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On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics

Author

Listed:
  • H. M. Barakat

    (Zagazig University)

  • E. M. Nigm

    (Zagazig University)

Abstract

Based on the notion of the associated copula for order statistics and some L 1-distances, we derive a symmetric nonparametric measure of asymptotic dependence between the order statistics under power normalization. This nonparametric criterion of dependence is extended to the generalized, as well as the dual generalized, order statistics.

Suggested Citation

  • H. M. Barakat & E. M. Nigm, 2010. "On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(6), pages 703-714, December.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:6:d:10.1007_s13226-010-0040-y
    DOI: 10.1007/s13226-010-0040-y
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    References listed on IDEAS

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    1. Barakat, H.M., 2006. "Comments on the rate of convergence to asymptotic independence between order statistics," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 35-38, January.
    2. Marco Burkschat & Erhard Cramer & Udo Kamps, 2003. "Dual generalized order statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 13-26.
    3. Subramanya, U. R., 1994. "On max domains of attraction of univariate p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 271-279, March.
    4. Christoph, Gerd & Falk, Michael, 1996. "A note on domains of attraction of p-max stable laws," Statistics & Probability Letters, Elsevier, vol. 28(3), pages 279-284, July.
    5. H. Barakat & E. Nigm & Magdy El-Adll, 2010. "Comparison between the rates of convergence of extremes under linear and under power normalization," Statistical Papers, Springer, vol. 51(1), pages 149-164, January.
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