The exponentiated generalized gumbel distribution
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/49656 |
Resumo: | A class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The density function of the order statistic is derived. The method of maximum likelihood is used to estimate model parameters. We determine the observed information matrix. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters and two applications to real data to illustrate the importance of the new model. |
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Andrade, ThiagoRodrigues, HeloisaBourguignon, MarceloCordeiro, Gauss2022-10-31T20:33:20Z2022-10-31T20:33:20Z2015-01ANDRADE, T. et al. The Exponentiated Generalized Gumbel Distribution. Revista Colombiana de Estadistica, v. 38, p. 123-143, 2015. Disponível em: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=es&nrm=iso&tlng=en. Acesso em: 07 dez. 2017https://repositorio.ufrn.br/handle/123456789/4965610.15446Revista Colombiana de EstadisticaGumbel distributionMaximum likelihoodMomentRényi entropyThe exponentiated generalized gumbel distributioninfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleA class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The density function of the order statistic is derived. The method of maximum likelihood is used to estimate model parameters. We determine the observed information matrix. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters and two applications to real data to illustrate the importance of the new model.info:eu-repo/semantics/openAccessengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNORIGINALTheExponentiatedGeneralized_2015.pdfTheExponentiatedGeneralized_2015.pdfapplication/pdf1063380https://repositorio.ufrn.br/bitstream/123456789/49656/1/TheExponentiatedGeneralized_2015.pdf48a901a45c0a69ec648e9346d0a48a56MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.ufrn.br/bitstream/123456789/49656/2/license.txt8a4605be74aa9ea9d79846c1fba20a33MD52123456789/496562022-10-31 17:34:43.613oai:https://repositorio.ufrn.br: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Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2022-10-31T20:34:43Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
The exponentiated generalized gumbel distribution |
title |
The exponentiated generalized gumbel distribution |
spellingShingle |
The exponentiated generalized gumbel distribution Andrade, Thiago Gumbel distribution Maximum likelihood Moment Rényi entropy |
title_short |
The exponentiated generalized gumbel distribution |
title_full |
The exponentiated generalized gumbel distribution |
title_fullStr |
The exponentiated generalized gumbel distribution |
title_full_unstemmed |
The exponentiated generalized gumbel distribution |
title_sort |
The exponentiated generalized gumbel distribution |
author |
Andrade, Thiago |
author_facet |
Andrade, Thiago Rodrigues, Heloisa Bourguignon, Marcelo Cordeiro, Gauss |
author_role |
author |
author2 |
Rodrigues, Heloisa Bourguignon, Marcelo Cordeiro, Gauss |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Andrade, Thiago Rodrigues, Heloisa Bourguignon, Marcelo Cordeiro, Gauss |
dc.subject.por.fl_str_mv |
Gumbel distribution Maximum likelihood Moment Rényi entropy |
topic |
Gumbel distribution Maximum likelihood Moment Rényi entropy |
description |
A class of univariate distributions called the exponentiated generalized class was recently proposed in the literature. A four-parameter model within this class named the exponentiated generalized Gumbel distribution is defined. We discuss the shapes of its density function and obtain explicit expressions for the ordinary moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. The density function of the order statistic is derived. The method of maximum likelihood is used to estimate model parameters. We determine the observed information matrix. We provide a Monte Carlo simulation study to evaluate the maximum likelihood estimates of model parameters and two applications to real data to illustrate the importance of the new model. |
publishDate |
2015 |
dc.date.issued.fl_str_mv |
2015-01 |
dc.date.accessioned.fl_str_mv |
2022-10-31T20:33:20Z |
dc.date.available.fl_str_mv |
2022-10-31T20:33:20Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ANDRADE, T. et al. The Exponentiated Generalized Gumbel Distribution. Revista Colombiana de Estadistica, v. 38, p. 123-143, 2015. Disponível em: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=es&nrm=iso&tlng=en. Acesso em: 07 dez. 2017 |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/49656 |
dc.identifier.doi.none.fl_str_mv |
10.15446 |
identifier_str_mv |
ANDRADE, T. et al. The Exponentiated Generalized Gumbel Distribution. Revista Colombiana de Estadistica, v. 38, p. 123-143, 2015. Disponível em: http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=es&nrm=iso&tlng=en. Acesso em: 07 dez. 2017 10.15446 |
url |
https://repositorio.ufrn.br/handle/123456789/49656 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Revista Colombiana de Estadistica |
publisher.none.fl_str_mv |
Revista Colombiana de Estadistica |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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Universidade Federal do Rio Grande do Norte (UFRN) |
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UFRN |
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UFRN |
reponame_str |
Repositório Institucional da UFRN |
collection |
Repositório Institucional da UFRN |
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