A Combined Family of Ratio Estimators for Population Mean using an Auxiliary Variable in Simple Random Sampling

Uraiwan Jaroengeratikun, Nuanpan Lawson

Abstract


This paper proposes two new classes of ratio estimators for population mean when information on a known auxiliary variable is available in simple random sampling. A combined family of ratio estimators for estimating population mean by combining the two new estimators together in order to minimize the mean square error (MSE) is then suggested. The expressions for the bias and mean square error of all proposed estimators up to the first order of approximation were obtained. The performance of the proposed estimators was compared with that of existing estimators using both a theoretical and a simulation study. The proposed family of estimators was found to be more efficient than the existing estimators.


Keywords


bias; combined family of ratio estimators; mean square error; percentage relative efficiency; ratio estimator

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References


Cochran, W.G., Sampling Techniques, 3rd ed., John Wiley and Sons, New York, 1997.

Sisodia, B.V. & Dwivedi, V.K., A Modified Ratio Estimator Using Coefficient of Variation of Auxiliary Variable, Journal Indian Society of Agricultural Statistics, 8(1), pp. 20-25, 1991.

Singh, H.P. & Upadhyaya, L.N., A Dual to Modified Ratio Estimator Using Coefficient of Variation of Auxiliary Variable, Proceedings National Academy of Sciences, India, 56A(4), pp. 336-340, 1986.

Pandey, B.N. & Dubey, V., Modified Product Estimator Using Coefficient of Variation of Auxiliary Variate, Assam Statistical Review, 2(2), pp. 64-66, 1988.

Singh, H.P. & Tailor, R., Use of Known Correlation Coefficient in Estimating the Finite Population Mean, Statistics in Transition, 6, pp. 555-560, 2003.

Soponviwatkul, K. & Lawson, N., New Ratio Estimators for Estimating Population Mean in Simple Random Sampling Using a Coefficient of Variation, Correlation Coefficient and a Regression Coefficient, Gazi University Journal of Science, 30(4), pp. 610-621, 2017.

Kadilar, C. & Cingi, H., Ratio Estimators in Simple Random Sampling, Applied Mathematics and Computation, 151, pp. 893-902, 2004.

Kadilar, C. & Cingi, H., New Ratio Estimators Using Correlation Coefficient, Interstat, 4, pp. 1-11, 2006.

Subramani, J. & Kumarapandiyan, G., Modified Ratio Estimators for Population Mean Using Function of Quartiles of Auxiliary Variable, Bonfring International Journal of Industrial Engineering and Management Science, 2(2), pp.19-23, 2012.

Subramani, J. & Kumarapandiyan, G., A Class of Modified Ratio Estimators Using Deciles of an Auxiliary Variable, Bonfring International Journal of Statistics and Application, 2(6), pp. 101-107, 2012.

Khoshnevisan, M., Singh, R., Chauhan, P., Sawan, N. & Smarandache, F., A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s), Far East Journal of Theoretical Statistics, 22, 181-191, 2007.

Kumar, S., Improved Estimators in Finite Population Surveys: Theory and Application, Journal of Applied Modern Statistical Method, 12(1), pp. 120-127, 2013.

Upadhyaya, L.N. & Singh, H.P., Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean, Biometrical Journal, 41, pp. 627-636, 1999.

Singh, G.N., On the Improvement of Product Method of Estimation in Sample Surveys, Jour. Ind. Soc. Agri. Statistics, 56(3), pp. 267-265, 2003.

Alomari, A.I., Jemain, A. A. & Ibrahim, K., New Ratio Estimators of the Mean Using Simple Random Sampling and Ranked Set Sampling Methods, Revista Investigation Operational, 30(2), pp. 97-108, 2009.

Yan, Z. & Tian, B., Ratio Method to the Mean Estimation Using Coefficient of Skewness of Auxiliary Variable, ICICA 2010, Part II, CCIS 106, pp. 103-110, 2010.

Yadav, S.K., Mishra, S.S. & Shukla, A., Improved Ratio Estimators for Population Mean Based on Median Using Linear Combination of Population Mean and Median of an Auxiliary Variable, American Journal of Operations Research, Scientific and Academic Publishing, 4(2), pp. 21-27, 2014.

Subramani, J. & Kumarapandiyan, G., Estimation of Population Mean Using Known Median and Coefficient of Skewness, American Journal of Mathematics and Statistics, 2(5), pp. 101-107, 2012.

Lawson, N., Ratio Estimators of Population Means Using Quartile Function of Auxiliary Variable Using Double Sampling, Songklanakarin Journal of Science and Technology, submitted for publication.

Enang, E.I., Akpan, V.M. & Ekpenyong, E.J., Alternative Ratio Estimator of Population Mean in Simple Random Sampling, Journal of Mathematics Research, 6(3), pp. 54-61, 2014.




DOI: http://dx.doi.org/10.5614%2Fj.math.fund.sci.2019.51.1.1

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