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

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.

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.

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References

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

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

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

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.         [ Links ]

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

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.         [ Links ]

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

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

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

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

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.         [ Links ]

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.         [ Links ]

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.         [ Links ]

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.         [ Links ]

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.         [ Links ]

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.         [ Links ]

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

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

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.         [ Links ]

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