COMPARING THE EFFICIENCY OF THE ESTIMATORS FOR THE POPULATION MEAN UNDER DIFFERENT DESIGNS OF RANKED SET SAMPLING

Abstract

ABSTRACT

Ranked set sampling is a cost efficient sampling technique when actually measuring sampling units is difficult but ranking them is relatively easy. The mean of the usual balanced ranked set sample is more efficient as an estimator of the population mean than the mean of a simple random sample. In this study, different ranked set sampling plans are considered for estimating of population mean. These estimators are theoretical compared in terms of relative efficiency under uniform, normal, exponential and weibull distribution.

Keywords

• Key Words: Ranked set sampling, Relative Efficiency, Mean Square Error

Abstract

Sıralı küme örneklemesi, örnekleme birimlerini ölçmek zor ancak bunları sıralamak daha kolay olduğu durumda maliyet etkili bir örnekleme tekniğidir. Yığın ortalamasının tahmin edicisi olarak, sıralı küme örneğinin ortalaması, basit tesadüfi örneğin ortalamasından daha etkindir. Bu çalışmada, yığın ortalamasının tahmini için farklı sıralı küme örneklemesi tasarımları incelenmiştir. Bu tahmin ediciler tekdüze, normal, üstel ve weibull dağılımları altında göreli etkinlikleri bakımından teorik olarak karşılaştırılmıştır

Keywords

• Sıralı Küme örneklemesi, Göreli Etkinlik, Ortalama Hata Kare

References

1. Al-Saleh M.F., “On the totality of ranked set sampling”, Applied Mathematics and Computation, Inpress , (2003)
2. Arnold, B., Balakrishnan,N. and Nagaraja,H.N., “A First Course in Order Statistics”,John Wiley,New York. (1993)
3. Balakrishnan,N. and Cohen,C. “Order Statistics and Inference:Estimation Methods”, Academic Press ,San Diego. (1991)
4. David,H.A. “Order Statistics”, John Wiley, New York., (1970)
5. Dell,D.R. and Clutter, J.L. “ Ranked set sampling theory with order statistics background”.Biometrics, 28, 545-555, (1972).
6. McIntyre, G.A. “A method of unbiased selective sampling, using ranked sets.”Australian Journal of Agricaltural Research, 3, 385-390 (1952).
7. Patil,G.P.,Sinha, A.K. and Taillie,C. “ Ranked set sampling. A Handbook of Statistics, vol.12, pp 167-200, (1994).
8. Sinha B.K., Sinha B.K. and Purkayasta , S., “On some aspects of ranked set sampling for estimation of normal and exponential parameters.” Statistical Desicions, 14, 223-240, (1996).

9. Stokes, L.S. “Estimation of variance using judgement ordered ranked set samples” Biometrics, 36, 35-42, (1980).
10. Takahasi ,K. And Wakimoto, K. “On Unbiased estimates of the population mean based on the sample stratified by means of ordering” Annals of The Institude of Statistical Mathematics. 21,249-255 (1968).