Improved Ratio Estimators of Variance Based on Robust Measures

Document Type : Article

Authors

1 Department of Statistics, Government College University, Faisalabad, 38000, Pakistan.

2 Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, 47040, Pakistan.

3 Department of Statistics, University of Sargodha, Sargodha, 40100, Pakistan.

4 Department of Mathematics and Statistics, King Fahad University of Petroleum and Minerals, Dhahran, 31261, Saudi, Arabia.

Abstract

In this study, we develop some new estimators for estimating the population variance by utilizing the information on midrange and inter decile range of an auxiliary variable. A general class of estimators is also suggested. The derivations of the bias and the mean squared error are presented. Conditions are determined to verify the efficiency of the proposed estimators over existing estimators considered in this study. An Empirical study is also provided for illustration and verification.  Moreover, a robust study is also carried out to evaluate the performance of proposed estimators as compared to existing estimators in case of extreme values. From the theoretical and empirical study, it is found that the suggested estimators perform more efficiently as compared to the existing estimators considered in this study.

Keywords

Main Subjects


1. Neyman, J. Contribution to the theory of sampling human populations", Journal of American Statistical Association, 33, pp. 101-116 (1938). 2. Cochran, W.G. The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce", Journal of Agricultural Sciences, 30, pp. 262-275 (1940). 3. Isaki, C.T. Variance estimation using auxiliary information", Journal of the American Statistical Association, 78, pp. 117-123 (1983). 4. Prasad, B. and Singh, H.P. Some improved ratio type estimators of _nite population variance in sample surveys", Communications in Statistics-Theory and Methods, 19, pp. 1127-1139 (1990). M. Abid et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 2484{2494 2493 5. Arcos, A., Rueda, M., Martinez, M.D., Gonzalez, S., and Roman, Y. Incorporating the auxiliary information available in variance estimation", Applied Mathematics and Computation, 160, pp. 387-399 (2005). 6. Agarwal, M.C. and Sithapit, A.B. Unbiased ratio type estimation", Statistics and Probability Letters, 25, pp. 361-364 (1995). 7. Ahmed, M.S., Rahman, M.S., and Hossain, M.I. Some competitive estimators of _nite population variance using multivariate auxiliary information", Information and Management Sciences, 11(1), pp. 49-54 (2000). 8. Arcos, A. and Rueda, M. Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator", Metrika, 45, pp. 171-178 (1997). 9. Al-Jararha, J. and Al-Haj Ebrahem, M. A ratio estimator under general sampling design", Australian Journal of Statistics, 41(2), pp. 105-115 (2012). 10. Bhushan, S. Some e_cient sampling strategies based on ratio type estimator", Electronic Journal of Applied Statistical Analysis, 5(1), pp. 74-88 (2012). 11. Das, A.K. and Tripathi, T.P. Use of auxiliary information in estimating the _nite population variance", Sankhy~a, 40, pp. 139-148 (1978). 12. Cebri_an, A. and Garc_a, M. Variance estimation using auxiliary information: An almost unbiased multivariate ratio estimator", Metrika, 45(1), pp. 171-178 (1997). 13. Gupta, S. and Shabbir, J. Variance estimation in simple random sampling using auxiliary information", Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, 37(1), pp. 57-67 (2008). 14. Reddy, V.N. On Transformed ratio method of estimation", Sankhy~a, 36, pp. 59-70 (1974). 15. Singh, H.P., Upadhyaya, U.D., and Namjoshi, U.D. Estimation of _nite population variance", Current Science, 57(24), pp. 1331-1334 (1988). 16. Singh, H.P., Chandra, P., and Singh, S. Variance estimation using multi-auxiliary information for random non-response in survey sampling", Statistica, 63, pp. 23-40 (2003). 17. Upadhyaya, L.N. and Singh, H.P. Almost unbiased ratio and product-type estimators of _nite population variance in sample surveys", Statistics in Transition, 7(5), pp. 1087-1096 (2006). 18. Wolter, K.M., Introduction to Variance Estimation, Springer-Verlag, Berlin (1985). 19. Upadhyaya, L.N. and Singh, H.P. An estimator of population variance that utilizes the kurtosis of an auxiliary variable in sample surveys", Vikram Mathematical Journal, 19, pp. 14-17 (1999). 20. Kadilar, C. and Cingi, H. Improvement in variance estimation using auxiliary information", Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, 35(1), pp. 111- 115 (2006). 21. Subramani, J. and Kumarapandiyan, G. Variance estimation using median of the auxiliary variable", International Journal of Probability and Statistics, 1(3), pp. 36-40 (2012). 22. Subramani, J. and Kumarapandiyan, G. Variance estimation using quartiles and their functions of an auxiliary variable", International Journal of Statistics and Applications, 2(5), pp. 67-72 (2012). 23. Subramani, J. and Kumarapandiyan, G. Estimation of variance using deciles of an auxiliary variable", Proceedings of International Conference on Frontiers of Statistics and Its Applications, 33, pp. 143-149 (2012). 24. Subramani, J. and Kumarapandiyan, G. Estimation of variance using known coe_cient of variation and median of an auxiliary variable", Journal of Modern Applied Statistical Methods, 12(1), pp. 58-64 (2013). 25. Khan, M. and Shabbir, J. A ratio type estimators for the estimation of population variance using quartiles of an auxiliary variable", Journal of Statistics Applications and Probability, 2(3), pp. 319-325 (2013). 26. Ferrell, E.B. Control charts using midranges and medians", Industrial Quality Control, 9, pp. 30-34 (1953). 27. Rana, S., Siraj-Ud-Doulah, Md., Midi, H., and Imon, A.H.M.R. Decile mean: A new robust measure of central tendency", Chiang Mai Journal of Science, 39(3), pp. 478-485 (2012). 28. Abid, M., Abbas, N., Nazir, H.Z., and Lin, Z. Enhancing the mean ratio estimators for estimating population mean using non-conventional location parameters", Revista Colombiana de Estadistica, 39(1), pp. 63-79 (2016). 29. Abid, M., Abbas, N., and Riaz, M. Improved modi_ed ratio estimators of population mean based on deciles", Chiang Mai Journal of Science, 43(1), pp. 1311-1323 (2016). 30. 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), pp. 353-367 (2016). 31. Abid, M., Sherwani, R.A.K., Abbas, N., and Raza, M.A. Some Improved Modi_ed Ratio Estimators Based on Decile Mean of an Auxiliary Variable", Pakistan Journal of Statistics and Operation Research, 12(4), pp. 787-797 (2016). 32. Murthy, M.N., Sampling Theory and Methods, Statistical Publishing Society, Calcutta, India (1967). 2494 M. Abid et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 2484{2494 33. Cochran, W.G., Sampling Techniques, John Wiley and Sons, New York (1977). 34. IBEP (2004). http://www.os servatorio nazionaleri-_uti.it/elencodocpub.asp?A tipodoc=6