GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Abstract

In a finite population setting, Ozdemir and Gokpinar (A Generalized formula for inclusion probabilities in ranked set sampling, Hacettepe J. Math. Stat 36 (1), 89–99, 2007) obtained a generalized formula for inclusion probabilities in Ranked Set Sampling for all set sizes when the cycle size is 1. This paper extends the generalized formula for inclusion probabilities to all set and cycle sizes. We also support this formula with a numerical example.

Keywords

• Finite population,Inclusion probability,Ranked set sampling,Simple random sampling,2000 AMS Classification: Primary 62 D 05; Secondary 65 C 60

GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Abstract

References

1. Al-Saleh, M. F. and Al-Omari, A. Multistage ranked set sampling, Statistical Planning and Inference 102, 273–286, 2002.
2. Al-Saleh, M. F. and Samawi H. M. A note on inclusion probability in ranked set sampling and some of its variationsTest 16 (1), 198–209, 2007.
3. Dell, D. R. and Clutter, J. L. Ranked set sampling theory with order statistics background, Biometrics 28, 545–555, 1972.
4. Deshpande, J. V., Frey, J. and Ozt¨urk, O. Nonparametric ranked-set sampling confidence intervals for quantiles of a finite population, Environmental and Ecological Statistics 13, 25–40, 2006.
5. Hossain, S. S. Non-parametric selected ranked set sampling, Biometrical Journal 43, 97–105, 2001.
6. McIntyre, G. A. A method of unbiased selective sampling, using ranked sets, Australian Journal of Agricaltural Research 3, 385–390, 1952.
7. Muttlak, H. A. Median ranked set sampling, Applied Statistical Science 6, 245–255, 1997.
8. Ozdemir, Y. A. and Gokpinar, F. A Generalized formula for inclusion probabilities in ranked set sampling, Hacettepe J. Math. Stat. 36 (1), 89–99, 2007.

9. Ozdemir, Y. A. and Gokpinar, F. A new formula for inclusion probabilities in median ranked set sampling, Communications in Statistics: Theory and Methods 37, 2022–2033, 2008.
10. Ozt¨urk, O., Bilgin, O. C. and Wolfe, D. A. Estimation of population mean and variance in flock management: A ranked set sampling approach in a finite population setting, Journal of Statistical Computation and Simulation 75, 905–919, 2005.
11. Patil, G. P., Sinha, A. K. and Taillie, C. Finite population correction for ranked set sampling, Annals of The Institute of Statistical Mathematics 47, 621–636, 1995.
12. Samawi, H. M., Ahmed, M. S. and Abu-Dayyeh, W. Estimation the population mean using extreme ranked set sampling, Biometrical Journal 38, 577–586, 1996.
13. Takahasi, K. and Futatsuya, M. Ranked set sampling from a finite population, Proceeding of the Institute Statistical Mathematics 36, 55–68, 1988.
14. Takahasi, K. and Futatsuya, M. Dependence between order statistics in samples from finite population and its application to ranked set sampling, Proceeding of the Institute Statistical Mathematics 50, 49–70, 1998.
15. 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.