NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING Sibel Al Hacettepe University, Department of Statistics, Ankara, Turkey Hulya Cingi Hacettepe University, Department of Statistics, Ankara, Turkey

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

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

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

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

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

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

Suggested Median Estimators Proposed 1 6/14/2015 8

Suggested Median Estimators Proposed 1 6/14/2015 9

Suggested Median Estimators Proposed 2 6/14/

Suggested Median Estimators Proposed 2 6/14/

Suggested Median Estimators Proposed 2 6/14/

Suggested Median Estimators Proposed 3 6/14/

Suggested Median Estimators Proposed 3 6/14/

Suggested Median Estimators A Family of Estimators 6/14/

Suggested Median Estimators A Family of Estimators 6/14/

Efficiency Comparisons 6/14/

Efficiency Comparisons 6/14/

Efficiency Comparisons 6/14/

Numerical Comparisons Data sets and statistics 6/14/

Members of the proposed family of estimators 6/14/

Mean Square Errors of the Estimators 6/14/

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/

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, 106K Gross, T.S. (1980). Median estimation in sample surveys. Proc. Surv. Res. Meth. Sect. Amer. Statist. Ass 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, Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics Theory Methods, 18, Searls, D.T. (1964). The utilization of a known coefficient of variation in the estimation procedure. Journal of the American Statistical Association, 59, 1225– 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, Singh, H.P., Singh, S., Puertas, S.M. (2003b). Ratio type estimators for the median of finite populations. Allgemeines Statistisches Archiv, 87, /14/

NEW ESTIMATORS FOR THE POPULATION MEDIAN IN SIMPLE RANDOM SAMPLING Sibel Al Hacettepe University, Department of Statistics, Ankara, Turkey Hulya Cingi Hacettepe University, Department of Statistics, Ankara, Turkey