Efficient estimation of population median using supplementary variable

Document Type : Article

Authors

1 Department of Statistics, University of Peshawar, Peshawar, Pakistan

2 Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

Abstract

In this paper, we propose an exponential cum ratio-product type estimators for population median (M_y) under simple random sampling scheme (SRS). The expressions of bias and mean square error (MSE) are obtained up to first order of approximation. The proposed estimators is more efficient as compared to all other considered estimators under certain conditions. Both numerical and simulation studies show that the proposed estimators perform better as compared to all other considered estimators. Four real data sets and simulation studies are carried out to observe the performances of the estimators. It is observed that the proposed estimators is perform more efficient in all situations.

Keywords


References:
1. Gross, S.T., Median Estimation in Sample Surveys, Survey Research Method Section, American Statistical Association, pp. 181-184 (1980).
2. Kuk, Y.C.A. and Mak, T.K. "Median estimation in the presence of auxiliary information", Journal of Royal Statistical Society, B, 51, pp. 261-269 (1989).
3. Singh, S., Joarder, A.H., and Tracy, D.S. "Median estimation using double sampling", Australian and Newzeland Journal of Statistics, 43(1), pp. 33-46 (2001).
4. Singh, H.P., Singh, S., and Joarder, A.H. "Estimation of population median when mode of an auxiliary variable is known", J. Statist. Res., 37(1), pp. 57-63 (2003).
5. Singh, H.P., Sidhu, S.S., and Singh, S. "Median estimation with known interquartile range of auxiliary variable", Int. J. Appl. Math. Statist., 4, pp. 68-80 (2006).
6. Singh, S., Singh, H.P., Upadhyaya, L.N. "Chain ratio and regression type estimators for median estimation in survey sampling", Statistical Papers, 48(1), pp. 23-46 (2007).
7. Gupta, S., Shabbir, J., and Ahmad, S. "Estimation of median in two phase sampling using two auxiliary variables", Communications in Statistics-Theory and Methods, 37(11), pp. 1815-1822 (2008).
8. Aladag, S. and Cingi, H. "New estimators for the population median in simple random sampling", Proceedings of the Tenth Islamic Countries Conference on Statistical Sciences (ICCS-X), Held in New Cairo, Egypt, pp. 375-383 (2009).
9. Singh, H.P. and Solanki R.S. "Some classes of estimators for the population median using auxiliary information", Communications in Statistics-Theory and Methods, 42, pp. 4222-4238 (2013).
10. Jhajj, H.S., Kaur, H., and Walia, G. "Efficient family of ratio-product type estimators of median", Model Assisted Statistics and Applications, 9, pp. 277-282 (2014).
11. Sharma, P. and Singh, R. "Generalized class of estimators for population median using auxiliary information", Hacettepe Journal of Mathematics and Statistics, 44(2), pp. 443-453 (2015).
12. Aladag, S. and Cingi, H. "Improvement in estimating the population median in simple random sampling and stratified random sampling using auxiliary information", Communications in Statistics-Theory and Methods, 44, pp. 1013-1032 (2015).
13. Shabbir, J. and Gupta, S. "Improved estimation of finite population median under two-phase sampling when using two auxiliary variables", Scientia Iranica, 22(3), pp. 1271-1277 (2015).
14. Shabbir, J. and Gupta, S. "A generalized class of difference-type estimator for population median in survey sampling", Hacettepe Journal of Mathematics and Statistics, 46(5), pp. 1015-1028 (2017).
15. Solanki, R.S. and Singh, H.P. "Some classes of estimators for median estimation in survey sampling", Communications in Statistics-Theory and Methods, 44(7), pp. 1450-1465 (2015).
16. Enang, E.I., Etuk, S.I., Ekpenyong, E.J., and Akpan, V.M. "An alternative exponential estimator of population median", International Journal of Statistics and Economics, 17(3), pp. 85-97 (2016).
17. Jhajj, H.S., Kaur, H., and Jhajj, P. "Efficient family of estimators of median using twophase sampling design", Communications in Statistics-Theory and Methods, 45(15), pp. 4325-31 (2016).
18. Koyuncu, N. "Improved ratio estimation of population mean under median and neoteric ranked set sampling",AIP Conference Proceedings, AIP Publishing, 1863(1), pp. 1200-1204 (2017).
19. Irfan, M., Javed, M., and Lin, Z. "Efficient ratiotype estimators of finite population mean based on correlation coefficient", Scientia Iranica, 25(4), pp.2361-2372 (2018).
20. Yadav, D.K., Shukla, A.K., Tomer, S., and Kumar, B. "Predictive estimation of finite population mean using coefficient of kurtosis and median of an auxiliary variable under simple random sampling scheme", International Journal of Mathematical Archive EISSN 2229-5046, 9(5), pp. 137-43 (2018).
21. Bandyopadhyay, A., Singh, G.N., and Das, S. "Estimation of population median in presence of non-response under two-phase sampling", Sri Lankan Journal of Applied Statistics, 17(2), pp. 112-133 (2018).
22. Javed, M., Irfan, M., and Pang, T. "Hartley-Ross type unbiased estimators of population mean Using two auxiliary variables", Scientia Iranica, E, 26(6), pp. 3835-3845 (2019). DOI: 10.24200/SCI.2018.5648.1397.
23. Baig, A., Masood, S., and Tarray, T.A. "Improved class of difference-type estimators for population median in survey sampling", Communications in Statistics-Theory and Methods, 49(23), pp. 5778-5793 (2019). DOI: 10.1080/03610926.2019.1622017.
24. Muneer, S., Khalil, A., Shabbir, J., and Narjis, G. "A new improved ratio-product type exponential estimator of finite population variance using auxiliary information", Journal of Statistical Computation and Simulation, 88(16), pp. 3179-3192 (2018).
25. "PDS Punjab Development Statistics", Bureau of Statistics, Government of the Punjab, Lahore, Pakistan,pp. 114-116 (2012).
26. Amir, M., Shabri, A., and Ishaq, M. "Improving forecasting accuracy of crude oil price using decomposition ensemble model with reconstruction of IMFs based on ARIMA model", Malaysian Journal of Fundamental and Applied Sciences, 14(4), pp. 471-483 (2018).