Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood

We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer...

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Main Authors: Mahdi, Smail, Cenac, Myrtene
Format: artículo científico
Language: Español
Published: 2015
Online Access: http://revistas.ucr.ac.cr/index.php/matematica/article/view/259
http://hdl.handle.net/10669/12905
id RepoKERWA12905
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spelling RepoKERWA129052021-05-02T23:20:40Z Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood Mahdi, Smail Cenac, Myrtene We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer orders are considered in the probability weighted moments method. Overall, the results show that the probability weighted moments method outperforms the other methods in the estimation of both $\alpha$ and $\epsilon$ parameters. Derivamos estimadores para los parámetreos de la distribución de Gumbel usando tres métodos, esto es, los momentos ponderados de probabilidad, el momento y la máxima verosimilitud. Además, comparamos el rendimiento de estos estimadores usando simulaciones. Tanto el orden entero como no entero son considerados en el método de momentos de probabilidad ponderado. Los resultados muestran, sobre todo, que el método de momentos de probabilidad ponderada es mejor que los demás en la estimación de los parámetros y . 2015-05-19T18:43:02Z 2015-05-19T18:43:02Z 2012-03-02 00:00:00 2015-05-19T18:43:02Z artículo científico http://revistas.ucr.ac.cr/index.php/matematica/article/view/259 http://hdl.handle.net/10669/12905 10.15517/rmta.v12i1-2.259 es Revista de Matemática: Teoría y Aplicaciones Vol. 12 Núm. 1-2 2012 151-156 application/pdf
institution Universidad de Costa Rica
collection Repositorio KERWA
language Español
description We derive here estimators for the parameters of the Gumbel distribution using three estimating methods, namely, the probability weighted moments, the moment and the maximum likelihood methods. Furthermore, we compare the performance of these estimators using simulations. Both integer and non-integer orders are considered in the probability weighted moments method. Overall, the results show that the probability weighted moments method outperforms the other methods in the estimation of both $\alpha$ and $\epsilon$ parameters.
format artículo científico
author Mahdi, Smail
Cenac, Myrtene
spellingShingle Mahdi, Smail
Cenac, Myrtene
Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
author_sort Mahdi, Smail
title Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
title_short Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
title_full Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
title_fullStr Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
title_full_unstemmed Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood
title_sort estimating parameters of gumbel distribution using the methods of moments, probability weighted moments and maximum likelihood
publishDate 2015
url http://revistas.ucr.ac.cr/index.php/matematica/article/view/259
http://hdl.handle.net/10669/12905
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