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

H. M. Barakat (), E. M. Nigm, O. M. Khaled and H. A. Alaswed
Additional contact information
H. M. Barakat: Zagazig University
E. M. Nigm: Zagazig University
O. M. Khaled: Port-Said University
H. A. Alaswed: University of Sebha

AStA Advances in Statistical Analysis, 2018, vol. 102, issue 3, No 6, 454 pages

Abstract: 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.

Keywords: Power normalization; Generalized Pareto distributions; Hill estimators; Moment estimator; Moment ratio estimator; 62G32; 62G30 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10182-017-0314-3

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