1. NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING Sibel Al Hacettepe University, Department of Statistics, Ankara, Turkey Email:sibelal@hacettepe.edu.tr Hulya Cingi Hacettepe University, Department of Statistics, Ankara, Turkey Email:hcingi@hacettepe.edu.tr

2. Outline Introduction Median estimators in SRS ▫ Gross (1980) ▫ Kuk and Mak (1989) ▫ Singh, Singh and Puertas(2003) Suggested median estimators ▫ Proposed 1 ▫ Proposed 2 ▫ Proposed 3 ▫ A family of estimators Efficiency comparisons Numerical comparisons Conclusion 6/14/2015 2

3. Introduction Median is a measure which divides the population into exactly two equal parts and it is denoted by M Y. 6/14/2015 3

4. Median Estimators in SRS Gross (1980) 6/14/2015 4

5. Median Estimators in SRS Kuk and Mak (1989) 6/14/2015 5

6. Median Estimators in SRS Kuk and Mak (1989) 6/14/2015 6

7. Median Estimators in SRS Singh, Singh and Puertas (2003) 6/14/2015 7

8. Suggested Median Estimators Proposed 1 6/14/2015 8

9. Suggested Median Estimators Proposed 1 6/14/2015 9

10. Suggested Median Estimators Proposed 2 6/14/2015 10

11. Suggested Median Estimators Proposed 2 6/14/2015 11

12. Suggested Median Estimators Proposed 2 6/14/2015 12

13. Suggested Median Estimators Proposed 3 6/14/2015 13

14. Suggested Median Estimators Proposed 3 6/14/2015 14

15. Suggested Median Estimators A Family of Estimators 6/14/2015 15

16. Suggested Median Estimators A Family of Estimators 6/14/2015 16

17. Efficiency Comparisons 6/14/2015 17

18. Efficiency Comparisons 6/14/2015 18

19. Efficiency Comparisons 6/14/2015 19

20. Numerical Comparisons Data sets and statistics 6/14/2015 20

21. Members of the proposed family of estimators 6/14/2015 21

22. Mean Square Errors of the Estimators 6/14/2015 22

23. Conclusion We suggest new median estimators using a known constant. We theoretically show that these estimators are always more efficient than classical estimators. In the numerical examples, the theoretical results are also supported. In future works, we hope to adapt the estimators proposed in this study to stratified random sampling. 6/14/2015 23

24. References 1.Chen, Z., Bai, Z., Sinha, B.K. (2004). Ranked Set Sampling Theory and Applications. New York: Springer-Verlag. 2.Cingi, H., Kadilar, C., Kocberber, G. (2007). Examination of educational opportunities at primary and secondary schools in Turkey suggestions to determined issues. TUBITAK, SOBAG, 106K077. http://yunus.hacettepe.edu.tr/~hcingi/http://yunus.hacettepe.edu.tr/~hcingi/ 3.Gross, T.S. (1980). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Ass. 181-184. 4.Kuk, A.Y.C., Mak, T.K. (1989). Median estimation in the presence of auxiliary information. Journal of the Royal Statistical Society Series, B, 51, 261-269. 5.Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics Theory Methods, 18, 379-392. 6.Searls, D.T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 1225–1226. 7.Singh, S. (2003). Advanced Sampling Theory with Applications: How Michael ‘selected’ Amy. London: Kluwer Academic Publishers. 8.Singh, H.P., Singh, S., Joarder, A.H. (2003a). Estimation of population median when mode of an auxiliary variable is known. Journal of Statistical Research, 37, 1, 57-63. 9. Singh, H.P., Singh, S., Puertas, S.M. (2003b). Ratio type estimators for the median of finite populations. Allgemeines Statistisches Archiv, 87, 369-382. 6/14/2015 24

25. NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING Sibel Al Hacettepe University, Department of Statistics, Ankara, Turkey Email:sibelal@hacettepe.edu.tr Hulya Cingi Hacettepe University, Department of Statistics, Ankara, Turkey Email:hcingi@hacettepe.edu.tr