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GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Year 2010, Volume: 39 Issue: 1, 89 - 95, 01.01.2010

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.

References

  • Al-Saleh, M. F. and Al-Omari, A. Multistage ranked set sampling, Statistical Planning and Inference 102, 273–286, 2002.
  • 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.
  • Dell, D. R. and Clutter, J. L. Ranked set sampling theory with order statistics background, Biometrics 28, 545–555, 1972.
  • 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.
  • Hossain, S. S. Non-parametric selected ranked set sampling, Biometrical Journal 43, 97–105, 2001.
  • McIntyre, G. A. A method of unbiased selective sampling, using ranked sets, Australian Journal of Agricaltural Research 3, 385–390, 1952.
  • Muttlak, H. A. Median ranked set sampling, Applied Statistical Science 6, 245–255, 1997.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Takahasi, K. and Futatsuya, M. Ranked set sampling from a finite population, Proceeding of the Institute 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 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 Institude of Statistical Mathematics 21, 249–255, 1968.

GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Year 2010, Volume: 39 Issue: 1, 89 - 95, 01.01.2010

Abstract

References

  • Al-Saleh, M. F. and Al-Omari, A. Multistage ranked set sampling, Statistical Planning and Inference 102, 273–286, 2002.
  • 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.
  • Dell, D. R. and Clutter, J. L. Ranked set sampling theory with order statistics background, Biometrics 28, 545–555, 1972.
  • 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.
  • Hossain, S. S. Non-parametric selected ranked set sampling, Biometrical Journal 43, 97–105, 2001.
  • McIntyre, G. A. A method of unbiased selective sampling, using ranked sets, Australian Journal of Agricaltural Research 3, 385–390, 1952.
  • Muttlak, H. A. Median ranked set sampling, Applied Statistical Science 6, 245–255, 1997.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Takahasi, K. and Futatsuya, M. Ranked set sampling from a finite population, Proceeding of the Institute 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 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 Institude of Statistical Mathematics 21, 249–255, 1968.
There are 15 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

Fikri Gokpinar This is me

Yaprak A. Ozdemir This is me

Publication Date January 1, 2010
Published in Issue Year 2010 Volume: 39 Issue: 1

Cite

APA Gokpinar, F., & Ozdemir, Y. A. (2010). GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING. Hacettepe Journal of Mathematics and Statistics, 39(1), 89-95.
AMA Gokpinar F, Ozdemir YA. GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING. Hacettepe Journal of Mathematics and Statistics. January 2010;39(1):89-95.
Chicago Gokpinar, Fikri, and Yaprak A. Ozdemir. “GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING”. Hacettepe Journal of Mathematics and Statistics 39, no. 1 (January 2010): 89-95.
EndNote Gokpinar F, Ozdemir YA (January 1, 2010) GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING. Hacettepe Journal of Mathematics and Statistics 39 1 89–95.
IEEE F. Gokpinar and Y. A. Ozdemir, “GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING”, Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 1, pp. 89–95, 2010.
ISNAD Gokpinar, Fikri - Ozdemir, Yaprak A. “GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING”. Hacettepe Journal of Mathematics and Statistics 39/1 (January 2010), 89-95.
JAMA Gokpinar F, Ozdemir YA. GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING. Hacettepe Journal of Mathematics and Statistics. 2010;39:89–95.
MLA Gokpinar, Fikri and Yaprak A. Ozdemir. “GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING”. Hacettepe Journal of Mathematics and Statistics, vol. 39, no. 1, 2010, pp. 89-95.
Vancouver Gokpinar F, Ozdemir YA. GENERALIZATION OF INCLUSION PROBABILITIES IN RANKED SET SAMPLING. Hacettepe Journal of Mathematics and Statistics. 2010;39(1):89-95.