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.
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The authors are immensely grateful to Professor Yarema Okhrin, the Editor in Chief of ASTB, as well as the anonymous referees for their careful reading of the manuscript and their constructive detailed comments.
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Barakat, H.M., Nigm, E.M., Khaled, O.M. et al. The estimations under power normalization for the tail index, with comparison. AStA Adv Stat Anal 102, 431–454 (2018). https://doi.org/10.1007/s10182-017-0314-3
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DOI: https://doi.org/10.1007/s10182-017-0314-3
Keywords
- Power normalization
- Generalized Pareto distributions
- Hill estimators
- Moment estimator
- Moment ratio estimator