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The estimations under power normalization for the tail index, with comparison

Author

Listed:
  • H. M. Barakat

    (Zagazig University)

  • E. M. Nigm

    (Zagazig University)

  • O. M. Khaled

    (Port-Said University)

  • H. A. Alaswed

    (University of Sebha)

Abstract

It is well known that the max-stable laws under power normalization attract more distributions than that under linear normalization. This fact practically means that the classical linear model (L-model) may fail to fit the given extreme data, while the power model (P-model) succeeds to do that. The main object of this paper is developing the modeling of extreme values via P-model by suggesting a simple technique to obtain a parallel estimator of the extreme value index (EVI) in the P-model for every known estimator to the corresponding parameter in L-mode. An application of this technique yields two classes of moment and moment ratio estimators for EVI in the P-model. The performances of these estimators are assessed via a simulation study. Moreover, an efficient criterion for comparing the L and P models is proposed to choose the best model when the two models successfully work.

Suggested Citation

  • H. M. Barakat & E. M. Nigm & O. M. Khaled & H. A. Alaswed, 2018. "The estimations under power normalization for the tail index, with comparison," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 431-454, July.
    • Handle: RePEc:spr:alstar:v:102:y:2018:i:3:d:10.1007_s10182-017-0314-3
    DOI: 10.1007/s10182-017-0314-3
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