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Abstract

In this paper, permutation test of comparing two-independent samples is investigated in the context of extreme ranked set sampling (ERSS). Three test statistics are proposed. The statistical power of these new test statistics are evaluated numerically. The results are compared with the statistical power of the classical independent two-sample $t$-test, Mann-Whitney $U$ test, and the usual two-sample permutation test under simple random sampling (SRS). In addition, the method of computing a confidence interval for the two-sample permutation problem under ERSS is explained. The performance of this method is compared with the intervals obtained by SRS and Mann-Whitney procedures in terms of empirical coverage probability and expected length. The comparison shows that the proposed statistics outperform their counterparts. Finally, the application of the proposed statistics is illustrated using a real life example.

Keywords

Permutation test Extreme ranked set sampling Power level Type I error probability

Article Details

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Author Biographies

Monjed H. Samuh, Associate Professor of Statistics, Applied Mathematics and Physics Department, Palestine Polytechnic University Hebron - PALESTINE

Dr. Monjed H. Samuh is an associate professor of Statistics at the department of Applied Mathematics and Physics, Palestine Polytechnic University, Palestine. He obtained his PhD in Statistics from Padua University, Italy in 2012. He published about 20 research papers in peer-reviewed journals and attended 14 international conferences. His research interests include Permutation Testing, Sampling Theory, and Distribution Theory. Dr. Samuh is currently the head of Applied Mathematics and Physics Department at Palestine Polytechnic University.

Ridwan A. Sanusi, Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong, China

Ridwan Adeyemi SANUSI received his Ph.D. from the department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong. During his PhD program, he was a visiting scholar at the department of Industrial Engineering, Tsinghua University, Beijing, China. Prior to these, he received his M.Sc. in Applied Statistics from King Fahd University of Petroleum & Minerals, Saudi Arabia, and B.Sc. in Statistics (First Class Honors) from University of Ibadan, Nigeria. His research areas are applied statistics, industrial engineering, nonparametric statistics, statistical process control, among others. He has published in top journals, presented in international conferences, and has few international awards to his name. 
How to Cite
Samuh, M. H., & Sanusi, R. A. (2020). Permutation Tests for Two-sample Location Problem Under Extreme Ranked Set Sampling. Pakistan Journal of Statistics and Operation Research, 16(2), 387-408. https://doi.org/10.18187/pjsor.v16i2.2746
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References

  1. Abu-Dayyeh, W. A., Al-Subh, S. A., and Muttlak, H. A. (2004). Logistic parameters estimation using simple random sampling and ranked set sampling data. Applied Mathematics and Computation, 150(2):543-554.
  2. Adatia, A. (2000). Estimation of parameters of the half-logistic distribution using generalized ranked set sampling. Computational Statistics & Data Analysis, 33(1):1-13.
  3. Al-Saleh, M. F. and Al-Kadiri, M. A. (2000). Double-ranked set sampling.Statistics & Probability Letters, 48(2):205-212.
  4. Al-Saleh, M. F. and Al-Omari, A. I. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inference, 102(2):273-286.
  5. Al-Saleh, M. F. and Diab, Y. A. (2009). Estimation of the parameters of downton's bivariate exponential distribution using ranked set sampling scheme. Journal of Statistical Planning and Inference, 139(2):277 286.
  6. Amro, L. and Samuh, M. H. (2017). More powerful permutation test based on multistage ranked set sampling.Communications in Statistics - Simulation and Computation, 46(7):5271-5284.
  7. Bhoj, D. S. (1997). Estimation of parameters of the extreme value distribution using ranked set sampling. Communications in Statistics-Theory and Methods, 26(3):653-667.
  8. Bhoj, D. S. and Ahsanullah, M. (1996). Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52(2):685-694.
  9. Bohn, L. L. and Wolfe, D. A. (1992). Nonparametric two-sample procedures for ranked-set samples data. Journal of the American Statistical Association, 87(418):552-561.
  10. Bohn, L. L. and Wolfe, D. A. (1994). The effect of imperfect judgment rankings on properties of procedures based on the ranked-set samples analog of the Mann-Whitney-Wilcoxon statistic. Journal of the American Statistical Association, 89(425):168-176.
  11. Chacko, M. and Thomas, P. Y. (2007). Estimation of a parameter of bivariate pareto distribution by ranked set sampling. Journal of Applied Statistics, 34(6):703-714.
  12. Chacko, M. and Thomas, P. Y. (2008). Estimation of a parameter of morgenstern type bivariate exponential distribution by ranked set sampling. Annals of the Institute of Statistical Mathematics, 60(2):301-318.
  13. Fisher, R. A. (1934). Statistical Methods for Research Workers. Oliver and Boyd, Edinburgh.
  14. Koti, K. M. and Jogesh Babu, G. (1996). Sign test for ranked-set sampling. Communications in Statistics- Theory and Methods, 25(7):1617-1630.
  15. Lam, K., Sinha, B. K., and Wu, Z. (1994). Estimation of parameters in a two-parameter exponential distribu- tion using ranked set sample. Annals of the Institute of Statistical Mathematics, 46(4):723-736.
  16. Liangyong, Z. and Xiaofang, D. (2010). Optimal ranked set sampling design for the sign test. , 26(3):225-233.
  17. Liptak, T. (1958). On the combination of independent tests. Magyar Tud Akad Mat Kutato Int Kozl, 3:171-197.
  18. McIntyre, G. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3(4):385-390.
  19. McIntyre, G. (2005). A method for unbiased selective sampling, using ranked sets. The American Statistician,59:230-232.
  20. Mudholkar, G. S. and George, E. O. (1977). The logit statistic for combining probabilities-an overview. Technical report, DTIC Document.
  21. Muttlak, H. (1997). Median ranked set sampling. Journal of Applied Statistical Science, 6:245-255.
  22. Navarro, J., Rychlik, T., and Shaked, M. (2007). Are the order statistics ordered? a survey of recent results. Communications in Statistics - Theory and Methods, 36(7):1273-1290.
  23. Ö Öztürk. (1999). Two-sample inference based on one-sample ranked set sample sign statistics. Journal of Nonparametric Statistics, 10(2):197-212.
  24. Ö Öztürk. and Wolfe, D. A. (2000). Optimal allocation procedure in ranked set two-sample median test. Journal of Nonparametric Statistics, 13(1):57-76.
  25. Paul, J. and Thomas, P. Y. (2017). Concomitant record ranked set sampling. Communications in Statistics - Theory and Methods, 46(19):9518-9540.
  26. Pesarin, F. and Salmaso, L. (2010). Permutation Tests for Complex Data: Theory, Application and Software. John Wiley & Sons, Ltd., Chichester.
  27. Samawi, H. M., Ahmed, M. S., and Abu-Dayyeh, W. (1996). Estimating the population mean using extreme ranked set sampling. Biometrical Journal, 38(5):577-586.
  28. Samuh, M. H. (2012). Some Advances in Permutation Testing. PhD thesis, Department of Statistical Science, Padua University.
  29. Samuh, M. H. (2017). Ranked set two-sample permutation test. Statistica, 77(3):237-249.
  30. Samuh, M. H. and Pesarin, F. (2018). Applications of conditional power function of two-sample permutation test. Computational Statistics, 33(4):1847-1862.
  31. Sarikavanij, S., Kasala, S., Sinha, B. K., and Tiensuwan, M. (2014). Estimation of location and scale parameters in two-parameter exponential distribution based on ranked set sample. Communications in Statistics-Simulation and Computation, 43(1):132-141.
  32. Shaibu, A. B. and Muttlak, H. A. (2004). Estimating the parameters of the normal, exponential and gamma distributions using median and extreme ranked set samples. Statistica, 64(1):75-98.
  33. horack, G. R. and Wellner, J. A. (1986). Empirical Processes with Applications to Statistics. Wiley Series in Probability & Mathematical Statistics, New York.
  34. 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):1-31.