SIMPLE COMPUTATIONAL FORMULAS FOR INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Abstract

SIMPLE COMPUTATIONAL FORMULAS FOR INCLUSION PROBABILITIES IN RANKED SET SAMPLING

Abstract

In this study, we derived new formulations for the first and secondorder inclusion probabilities of a ranked set sample in a finite populationsetting. G¨okpınar and ¨Ozdemir (2010) developed a formula to calculatethe first order inclusion probabilities. However, the formula given inthis study is much easier than the one given by G¨okpınar and ¨Ozdemir(2010). Second order inclusion probabilities are computed based onthe formulas which are used for the calculation of first order inclusionprobabilities. Also, we give a numerical example to show the calculationof the formulas and Matlab codes which give first and second inclusionprobabilities for any set and population sizes.

Keywords

• Ranked Set Sampling, First Order Inclusion Probability, Second OrderInclusion Probability, Finite Population Setting.,2000 AMS Classification: 62D05

References

1. Al Saleh, M.F. and Samawi H.M. A note on inclusion probability in ranked set sampling and some of its variations, Test 16, 198-209, 2007.
2. Al-Saleh, M.F. and Al-Shrafat K. Estimation of average milk yield using ranked set sampling, Environmetrics 12(4), 395-399, 2000.
3. Bouza, C. N. Sampling using ranked sets: Concepts, results and perspectives, Revista Investigaci´ on Operacional 26 (3), 275-292, 2005.
4. Deshpande, J.V., Frey, J., Ozt¨ urk, O. Nonparametric ranked-set sampling confidence intervals for quantiles of a finite population, Environmental and Ecological Statistics 13, 25-40, 200 Johnson, G.D., Myers, W.L. Potential of ranked-set sampling for disaster assessment. IUFRO S4.02 Conference on Inventory and Management Techniques in the Context of Catastrophic Events, 1993.
5. G¨ okpınar, F., ¨ Ozdemir, Y. A. Generalization of the inclusion probabilities in ranked set sampling, Hacettepe Journal of Mathematics and Statistics 39(1), 89-95, 2010.
6. G¨ okpınar, F., ¨ Ozdemir, Y. A. Horvitz-Thompson Estimator Of The Population Mean Using Inclusion Probabilities Of Ranked Set Sampling, Communications In Statistics: Theory and Methods 41(6), 1029-1039, 2011.
7. Jafari Jozani, M. and Johnson, B.C. Design based estimation for ranked set sampling in finite populations, Environ. Ecol. Stat. 18, 663-685, 2011.
8. McIntyre, G.A. A method of unbiased selective sampling, using ranked sets, Australian Journal of Agricaltural Research 3, 385-390, 1952.

9. ¨ Ozdemir, Y.A. and G¨ okpınar, F. A Generalized formula for inclusion probabilities in ranked set sampling, Hacettepe University Bulletin of Natural Sciences & Engineering Series B: Mathematics & Statistics 36, 89-99, 2007.
10. ¨ Ozdemir, Y.A. and G¨ okpınar, F. A new Formula for inclusion probabilities in median ranked set Sampling, Communications In Statistics:Theory and Methods. 37, 2022-2033, 2008.