DOI QR코드

DOI QR Code

Other approaches to bivariate ranked set sampling

  • 투고 : 2018.02.03
  • 심사 : 2018.04.06
  • 발행 : 2018.05.31

초록

Ranked set sampling, as introduced by McIntyre (Australian Journal of Agriculture Research, 3, 385-390, 1952), dealt with the estimation of the mean of one population. To deal with two or more variables, different forms of bivariate and multivariate ranked set sampling were suggested. For a technique to be useful, it should be easy to implement in practice. Bivariate ranked set sampling, as introduced by Al-Saleh and Zheng (Australian & New Zealand Journal of Statistics, 44, 221-232, 2002), is not easy to implement in practice, because it requires the judgment ranking of each of the combination of the order statistics of the two characteristics. This paper investigates two modifications that make the method easier to use. The first modification is based on ranking one variable and noting the rank of the other variable for one cycle, and do the reverse for another cycle. The second approach is based on ranking of one variable and giving the second variable the same rank (Concomitant Order Statistic) for one cycle and do the reverse for the other cycle. The two procedures are investigated for an estimation of the means of some well-known distributions. It is show that the suggested approaches can be used in practice and can be more efficient than using SRS. A real data set is used to illustrate the procedure.

키워드

참고문헌

  1. Al-Odat MT and Al-Saleh MF (2001). A variation of ranked set sampling, Journal of Applied Statistical Science, 10, 137-146.
  2. Al-Omari AI and Al-Saleh MF (2009). Quartile double ranked set sampling for estimating the population mean, Stochastics and Quality Control, 24, 243-253.
  3. Al-Saleh MF and Ababneh A (2015). Test for accuracy in ranking in moving extreme ranked set sampling, International Journal of Computational and Theoretical Statistics, 2, 67-77. https://doi.org/10.12785/ijcts/020201
  4. Al-Saleh MF and Al-Ananbeh AM (2007). Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable, Statistical Papers, 48, 179-195. https://doi.org/10.1007/s00362-006-0325-8
  5. Al-Saleh MF and Aldarabseh MZ (2017). Inference on the skew normal distribution using ranked set sampling, International Journal of Computational and Theoretical Statistics, 4, 65-76. https://doi.org/10.12785/ijcts/040105
  6. Al-Saleh MF and Al-Hadrami SA (2003a). Parametric estimation for the location parameter for symmetric distributions using moving extremes ranked set sampling with application to trees data, Environmetrics, 14, 651-664. https://doi.org/10.1002/env.610
  7. Al-Saleh MF and Al-Hadrami SA (2003b). Estimation of the mean of the exponential distribution using moving extremes ranked set sampling, Statistical Papers, 44, 367-382. https://doi.org/10.1007/s00362-003-0161-z
  8. Al-Saleh MF and Al-Kadiri MA (2000). Double-ranked set sampling, Statistics & Probability Letters, 48, 205-212. https://doi.org/10.1016/S0167-7152(99)00206-0
  9. Al-Saleh MF and Al-Omari AI (2002). Multistage ranked set sampling, Journal of Statistical Planning and Inference, 102, 273-286. https://doi.org/10.1016/S0378-3758(01)00086-6
  10. Al-Saleh MF and Diab YA (2009). Estimation of the parameters of Downton's bivariate exponential distribution using ranked set sampling scheme, Journal of Statistical Planning and Inference, 139, 277-286. https://doi.org/10.1016/j.jspi.2008.04.021
  11. Al-Saleh MF and Na'amneh AK (2014). Properties of the elements of simple, ranked set and moving extreme ranked set samples, Journal of Applied Statistical Science, 22, 75-85.
  12. Al-Saleh MF and Zheng G (2002a). Estimation of bivariate characteristics using ranked set sampling, Australian & New Zealand Journal of Statistics, 44, 221-232. https://doi.org/10.1111/1467-842X.00224
  13. Al-Saleh MF and Zheng G (2002b). Modified maximum likelihood estimators based on ranked set sampling, Annals of the Institute of Statistical Mathematics, 54, 641-658. https://doi.org/10.1023/A:1022475413950
  14. Downton F (1970). Bivariate exponential distribution in reliability theory, Journal of the Royal Statistical Society. Series B (Methodological), 32, 408-417.
  15. Fery JC (2007). New imperfect ranking models for ranked set sampling, Journal of Statistical Planning and Inference, 137, 1433-1445. https://doi.org/10.1016/j.jspi.2006.02.013
  16. Hanandeh AA and Al-Saleh MF (2013). Inference on Downton's bivariate exponential distribution based on moving extreme ranked set sampling, Austrian Journal of Statistics, 42, 161-179.
  17. McIntyre GA (1952). A method of unbiased selective sampling, using ranked set, Australian Journal of Agriculture Research, 3, 385-390. https://doi.org/10.1071/AR9520385
  18. Norris RC, Patil GP, and Sinha AK (1995). Estimation of multiple characteristics by ranked set sampling methods, Coenoses, 10, 95-111.
  19. Patil GP, Sinha AK, and Taillie C (1994). Ranked set sampling for multiple characteristics, International Journal of Ecology and Environmental Sciences, 20, 357-373.
  20. Pordan M (1968). Forest Biometric, Pergamum Press, London.
  21. Ridout MS (2003). On ranked set sampling for multiple characteristics, Environmental and Ecological Statistics, 10, 255-262. https://doi.org/10.1023/A:1023694729011
  22. Samawi HM and Al-Saleh MF (2007) On bivariate ranked set sampling for ratio and regression estimators, International Journal of Modeling and Simulation, 27, 299-305. https://doi.org/10.1080/02286203.2007.11442430
  23. Scheaffer RL, Mendenhall W, Ott RL, and Gerow KG (2011). Elementary Survey Sampling (7th ed), Duxbury Press, London.
  24. Stokes SL (1977). Ranked set sampling with concomitant variables, Communications in Statistics-Theory and Methods, 6, 1207-12011. https://doi.org/10.1080/03610927708827563
  25. Takahasi K and Wakimoto K (1968). On unbiased estimates of the population mean based on the sample stratified by means of ordering, Annals of the Institute of Statistical Mathematics, 20, 1-31. https://doi.org/10.1007/BF02911622
  26. Yang SS (1977). General distribution theory of the concomitant of order statistics, The Annals of Statistics, 5, 996-1002. https://doi.org/10.1214/aos/1176343954
  27. Zamanzade E and Mohammadi M (2016). Some modified mean estimators in ranked set sampling using a covariate, Journal of Statistical Theory and Applications, 15, 142-152. https://doi.org/10.2991/jsta.2016.15.2.4