A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling

Y. A. Özdemir; F. Gökpınar

Research Article

A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling

Year 2007, Volume: 36 Issue: 1, 89 - 99, 01.01.2007

Y. A. Özdemir F. Gökpınar

Abstract

References

Al Saleh, M. F. and Samawi, H. M. A note on inclusion probability in ranked set sampling and some of its variations. Test.(In Press)
Dell, D. R. and Clutter, J. L. Ranked set sampling theory with order statistics background, Biometrics 28, 545–555, 1972.
McIntyre, G. A. A method of unbiased selective sampling, using ranked sets, Australian Jour- nal of Agricultural Research 3, 385–390, 1952.
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.
¨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.
Takahasi, K. and Futatsuya, M. Ranked set sampling from a finite population, Proceedings of the institute of statistical mathematics 36, 55–68, 1988.
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 of statistical mathematics 50, 49–70, 1998.
Takahasi, K. and Wakimoto, K. On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics 21, 249–255, 1968.

A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling

Year 2007, Volume: 36 Issue: 1, 89 - 99, 01.01.2007

Y. A. Özdemir F. Gökpınar

Abstract

In probability sampling, the inclusion probability of any element in the
population is the probability of the element which will be chosen in
the sample. Al-Saleh and Samawi (A note on inclusion probability in
ranked set sampling and some of its variations, Test., in press) introduced inclusion probabilities in ranked set sampling for sample sizes 2
and 3. In this paper we gave a generalized formula of these inclusion
probabilities for any sample size. Also we compare these probabilities
with simple random samplings for various given samples and population
sizes.

Keywords

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

References

Al Saleh, M. F. and Samawi, H. M. A note on inclusion probability in ranked set sampling and some of its variations. Test.(In Press)
Dell, D. R. and Clutter, J. L. Ranked set sampling theory with order statistics background, Biometrics 28, 545–555, 1972.
McIntyre, G. A. A method of unbiased selective sampling, using ranked sets, Australian Jour- nal of Agricultural Research 3, 385–390, 1952.
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.
¨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.
Takahasi, K. and Futatsuya, M. Ranked set sampling from a finite population, Proceedings of the institute of statistical mathematics 36, 55–68, 1988.
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 of statistical mathematics 50, 49–70, 1998.
Takahasi, K. and Wakimoto, K. On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics 21, 249–255, 1968.

There are 8 citations in total.

Details

Primary Language	English
Subjects	Statistics
Journal Section	Mathematics
Authors	Y. A. Özdemir This is me F. Gökpınar This is me
Publication Date	January 1, 2007
Published in Issue	Year 2007 Volume: 36 Issue: 1

Cite

APA	Özdemir, Y. A., & Gökpınar, F. (2007). A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics, 36(1), 89-99.
AMA	Özdemir YA, Gökpınar F. A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics. January 2007;36(1):89-99.
Chicago	Özdemir, Y. A., and F. Gökpınar. “A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 36, no. 1 (January 2007): 89-99.
EndNote	Özdemir YA, Gökpınar F (January 1, 2007) A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics 36 1 89–99.
IEEE	Y. A. Özdemir and F. Gökpınar, “A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling”, Hacettepe Journal of Mathematics and Statistics, vol. 36, no. 1, pp. 89–99, 2007.
ISNAD	Özdemir, Y. A. - Gökpınar, F. “A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics 36/1 (January 2007), 89-99.
JAMA	Özdemir YA, Gökpınar F. A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics. 2007;36:89–99.
MLA	Özdemir, Y. A. and F. Gökpınar. “A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling”. Hacettepe Journal of Mathematics and Statistics, vol. 36, no. 1, 2007, pp. 89-99.
Vancouver	Özdemir YA, Gökpınar F. A Generalized Formula for Inclusion Probabilities in Ranked Set Sampling. Hacettepe Journal of Mathematics and Statistics. 2007;36(1):89-9.