Statistical Papers

, Volume 44, Issue 3, pp 367–382 | Cite as

Estimation of the mean of the exponential distribution using moving extremes ranked set sampling

  • Mohammad Fraiwan Al-SalehEmail author
  • Said Ali Al-Hadhrami


Moving Extremes Ranked Set Sampling (MERSS) is a useful modification of Ranked Set Sampling (RSS). Unlike RSS, MERSS allows for an increase of set size without introducing too much ranking error. The method is considered parametrically under exponential distribution. Maximum likelihood estimator (MLE), and a modified MLE are considered and their properties are studied. The method is studied under both perfect and imperfect ranking (with error in ranking). It appears that these estimators can be real competitors to the MLE using the usual simple random sampling (SRS).


Ranked Set Sampling Moving Extremes Ranked Set Sampling Error in Ranking Maximum Likelihood Estimator Modified Maximum Likelihood Estimator 


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  1. Al-Saleh, M. Fraiwan and Al-Omary. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inferences 102, 31–44.Google Scholar
  2. Al-Odat, M.T. and Al-Saleh, M. Fraiwan (2001). A variation of ranked set sampling. Journal of Applied Statistical Science 10, 137–146.MathSciNetGoogle Scholar
  3. Al-Saleh, M. Fraiwan and Al-Sharfat, K. (2001). Estimation of average milk yield using ranked set sampling. Environmetrics 12, 395–399.CrossRefGoogle Scholar
  4. Al-Saleh, M. Fraiwan and Zheng, G. (2000). Estimation of bivariate characteristics using ranked set sampling. The Australian and New Zealand Journal of Statistics 44, 221–232.CrossRefMathSciNetGoogle Scholar
  5. Al-Saleh, M. Fraiwan and Al-Kadiri, M. (2000). Double ranked Set Sampling. Statistics and Probability Letters 48, 205–212.zbMATHCrossRefMathSciNetGoogle Scholar
  6. Barabesi, L. and El-Sharaawi A. (2001). The efficiency of ranked set sampling for parameter estimation. Statistics and Probability Letters 53, 189–199.zbMATHCrossRefMathSciNetGoogle Scholar
  7. Bohn, L.L. and Wolfe, D.A. (1994). The effect of imperfect judgment ranking on properties of procedures based on the ranked set samples analogue of the Mann-Whitey-Wilcoxon statistic. J.Amer.Statist.Assoc. 89, 168–176.zbMATHCrossRefMathSciNetGoogle Scholar
  8. Dell, T.R. & Clutter, J.L. (1972). Ranked Set Sampling Theory with Order Statistics Background. Biometrics 28, 545–555.CrossRefGoogle Scholar
  9. Diaconis (1988). Group representation in Probability. and Statistics, p. 174.Google Scholar
  10. Fei, H., Sinha, B.K and Wu, Z. (1994). Estimation of parameters in two-Parameter Weibull and extreme-value distributions using ranked set sampling. Journal of Statistical Research 28, 149–161.MathSciNetGoogle Scholar
  11. Lam, K., Sinha, B.K. and Wu, Z. (1994). Estimation of parameters in two-parameter Exponential distribution using ranked set sampling. Annals of the Institute of Statistical Mathematics 46(4), 723–736.zbMATHCrossRefMathSciNetGoogle Scholar
  12. Lehmann, E. L. (1983). Theory of point estimation. John Willey and Sons Inc.Google Scholar
  13. Maharota, K.G. and Nanda, P. (1974) Unbiased estimator of parameter; by order statistics in the case of censored samples, Biometrika 61, 601–606.CrossRefMathSciNetGoogle Scholar
  14. McIntyre, G.A. (1952). A method for unbiased selective sampling using ranked sets. Australian J. Agricul. Research 3, 385–390.CrossRefGoogle Scholar
  15. Mode, N., Conquest, L. and Marker, D. (1999). Ranked set sampling for ecological research: Accounting for the total cost of sampling. Environmetrics 10, 179–194.CrossRefGoogle Scholar
  16. Stokes, S.L. and Sager, T. (1988). Characterization of ranked set sample with application to estimating distribution functions. Journal of the American Statistical Association 83, 374–381.zbMATHCrossRefMathSciNetGoogle Scholar
  17. Stokes, S.L. (1980). Estimation of variance using judgment ordered ranked set samples. Bometrics 36, 35–42.zbMATHCrossRefMathSciNetGoogle Scholar
  18. Stokes, S.L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics-Theory and Methods A6, 1207–1211.CrossRefGoogle Scholar
  19. 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.zbMATHCrossRefMathSciNetGoogle Scholar
  20. Zheng, G and Al-Saleh, M. Fraiwan (2000). Modified Maximum Likelihood Estimator based on ranked set sampling. Annals of the Institute of Statistical Mathematics 54, 641–658CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  • Mohammad Fraiwan Al-Saleh
    • 1
    Email author
  • Said Ali Al-Hadhrami
    • 2
  1. 1.Department of StatisticsYarmouk UniversityYarmoukJordan
  2. 2.Department of Mathematics and StatisticsSultan Qaboos University, OmanOman

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