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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Universidad de Costa Rica
2012-03-01
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| Series: | Revista de Matemática: Teoría y Aplicaciones |
| Online Access: | https://revistas.ucr.ac.cr/index.php/matematica/article/view/259 |
| _version_ | 1797709985657913344 |
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| author | Smail Mahdi Myrtene Cenac |
| author_facet | Smail Mahdi Myrtene Cenac |
| author_sort | Smail Mahdi |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-12T06:45:40Z |
| format | Article |
| id | doaj.art-e64c627ed4fe481495a705993018c335 |
| institution | Directory Open Access Journal |
| issn | 2215-3373 |
| language | English |
| last_indexed | 2024-03-12T06:45:40Z |
| publishDate | 2012-03-01 |
| publisher | Universidad de Costa Rica |
| record_format | Article |
| series | Revista de Matemática: Teoría y Aplicaciones |
| spelling | doaj.art-e64c627ed4fe481495a705993018c3352023-09-03T00:39:41ZengUniversidad de Costa RicaRevista de Matemática: Teoría y Aplicaciones2215-33732012-03-01121-215115610.15517/rmta.v12i1-2.259244Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihoodSmail Mahdi0Myrtene Cenac1University of the West Indies, Department of Computer Science, Mathematics & PhysicsDepartment of Computer Science, Mathematics & Physics, University of the West Indies, Cave Hill Campus, BarbadosWe 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.https://revistas.ucr.ac.cr/index.php/matematica/article/view/259 |
| spellingShingle | Smail Mahdi Myrtene Cenac Estimating Parameters of Gumbel Distribution using the Methods of Moments, probability weighted Moments and maximum likelihood Revista de Matemática: Teoría y Aplicaciones |
| title | 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_short | 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 |
| url | https://revistas.ucr.ac.cr/index.php/matematica/article/view/259 |
| work_keys_str_mv | AT smailmahdi estimatingparametersofgumbeldistributionusingthemethodsofmomentsprobabilityweightedmomentsandmaximumlikelihood AT myrtenecenac estimatingparametersofgumbeldistributionusingthemethodsofmomentsprobabilityweightedmomentsandmaximumlikelihood |