Efficient ratio-type estimators of finite population mean based on correlation coefficient

Document Type : Article

Authors

1 Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou 310027, China

2 Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou 310027 China

3 Department of Mathematics, Institute of Statistics, Zhejiang University, Hangzhou 310027 China.

Abstract

We proposed efficient families of ratio-type estimators to estimate finite population mean using known correlation coefficient between study variable and auxiliary variable by adopting Singh and Tailor [Singh, H. P., and Tailor, R. “Use of known correlation coefficient in estimating the finite population means”, Statistics in Transition, 6(4), pp. 555-560 (2003)] estimator and Kadilar and Cingi [Kadilar, C., and Cingi, H. “An improvement in estimating the population mean by using the correlation coefficient”, Hacettepe Journal of Mathematics and Statistics, 35(1) pp. 103-109. (2006a)] class of estimators in simple random sampling without replacement. The newly proposed estimators behave efficiently as compared to the common unbiased estimator, traditional ratio estimator and the other competing estimators. Bias, mean squared error and minimum mean squared error of the proposed ratio-type estimators are derived. Moreover, theoretically findings are proved with cooperation of two real data sets.
 

Keywords

Main Subjects


References
1. Cochran, W.G. \The estimation of the yields of cereal
experiments by sampling for the ratio gain to total
produce", Journal of Agriculture Science, 30, pp. 262-
275 (1940).
2. Sisodia, B.V.S. and Dwivedi, V.K. \A modi ed ratio
estimator using coecient of variation of auxiliary
variable", Journal of the Indian Society of Agriculture
Statistics, 33(1), pp. 13-18 (1981).
3. Upadhyaya, L.N. and Singh, H.P. \Use of transformed
auxiliary variable in estimating the nite population
mean", Biometrical Journal, 41(5), pp. 627-636
(1999).
4. Singh, H.P. and Tailor, R. \Use of known correlation
coecient in estimating the nite population means",
Statistics in Transition, 6(4), pp. 555-560 (2003).
5. Kadilar, C. and Cingi, H. \Ratio estimators in simple
random sampling", Applied Mathematics and Computation,
151, pp. 893-902 (2004).
6. Kadilar, C. and Cingi, H. \Improvement in estimating
the population mean in simple random sampling",
Applied Mathematics Letters, 19, pp. 75-79 (2006c).
7. Singh, H.P., Tailor, R., Tailor, R., and Kakran, M.S.
\An improved estimator of population mean using
power transformation", Journal of the Indian Society
of Agriculture Statistics, 58(2), pp. 223-230 (2004).
8. Singh, R., Chauhan, P., and Sawan, N. \A family
of estimators for estimating population means using
known correlation coecient in two-phase sampling",
Statistics in Transition, New Series, 8(1), pp. 89-96
(2007).
9. Gupta, S. and Shabbir, J. \On improvement in estimating
the population mean in simple random sampling",
Journal of Applied Statistics, 35(5), pp. 559-
566 (2008).
10. Koyuncu, N. and Kadilar, C. \Ecient estimators for
the population mean", Hacettepe Journal of Mathematics
and Statistics, 38(2), pp. 217-225 (2009).
11. Koyuncu, N. and Kadilar, C. \On improvement in
estimating population mean in strati ed random sampling",
Journal of Applied Statistics, 37(6), pp. 999-
1013 (2010).
12. Yan, Z. and Tian, B. \Ratio method to the mean
estimation using coecient of skewness of auxiliary
variable", ICICA. Part II, CCIS, 106, pp. 103-110
(2010).
13. Haq, A. and Shabbir, J. \Improved family of ratio
estimators in simple and strati ed random sampling",
Communications in Statistics - Theory and Methods,
42, pp. 782-799 (2013).
14. Singh, H.P. and Solanki, R.S. \An ecient class of
estimators for the population mean using auxiliary information",
Communications in Statistics-Theory and
Methods, 42, pp. 145-163 (2013).
15. Yadav, S.K. and Kadilar, C. \Improved class of ratio
and product estimators", Applied Mathematics and
Computation, 219, pp. 10726-10731 (2013).
16. Subramani, J. and Kumarapandiyan, G. \Modi ed
ratio estimators using known median and coecient
of kurtosis", American Journal of Mathematics and
Statistics, 2(4), pp. 95-100 (2012).
17. Subramani, J. and Kumarapandiyan, G. \Estimation
of population mean using known correlation coecient
and median", Journal of Statistical Theory and Applications,
13(4), pp. 333-343 (2014).
18. Subramani, J. and Prabavathy, G. \Median based
modi ed ratio estimators with known quartiles of
an auxiliary variable", Journal of Modern Applied
Statistical Methods, 13(1), pp. 234-254 (2014).
19. Yadav, S.K., Misra, S., Shukla, A.K., and Tiwari,
V. \Improved estimation of population mean using
median and coecient of variation of auxiliary variable",
International Journal of Engineering Research
and Applications, 4(1), pp. 206-211 (2014).
20. Khan, S.A., Ali, H., Manzoor, S., and Alamgir. \A
class of transformed ecient ratio estimators of -
nite population mean", Pakistan Journal of Statistics,
31(4), pp. 353-362 (2015).
21. Kumar, S. \An estimator of the mean estimation of
study variable using median of auxiliary variable", Sri
Lankan Journal of Applied Statistics, 16(2), pp. 107-
115 (2015).
22. Irfan, M., Javed, M., Abid, M., and Lin, Z. \Improved
ratio type estimators of population mean based on
median of a study variable and an auxiliary variable",
Hacettepe Journal of Mathematics and Statistics,
47(3), pp. 659-673 (2018).
23. Walia, G.S., Kaur, H., and Sharma, M.K. \Ratio type
estimator of population mean through ecient linear
transformation", American Journal of Mathematics
and Statistics, 5(3), pp. 144-149 (2015).
24. Kadilar, C. and Cingi, H. \An improvement in estimating
the population mean by using the correlation
coecient", Hacettepe Journal of Mathematics and
Statistics, 35(1), pp. 103-109 (2006a).
25. Kadilar, C. and Cingi, H. \New ratio estimators using
correlation coecient", Interstat., pp. 1-11 (2006b).
26. Murthy, M.N., Sampling Theory and Methods, Statistical
Publishing Society, Calcutta, India (1967).
27. Munoz, J.F., Alvarez, E., and Rueda, M.M. \Optimum
design-based ratio estimators of the distribution function",
Journal of Applied Statistics, 41(7), pp. 1395-
1407 (2014).
28. Alvarez, E., Moya-Fernandez, P.J., Blanco-
Encomienda, F.J., and Munoz, J. F. \Methodological
insights for industrial quality control management:
The impact of various estimators of the standard
deviation on the process capability index", Journal of
King Saud University Science, 27, pp. 271-277 (2015).
2372 M. Irfan et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2361{2372