Modified Ratio Estimators for Population Mean Using Size of the Sample, selected from Population
Keywords:
Auxiliary Variable, Sample size, Simple Random Sampling, Bias, Mean Square Error, Relative Standard Error (RSE), Percent Relative Efficiency (PRE).Abstract
This paper deals with a modified ratio estimator for the estimation of population mean of study variable using the size of the sample, selected from the population under SRSWOR. The bias and mean square error of the proposed estimator up to the first order of approximation is derived [Appendix]. The constants, biases and mean square errors (MSEs) are computed using the data from Murthy [1] and Mukhopadhyay [3]. The percent relative efficiencies (PREs) are also computed for both existed and proposed estimators and compare the results accordingly for justifying the betterment of the proposed estimators over other mentioned modified estimators.
References
- Murthy, M.N. (1967): Sampling Theory and Methods; Statistical Publishing Society, Calcutta.
- Cochran, W.G. (1977): Sampling Techniques; 3rd edition. Wiley Eastern, New Delhi.
- Mukhopadhyay, P. (2009): Theory and Methods of Survey Sampling; 2nd edition. PHI Learning Pvt. Ltd., New Delhi.
- Sarjinder, S. (2003): Advanced Sampling Theory with Applications; Kluwer Academic Publishers Volume. (1&2)
- Subramani, J. & Kumarpandiyan, G. (2013): New Modified Ratio Estimation of Population Mean when Median of Auxiliary Variable is Known; Pak.j.stat.oper.res. Vol.IX No.2 2013 pp137 – 145.
- Sisodia, B.V.S. and Dwivedi, V.K. (1981): A Modified Ratio Estimator using Coefficient of Variation of Auxiliary Variable; Jour. of Indian. Soc. of Agri. Stat., Vol. 33(1). Pp. 13–18.
- Khan, M. & Shabbir, J. (2013): A Ratio Type Estimator for the Estimation of Population Variance using Quartiles of an Auxiliary Variable; J.Stat. Appl. Pro.2, No. 3, 319 –325.
- Upadhyaya, L.N. & Singh, H.P. (1999): Use of transformed auxiliary variable in estimating the finite population means, Biometrical Journal 41 (5), 627–636.
- Singh, H.P. & Kakran, M.S. (1993): A Modified Ratio Estimator Using Known Coefficient of Kurtosis of an Auxiliary Character, (unpublished).
- Yan, Z. & Tian, B. (2010): Ratio Method to the Mean Estimation using Coefficient of Skewness of Auxiliary Variable; ICICA, Part-II, CCIS 106, pp. 103 – 110.
- Singh, H.P. & Tailor, R. (2003). Use of known Correlation Coefficient in Estimating the finite Population Means; Statistics in Transition 6 (4), 555-560.
- Yadav, S.K., Mishra, S.S. and Shukla, A.K. (2014): Improved Ratio Estimators for Population Mean Based on Median Using Linear Combination of Population Mean and Median of an Auxiliary Variable; American Journal of Operational Research, 4(2): 21-27.
- Subramani, J., Kumarpandiyan, G. & Balamurli, S. (2014): Some Modified Linear Regression type Ratio Estimators for Estimation of Population Mean Using Known Parameters of an Auxiliary Variable; Journal of Building Research, 1(1): 28-42.
- Sangngam, P. (2014): Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation Modern Applied Science; Vol. 8, No. 5.
- Sukhatme, P.V. (1957): Sampling Theory of Surves with Applications, The Indian Society of Agricultural Statistics, New Delhi, India.
- Gun, A.M., Gupta, M.K. & Dasgupta, B. (2008): Fundamentals of Statistics, Vol–2; The World Press Pvt. Ltd., Kolkata.
- Barnett, V. (1999): Comparative Statistical Inference; 3rd edition, JohnWiley & Sons Ltd.
- Kadilar, C. & Cingi, H. (2004): Ratio Estimators in Simple Random Sampling; Applied Mathematics and Computation 151, 893–902
- Allen L. Webster (2010): Applied Statistics for Business and Economics, An Essentials Version; 3rd edition, Tata McGraw–Hill Education Pvt. Ltd.
- David A. Kay (2005): CliffsAP Statistics, Wiley Publishing, Inc., Hoboken, NJ
- Daniel, W.W. & Cross, C.L. (2013): Biostatistics, A Foundation for Analysis in Health Sciences, 10th edition; JohnWiley & Sons, Inc.