G. (2012b), ‘Estimation of population mean using known median and co-efficient of skewness’, American Journal of Mathematics and Statistics 2(5), 101–107.

Subramani, J. & Kumarapandiyan, G. (2012c), ‘Modified ratio estimators using known median and co-efficient of kurtosis’, American Journal of Mathematics and Statistics 2(4), 95–100.

Upadhyaya, L. N. & Singh, H. (1999), ‘Use of transformed auxiliary variable in estimating the finite population mean’, Biometrical Journal 41(5), 627–636.

Wang, T., Li, Y. & Cui, H. (2007), ‘On weighted randomly trimmed means’, Journal of Systems Science and Complexity 20(1), 47–65.

Yan, Z. & Tian, B. (2010), ‘Ratio method to the mean estimation using coefficient of skewness of auxiliary variable’, Information Computing and Applications 106, 103–110.

How to Cite

APA

Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. (2016). Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Revista Colombiana de Estadística, 39(1), 63–79. https://doi.org/10.15446/rce.v39n1.55139

ACM

[1]
Abid, M., Abbas, N., Nazir, H.Z. and Lin, Z. 2016. Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Revista Colombiana de Estadística. 39, 1 (Jan. 2016), 63–79. DOI:https://doi.org/10.15446/rce.v39n1.55139.

ACS

(1)
Abid, M.; Abbas, N.; Nazir, H. Z.; Lin, Z. Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Rev. colomb. estad. 2016, 39, 63-79.

ABNT

ABID, M.; ABBAS, N.; NAZIR, H. Z.; LIN, Z. Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Revista Colombiana de Estadística, [S. l.], v. 39, n. 1, p. 63–79, 2016. DOI: 10.15446/rce.v39n1.55139. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/55139. Acesso em: 28 mar. 2025.

Chicago

Abid, Muhammad, Nasir Abbas, Hafiz Zafar Nazir, and Zhengyan Lin. 2016. “Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters”. Revista Colombiana De Estadística 39 (1):63-79. https://doi.org/10.15446/rce.v39n1.55139.

Harvard

Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. (2016) “Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters”, Revista Colombiana de Estadística, 39(1), pp. 63–79. doi: 10.15446/rce.v39n1.55139.

IEEE

[1]
M. Abid, N. Abbas, H. Z. Nazir, and Z. Lin, “Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters”, Rev. colomb. estad., vol. 39, no. 1, pp. 63–79, Jan. 2016.

MLA

Abid, M., N. Abbas, H. Z. Nazir, and Z. Lin. “Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters”. Revista Colombiana de Estadística, vol. 39, no. 1, Jan. 2016, pp. 63-79, doi:10.15446/rce.v39n1.55139.

Turabian

Abid, Muhammad, Nasir Abbas, Hafiz Zafar Nazir, and Zhengyan Lin. “Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters”. Revista Colombiana de Estadística 39, no. 1 (January 1, 2016): 63–79. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/55139.

Vancouver

1.
Abid M, Abbas N, Nazir HZ, Lin Z. Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters. Rev. colomb. estad. [Internet]. 2016 Jan. 1 [cited 2025 Mar. 28];39(1):63-79. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/55139

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10. Housila P. Singh, Anita Yadav. (2020). A New Exponential Approach for Reducing the Mean Squared Errors of the Estimators of Population Mean Using Conventional and Non-Conventional Location Parameters. Journal of Modern Applied Statistical Methods, 18(1) https://doi.org/10.22237/jmasm/1568246400.

11. Mir Subzar, Showkat Maqbool, Tariq Ahmad Raja, Surya Kant Pal, Prayas Sharma. (2018). EFFICIENT ESTIMATORS OF POPULATION MEAN USING AUXILIARY INFORMATION UNDER SIMPLE RANDOM SAMPLING. Statistics in Transition New Series, 19(2), p.219. https://doi.org/10.21307/stattrans-2018-013.

12. Usman Shahzad, Nadia H. Al-Noor, Muhammad Hanif, Irsa Sajjad. (2021). An exponential family of median based estimators for mean estimation with simple random sampling scheme. Communications in Statistics - Theory and Methods, 50(20), p.4890. https://doi.org/10.1080/03610926.2020.1725828.

13. Usman Shahzad, Shabnam Shahzadi, Noureen Afshan, Nadia H. Al-Noor, David Anekeya Alilah, Muhammad Hanif, Malik Muhammad Anas, Amer Al-Omari. (2021). Poisson Regression-Based Mean Estimator. Mathematical Problems in Engineering, 2021, p.1. https://doi.org/10.1155/2021/9769029.

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16. Mir Subzar, Taghreed Alqurashi, Deeksha Chandawat, Shahid Tamboli, T. A. Raja, Amit Kumar Attri, Shahid Ahmad Wani. (2025). Generalized robust regression techniques and adaptive cluster sampling for efficient estimation of population mean in case of rare and clustered populations. Scientific Reports, 15(1) https://doi.org/10.1038/s41598-025-85328-0.

17. Farah Naz, Tahir Nawaz, Tianxiao Pang, Muhammad Abid. (2019). Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers. Symmetry, 12(1), p.16. https://doi.org/10.3390/sym12010016.

18. Muhammad Zohaib, Waqas Latif, Mubeen Alam. (2025). On Enhanced Ratio-Type Estimators Using Quantile Regression for Finite Population Mean under Robustness and Empirical Validation. Iranian Journal of Science, 49(1), p.169. https://doi.org/10.1007/s40995-024-01700-1.

19. Usman Shahzad, Ishfaq Ahmad, Ibrahim Mufrah Almanjahie, Amer Ibrahim Al-Omari, Anoop Kumar. (2022). Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme. PLOS ONE, 17(10), p.e0276514. https://doi.org/10.1371/journal.pone.0276514.

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22. Vinay Kumar Yadav, Shakti Prasad. (2025). Some new efficient linear regression ratio type estimators for estimating the population mean in sampling theory. Boletim da Sociedade Paranaense de Matemática, 43, p.1. https://doi.org/10.5269/bspm.68413.

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