ESTIMATING THE CORRELATION COEFFICIENT IN A BIVARIATE NORMAL DISTRIBUTION USING MOVING EXTREME RANKED SET SAMPLING WITH A CONCOMITANT VARIABLE

  • Published : 2005.06.01

Abstract

In this paper, we consider the estimation of the correlation coefficient in the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) that was introduced by Al-Saleh and Al-Hadhrami (2003a). The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered under different settings. The obtained estimators are compared to their counterparts that are obtained based simple random sampling (SRS). It appears that the suggested estimators are more efficient

Keywords

References

  1. AL-ODAT, M. T. AND AL-SALEH, M. FRAIWAN (2001). 'A Variation of Ranked Set Sampling', Journal of Applied Statistical Science, 10, 137-246
  2. AL-SALEH, M. FRAIWAN (2004). 'Steady State Ranked Set Sampling and Parametric Estimation', Journal of Statistical Planning and Inference, 123, 83-95 https://doi.org/10.1016/S0378-3758(03)00139-3
  3. AL-SALEH, M. FRAIWAN (2004). 'On the Totality of Ranked Set Sampling', Applied Mathematics and Computation, 147, 527-35 https://doi.org/10.1016/S0096-3003(02)00792-0
  4. AL-SALEH, M. FRAIWAN AND AL-HADHRAMI, S. (2003 a). 'Parametric Estimation for the Location Parameter for Symmetric Distribution Using Moving Extreme Ranked Set Sampling with Application to Trees Data', Enuironmetrics, 14, 651-664 https://doi.org/10.1002/env.610
  5. AL-SALEH, M. FRAIWAN AND AL-HADHRAMI, S. (2003 b). 'Estimation of the Mean of the Exponential Distribution using Moving Extreme Ranked Set Sampling', Statistical Papers, 44, 367-382 https://doi.org/10.1007/s00362-003-0161-z
  6. AL-SALEH, M. FRAIWAN AND AL-KADIRI (2000). 'Double Ranked Set Sampling', Statistics and Probability Letters, 48, 205-12 https://doi.org/10.1016/S0167-7152(99)00206-0
  7. AL-SALEH, M. FRAIWAN AND AL-OMARY (2002). 'Multi-Stage Ranked Set Sampling', Journal of Statistical Planning and Inference, 102, 273-86 https://doi.org/10.1016/S0378-3758(01)00086-6
  8. AL-SALEH, M. FRAIWAN AND AL-SHRAFAT, KHALAF (2001). 'Estimation Average Milk Yield Using Ranked Set Sampling', Enoironmeirics, 12, 395-399 https://doi.org/10.1002/env.478
  9. AL-SALEH, M. FRAIWAN AND SAMAWI, H. (2000). 'On the Efficiency of Monte Carlo Methods Using Steady State Ranked Simulated Samples', Communications in Statistics Simulation and Computation, 29, 941-954 https://doi.org/10.1080/03610910008813647
  10. AL-SALEH, M. FRAIWAN AND ZHENG, G. (2002). 'Estimation of Bivariate Characteristics using Ranked Set Sampling', The Australian & New Zealand Journal of Statistics, 44, 221-232 https://doi.org/10.1111/1467-842X.00224
  11. AL-SALEH, M. FRAIWAN AND ZHENG, G. (2003). 'Controlled Sampling Using Ranked Set Sampling', Journal of Nonparametric Statistics, 15, 505-16 https://doi.org/10.1080/10485250310001604640
  12. BALAKRISHNAN, N. AND KIM, J. A. (2004). EM algorithm for Type-II Right Censored Bivariate Normal Data. In Advances in Parametric Inference with Applications in Reliability, Survival Analysis and Quality of life, 177-210, Birkhauser, Boston
  13. BARABESI, L. AND PISANI, C. (2004). 'Steady-State Ranked Set Sampling for Replicated Environmental', Emnronmetrics 2004, 15, 45-56 https://doi.org/10.1002/env.625
  14. EVANS, M.J. (1967). 'Application of RSS to Regeneration Surveys in Area Direct-Seeded to Long Leeaf Pine', Master Thesis, Louisiana State University
  15. HALLS, L. AND DELL, T. (1966). 'Trials of Ranked Set Sampling for Forage Yields', Forest Science, 12, 22-26
  16. JOHNSON, N.L., AND KOTZ, S. (1972). Continuous Multivariate Distributions, John Wiley and Sons, New York
  17. KENDALL, M. G. AND STUART, A. (1963). The Advanced Theory of Statistics 1, Griffin, London
  18. McINTYRE, G.A. (1952). 'A Method for Unbiased Selective Sampling Using Ranked Set Sampling', Australian Journal of Agricultural Research, 3, 385-390 https://doi.org/10.1071/AR9520385
  19. MEHROTRA, K.G., AND NANDA, P. (1974). 'Unbiased Estimator of Parameter by Order Statistics in the Case of Censored Samples', Biometrika, 61, 601-606 https://doi.org/10.1093/biomet/61.3.601
  20. PATIL, G., SINHA, A., AND TAILLIE, C. (1999). 'Ranked Set Sampling: Bibliography', Environmental and Ecological Statistics, 6, 91-98 https://doi.org/10.1023/A:1009647718555
  21. SAMAWI, H. AND AL-SALEH, M. FRAIWAN (2004). 'On Bivariate Ranked Set Sampling for Quantile Estimation and Quantile Interval Estimation Using Ratio Estimator', Communications in Statistics- Theory and Methods, 33, 1801-1819 https://doi.org/10.1081/STA-120037442
  22. SAMAWI, H. AHMAD, M. AND ABU-DAYYEH, W. (1996). 'Estimating the Population Mean Using Extreme Ranked Set Sampling', Biometric of Journal, 30, 577-586 https://doi.org/10.1002/bimj.4710380506
  23. STOKES, S. L. AND SAGER, T. (1988). 'Characterization of RSS with Application to Estimating Distribution Functions', Journal of the American Statistical Association, 83, 374-381 https://doi.org/10.2307/2288852
  24. STOKES, S.L. (1977). 'Ranked Set Sampling With Concomitant Variables', Communications in Statistics- Theory and Methods, 6, 1207-1211 https://doi.org/10.1080/03610927708827563
  25. STOKES, S.L. (1980). 'Inferences on the Correlation Coefficient in Bivariate Normal Populations From Ranked Set Samples', Journal of the American Statistical Association, 75, 989-995 https://doi.org/10.2307/2287193
  26. TAKAHASI, K. 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
  27. YANG, S. S. (1977). 'General Distribution Theory of the Concomitants of Order Statistics', Ann. Statist., 5, 996-1002 https://doi.org/10.1214/aos/1176343954
  28. ZHENG, G. AND AL-SALEH, M. FRAIWAN (2003). 'Improving the Best Linear Unbiased Estimator for the Scale Parameter of Symmetric Distribution Using the Absolute Value of Ranked Set Sampling', Journal of Applied Statistics, 30, 253-65 https://doi.org/10.1080/0266476022000030039
  29. ZHENG, G. AND AL-SALEH, M. FRAIWAN (2002). 'Modified Maximum Likelihood Estimator Based on Ranked Set Sampling', Annals of the Institute of Statistical Mathematics, 54, 641-6 https://doi.org/10.1023/A:1022475413950