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Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling

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Abstract

Ranked set sampling is applicable whenever ranking of a set of sampling units can be done easily by a judgement method or based on the measurement of an auxiliary variable on the units selected. In this work, we consider ranked set sampling, in which ranking of units are done based on measurements made on an easily and exactly measurable auxiliary variable X which is correlated with the study variable Y. We then estimate the mean of the study variate Y by the BLUE based on the measurements made on the units of the ranked set sampling regarding the study variable Y, when (X ,Y) follows a Morgenstern type bivariate exponential distribution. We then consider unbalanced multistage ranked set sampling and estimate the mean of the study variate Y by the BLUE based on the observations made on the units of multistage ranked set sample regarding the study variable Y. Efficiency comparison is also made on all estimators considered in this work.

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References

  • Abo-Eleneen Z.A., Nagaraja H.N. (2002). Fisher information in an order statistic and its concomitant. Annals of the Institute of Statistical Mathematics, 54:667–680

    Article  MATH  MathSciNet  Google Scholar 

  • Al-Saleh M.F. (2004). Steady-state ranked set sampling and parametric inference. Journal of Statistical Planning and Inference, 123, 83–95

    Article  MATH  MathSciNet  Google Scholar 

  • Al-Saleh M.F., Al-Kadiri M. (2000). Double ranked set sampling. Statistics and Probability Letters, 48, 205–212

    Article  MATH  MathSciNet  Google Scholar 

  • Al-Saleh M.F., Al-Omari A. (2002). Multistage ranked set sampling. Journal of Statistical Planning and Inference, 102, 273–286

    Article  MATH  MathSciNet  Google Scholar 

  • Bain L.J. (1978). Statistical analysis of reliability and life testing models: theory and methods. New York, Marcel Dekker

    MATH  Google Scholar 

  • Barnett V., Moore K. (1997). Best linear unbiased estimates in ranked-set sampling with particular reference to imperfect ordering. Journal of Applied Statistics, 24, 697–710

    Article  Google Scholar 

  • Chen Z. (2000). The efficiency of ranked-set sampling relative to simple random sampling under multi-parameter families. Statistica Sinica, 10, 247–263

    MATH  MathSciNet  Google Scholar 

  • Chen Z., Bai Z. (2000). The optimal ranked set sampling scheme for parametric families. Sankhya Series A, 46, 178–192

    MathSciNet  Google Scholar 

  • Chen Z., Bai Z., Sinha B.K. (2004). Lecture notes in statistics, ranked set sampling, theory and applications. New York, Springer

    Google Scholar 

  • David H.A., Nagaraja H.N (2003). Order statistics. New York, Wiley

    MATH  Google Scholar 

  • Kotz S., Balakrishnan N., Johnson N.L. (2000). Distributions in statistics: continuous multivariate distributions. New York, Wiley

    Google Scholar 

  • Lam K., Sinha B.K., Wu Z. (1994). Estimation of a two-parameter exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723–736

    Article  MATH  MathSciNet  Google Scholar 

  • Lam K., Sinha B.K., Wu Z. (1995). Estimation of location and scale parameters of a logistic distribution using ranked set sample. In: Nagaraja H.N., Sen P.K., Morrison D.F. (eds) Statistical theory and applications: papers in honor of Herbert A. David. New-York, Springer

    Google Scholar 

  • McIntyre G.A. (1952). A method for unbiased selective sampling, using ranked sets. Australian Journal of Agricultural Research, 3, 385–390

    Article  Google Scholar 

  • Modarres R., Zheng G. (2004). Maximum likelihood estimation of dependence parameter using ranked set sampling. Statistics and Probability Letters, 68, 315–323

    Article  MATH  MathSciNet  Google Scholar 

  • Scaria J., Nair N.U. (1999). On concomitants of order statistics from Morgenstern family. Biometrical Journal, 41, 483–489

    Article  MATH  Google Scholar 

  • Stokes S.L. (1977). Ranked set sampling with concomitant variables. Communications in Statistics; Theory and Methods, 6:1207–1211

    Article  Google Scholar 

  • Stokes S.L. (1980). Inference on the correlation coefficient in bivariate normal populations from ranked Set Samples. Journal of the American Statistical Association, 75, 989–995

    Article  MATH  MathSciNet  Google Scholar 

  • Stokes S.L. (1995). Parametric ranked set sampling. Annals of the Institute of Statistical Mathematics, 47, 465–482

    MATH  MathSciNet  Google Scholar 

  • Zheng G., Modarres R. (2006). A robust estimate of correlation coefficient for bivariate normal distribution using ranked set sampling. Journal of Statistical Planning and Inference, 136, 298–309

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of Kerala, Trivandrum, 695 581, India

    Manoj Chacko & P. Yageen Thomas

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  1. Manoj Chacko
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  2. P. Yageen Thomas
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Correspondence to P. Yageen Thomas.

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Chacko, M., Thomas, P.Y. Estimation of a parameter of Morgenstern type bivariate exponential distribution by ranked set sampling. AISM 60, 301–318 (2008). https://doi.org/10.1007/s10463-006-0088-y

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  • DOI: https://doi.org/10.1007/s10463-006-0088-y

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