GENERALIZED FAMILY OF ESTIMATORS VIA TWO AUXILIARY VARIABLES FOR POPULATION VARIANCE

Authors

  • Hatice Oncel Cekim Department of Statistics, Hacettepe University, Ankara, Turkey
  • Cem Kadilar Department of Statistics, Hacettepe University, Ankara, Turkey

Keywords:

Variance Estimator, Auxiliary Information, Mean Squared Error, Efficiency

Abstract

The variance estimators have been recommended in sampling literature by many authors. It is highly popular to use auxiliary variable information to achieve more effective estimators. Moreover, the variance estimators have been studied using the information of two auxiliary variables in recent years. In this paper, we suggest three families of estimators using the information of two auxiliary variables for the estimation of the population variance in the simple random sampling method. The asymptotic expressions for the mean squared error (MSE) of the suggested family of estimators have been derived up to the first order of approximation. We show that the suggested estimators are more efficient than the classical estimators and the existing estimators in Literature under the determined conditions obtained in theory. We also support the performances of the suggested estimators with the aid of two real population data sets.

Downloads

Download data is not yet available.

References

Adichwal, N. K., Sharma, P. and Singh, R. (2017). Generalized class of estimators for population variance using information on two auxiliary variables, International Journal of Applied and Computational Mathematics, Vol. 3(2), p. 651-661.

Gupta S. and Shabbir, J. (2008).Variance estimation in simple random sampling using auxiliary information, Hacettepe Journal of Mathematics and Statistics, Vol. 37(1), p. 57-67.

Kadilar, C. and Cingi, H.(2006). Improvement in variance estimation using auxiliary information, Hacettepe Journal of Mathematics and Statistics, Vol. 35 (1), p. 111–115.

Lone, H. A., Tailor, R. and Verma, M. R. (2017). Efficient separate class of estimators of population mean in stratified random sampling, Communications in Statistics - Theory and Methods,Vol.46(2), p. 554-573,.

Muneer, S., Shabbir, J. and Khalil, A. (2017). Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables, Communications in Statistics - Theory and Methods, Vol. 46(5), p. 2181-2192.

Sanaullah, A., Asghar, A. and Hanif, M. (2017). General class of exponential estimator for estimating finite population variance, Journal of Reliability and Statistical Studies, Vol. 10(2), p. 1-16.

Shabbir, J. and Gupta, S. (2014). An improved generalized difference-cum- ratio type estimator for the population variance in two-phase sampling using two auxiliary variables, Communications in Statistics - Simulation and Computation, Vol. 43, p. 2540-2550.

Shabbir, J. and Gupta, S. (2017). Estimation of population coefficient of variation in simple and stratified random sampling under two phase sampling scheme when using two auxiliary variables, Communications in Statistics - Theory and Methods, Vol. 46 (16), p. 8113-8133.

Sidelel, E. B., Orwa, G. O. and Otieno, R. O. (2014). Variance estimation in stratified random sampling in the presence of two auxiliary random variables, International Journal of Science and Research, Vol. 3(9), p. 2453-2459.

Singh R. and Singh, V. K. (2015). Improved class of estimators for variance under single and two phase sampling, J. Stat. Appl., Vol. 4(1), p. 161-171.

Singh, H.P. and Pal, S.K. (2016). Improved estimation of finite population variance using auxiliary information in presence of measurement error, Rev. Investigacion Operacional, Vol. 37 (2), p. 147–162.

Singh, H.P. and Pal, S.K. (2017). A class of exponential-type ratio estimators of a general parameter, Communications in Statistics - Theory and Methods, Vol. 46 (8), p. 3957–3984.

Singh, R., Chauhan, P., Sawan, N. and Smarandache, F. (2011). Improved exponential estimator for population variance using two auxiliary variables, Italian Journal of Pure and Applied Mathematics, Vol. 28, p. 103- 110.

Singh, V. K. and Singh, R. (2015). A generalized family of estimators for estimating unknown variance using two auxiliary variables, Mathematical Journal of Interdisciplinary Sciences, Vol. 3(2), p. 193-207.

Singh, H. P. and Solanki, R. S. (2013). A new procedure for variance estimation in simple random sampling using auxiliary information, Stat. Papers, Vol. 54, p. 479–497.

Yadav, S. K., Kadilar, C., Shabbir J. and Gupta, S. (2015). Improved family of estimators of population variance in simple random sampling, Journal of Statistical Theory and Practice, Vol. 9, p. 219–226.

Yadav, S. K., Mishra, S. S., Shukla, A. K. and Tiwari, V. (2015). Improvement of estimator for population variance using correlation coefficient and quartiles of the auxiliary variable, J. Stat. Appl. Prob., Vol. 4 (2), p. 259-263.

Downloads

Published

2018-06-14

How to Cite

Cekim, H. O. ., & Kadilar, C. . (2018). GENERALIZED FAMILY OF ESTIMATORS VIA TWO AUXILIARY VARIABLES FOR POPULATION VARIANCE. Journal of Reliability and Statistical Studies, 11(01), 67–81. Retrieved from https://journals.riverpublishers.com/index.php/JRSS/article/view/20903

Issue

Section

Articles