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Asymptotic theory of extreme dual generalized order statistics

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  • Barakat, H.M.
  • El-Adll, Magdy E.

Abstract

In a wide subclass of dual generalized order statistics (dgos) (which contains the most important models of descendingly ordered random variables), when the parameters [gamma]1,...,[gamma]n are assumed to be pairwise different, we study the weak convergence of the lower extremes, under general strongly monotone continuous transformations. It is revealed that the weak convergence of the maximum order statistics guarantees the weak convergence of any lower extreme dgos. Moreover, under linear and power normalization and by a suitable choice of these normalizations, the possible weak limits of any rth upper extreme order statistic are the same as the possible weak limits of the rth lower extreme dgos.

Suggested Citation

  • Barakat, H.M. & El-Adll, Magdy E., 2009. "Asymptotic theory of extreme dual generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1252-1259, May.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:9:p:1252-1259
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Amany E. Aly, 2023. "Predictive inference of dual generalized order statistics from the inverse Weibull distribution," Statistical Papers, Springer, vol. 64(1), pages 139-160, February.
    2. H. M. Barakat & E. M. Nigm & Magdy E. El-Adll & M. Yusuf, 2018. "Prediction of future generalized order statistics based on exponential distribution with random sample size," Statistical Papers, Springer, vol. 59(2), pages 605-631, June.

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