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Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution

In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of inf...

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Autores principales: Martín, Jacinto, Parra, María Isabel, Pizarro, Mario Martínez, Sanjuán, Eva López
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8870988/
https://www.ncbi.nlm.nih.gov/pubmed/35205473
http://dx.doi.org/10.3390/e24020178
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author Martín, Jacinto
Parra, María Isabel
Pizarro, Mario Martínez
Sanjuán, Eva López
author_facet Martín, Jacinto
Parra, María Isabel
Pizarro, Mario Martínez
Sanjuán, Eva López
author_sort Martín, Jacinto
collection PubMed
description In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking into account the whole data set from the baseline distribution and the existing relations between the baseline and the limit GPD parameters in order to define highly informative priors. We make a comparison between the Bayesian Metropolis–Hastings algorithm with data over the threshold and the new methods when the baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Lévy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis–Hastings algorithm.
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spelling pubmed-88709882022-02-25 Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution Martín, Jacinto Parra, María Isabel Pizarro, Mario Martínez Sanjuán, Eva López Entropy (Basel) Article In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking into account the whole data set from the baseline distribution and the existing relations between the baseline and the limit GPD parameters in order to define highly informative priors. We make a comparison between the Bayesian Metropolis–Hastings algorithm with data over the threshold and the new methods when the baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Lévy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis–Hastings algorithm. MDPI 2022-01-25 /pmc/articles/PMC8870988/ /pubmed/35205473 http://dx.doi.org/10.3390/e24020178 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Martín, Jacinto
Parra, María Isabel
Pizarro, Mario Martínez
Sanjuán, Eva López
Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title_full Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title_fullStr Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title_full_unstemmed Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title_short Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution
title_sort baseline methods for the parameter estimation of the generalized pareto distribution
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8870988/
https://www.ncbi.nlm.nih.gov/pubmed/35205473
http://dx.doi.org/10.3390/e24020178
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