Improved inference for the generalized Pareto distribution under linear, power and exponential normalization

Osama Mohareb Khaled; Haroon Mohamed Barakat; Nourhan Khalil Rakha

Kybernetika (2022)

  • Volume: 58, Issue: 6, page 883-902
  • ISSN: 0023-5954

Abstract

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We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.

How to cite

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Mohareb Khaled, Osama, Mohamed Barakat, Haroon, and Khalil Rakha, Nourhan. "Improved inference for the generalized Pareto distribution under linear, power and exponential normalization." Kybernetika 58.6 (2022): 883-902. <http://eudml.org/doc/299545>.

@article{MoharebKhaled2022,
abstract = {We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.},
author = {Mohareb Khaled, Osama, Mohamed Barakat, Haroon, Khalil Rakha, Nourhan},
journal = {Kybernetika},
keywords = {generalized Pareto distribution; generalized extreme value distribution; method of moments; probability weighted moments; L-moments; linear-power-exponential normalization},
language = {eng},
number = {6},
pages = {883-902},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Improved inference for the generalized Pareto distribution under linear, power and exponential normalization},
url = {http://eudml.org/doc/299545},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Mohareb Khaled, Osama
AU - Mohamed Barakat, Haroon
AU - Khalil Rakha, Nourhan
TI - Improved inference for the generalized Pareto distribution under linear, power and exponential normalization
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 6
SP - 883
EP - 902
AB - We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits.
LA - eng
KW - generalized Pareto distribution; generalized extreme value distribution; method of moments; probability weighted moments; L-moments; linear-power-exponential normalization
UR - http://eudml.org/doc/299545
ER -

References

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