Improved ratio type estimators of population mean based on median of a study variable and an auxiliary variable

Year 2018, Volume: 47 Issue: 3, 659 - 673, 01.06.2018

Muhammad Irfan , Maria Javed Muhammad Abid , Zhengyan Lin

Abstract

This paper deals with efficient ratio type estimators for estimating finite population mean under simple random sampling scheme by using the knowledge of known median of a study and an auxiliary variable. Expressions for the bias and mean squared error of the proposed ratio type estimators are derived up to first order of approximation. It is found that our proposed estimators perform better as compared to the traditional ratio estimator, regression estimator, Subramani and Kumarapandiyan [23], Subramani and Prabavathy [24] and Yadav et al. [28] estimators. In addition, theoretical findings are veried with the help of real data sets.

Keywords

Auxiliary variables, Bias, Eciency, Median, Mean squared error, Ratio estimators, RRMSE

References

• Abid, M., Abbas, N., Nazir, H. Z. and Lin, Z. Enhancing the mean ratio estimators for es- timating population mean using non-conventional location parameters, Revista Colombiana de Estadistica 39 (1), 63-79, 2016(a).
• Abid, M., Abbas, N. and Riaz, M. Improved modied ratio estimators of population mean based on deciles, Chiang Mai Journal of Science 43 (1), 1311-1323, 2016(b).
• Abid, M., Abbas, N., Sherwani, R. A. K. and Nazir, H. Z. Improved ratio estimators for the population mean using non-conventional measures of dispersion, Pakistan Journal of Statistics and Operation Research 12 (2), 353-367, 2016(c).
• Alvarez, E., Moya-Fernandez, P. J., Blanco-Encomienda, F. J. and Munoz, J. F. Methodolog- ical 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, 271-277, 2015.
• 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, 262-275, 1940.
• Kadilar, C., and Cingi, H. Ratio estimators in simple random sampling, Applied Mathe- matics and Computation 151, 893-902, 2004.
• 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), 103-109, 2006.
• Koyuncu, N., and Kadilar, C. Ecient estimators for the population mean, Hacettepe Jour- nal of Mathematics and Statistics 38 (2), 217-225, 2009.
• Koyuncu, N., and Kadilar, C. On improvement in estimating population mean in stratied random sampling, Journal of Applied Statistics 37 (6), 999-1013, 2010.
• Kumar, S. An estimator of the median estimation of study variable using median of auxiliary variable, Sri Lankan Journal of Applied Statistics 16 (2), 107-115, 2015.
• Mukhopadhyay, P. Theory and methods of survey sampling, PHI Learning, 2nd edition, New Delhi 1988.
• Munoz, J. F., Alvarez, E. and Rueda, M. M. Optimum design-based ratio estimators of the distribution function, Journal of Applied Statistics 41 (7), 1395-1407, 2014.
• Murthy, M. N. Product method of estimation, Sankhya 26, 294-307, 1964.
• Prassad, B. Some improved ratio type estimators of population mean and ratio in nite population sample surveys, Communications in Statistics: Theory and Methods 18, 379- 392, 1989.
• Robson, D. S. Application of multivariate polykays to the theory of unbiased ratio type estimation, Journal of American Statistical Association 52, 411-422, 1957.
• Silva, P. N., and Skinner, C. J. Estimating distribution functions with auxiliary information using post stratication, Journal of Ocial Statistics 11 (3), 277-294, 1995.
• Singh, H. P., and Solanki, R. S. Generalized ratio and product methods of estimation in survey sampling, Pakistan Journal of Statistics and Operational Research 7 (2), 245-264, 2011.
• Singh, H. P., and Solanki, R. S. An ecient class of estimators for the population mean using auxiliary information in systematic sampling, Journal of Statistics Theory Practice 6, 274-285, 2012.
• Singh, H. P. and Tailor, R. Use of known correlation coecient in estimating the nite population means, Statistics in Transition 6 (4), 555-560, 2003.
• 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), 223-230, 2004.
• Singh, R., Kumar, M., Chaudhary, M. K., and Kadilar, C. Improved exponential estimator in stratied random sampling, Pakistan Journal of Statistics and Operational Research 5 (2), 67-82, 2009.
• Sisodia, B. V. S. and Dwivedi, V. K. A modied ratio estimator using coecient of variation of auxiliary variable, Journal of the Indian Society of Agriculture Statistics 33 (1), 13-18, 1981.
• Subramani, J. and Kumarapandiyan, G. New modied ratio estimator for estimation of pop- ulation mean when median of the auxiliary variable is known, Pakistan Journal of Statistics and Operational Research 9 (2), 137-145, 2013.
• Subramani, J. and Prabavathy, G. Median based modied ratio estimators with linear com- binations of population mean and median of an auxiliary variable, Journal of Reliability and Statistical Studies 7 (1), 1-10, 2014.
• Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the nite population mean, Biometrical Journal 41 (5), 627-636, 1999.
• Watson, D. J. The estimation of leaf area in eld crops, Journal of Agriculture Science 27, 474-483, 1937.
• Yadav, S. K., and Kadilar, C. Ecient family of exponential estimators for the population mean, Hacettepe Journal of Mathematics and Statistics 42 (6), 671-677, 2013.
• Yadav, S. K., Mishra, S. S. and Shukla, A. K. 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, 2014.
• Yan, Z. and Tian, B. Ratio method to the mean estimation using coecient of skewness of auxiliary variable, ICICA. Part II, CCIS 106, 103-110, 2010.