The Exponentiated Generalized Gumbel Distribution
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 expre...
- Autores:
-
Andrade, Thiago
Rodrigues, Heloisa
Bourguignon, Marcelo
Cordeiro, Gauss
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2015
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66545
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66545
http://bdigital.unal.edu.co/67573/
- Palabra clave:
- 51 Matemáticas / Mathematics
31 Colecciones de estadística general / Statistics
Gumbel Distribution
Maximum Likelihood
Moment
Rényi Entropy
Distribución Gumbel
Entropía de Rényi
Máxima verosimilitud
Momentos.
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Andrade, Thiagoc57b9acb-6216-4878-bdf2-ef676c4aefd7300Rodrigues, Heloisa30b489f9-5fd3-4dd4-a2ba-bc1fa70cc7a2300Bourguignon, Marcelo4f984102-a292-408f-bd07-396383617598300Cordeiro, Gauss6dc99ef2-3c3e-4e2b-b274-d1f6d383e3403002019-07-03T02:20:36Z2019-07-03T02:20:36Z2015-01-01ISSN: 2389-8976https://repositorio.unal.edu.co/handle/unal/66545http://bdigital.unal.edu.co/67573/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.Recientemente fue propuesta una clase de distribuciones univariadas conocida como la clase exponencializada generalizada. Dentro de esta clase se define un modelo con cuatro parámetros conocido como distribución Gumbel exponencializada generalizada. En este artículo estudiamos las formas de la función de densidad de este modelo, obtenemos expresiones explicitas para los momentos ordinarios, las funciones generadora de momentos y cuantílica, para los desvíos medios, las curvas de Bonferroni y Lorenz, y, para la entropía de Rényi. Derivamos la función de densidad de la estadística de orden. Usamos el método de máxima verosimilitud para estimar los parámetros del modelo. Determinamos la matriz de información observada. Presentamos una simulación de Monte Carlo que evalúa las estimativas de máxima verosimilitud de los parámetros del modelo y presentamos dos aplicaciones a datos reales que ilustran la importancia del modelo nuevo.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Estadísticahttps://revistas.unal.edu.co/index.php/estad/article/view/48806Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de EstadísticaRevista Colombiana de EstadísticaAndrade, Thiago and Rodrigues, Heloisa and Bourguignon, Marcelo and Cordeiro, Gauss (2015) The Exponentiated Generalized Gumbel Distribution. Revista Colombiana de Estadística, 38 (1). pp. 123-143. ISSN 2389-897651 Matemáticas / Mathematics31 Colecciones de estadística general / StatisticsGumbel DistributionMaximum LikelihoodMomentRényi EntropyDistribución GumbelEntropía de RényiMáxima verosimilitudMomentos.The Exponentiated Generalized Gumbel DistributionArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL48806-239245-1-PB.pdfapplication/pdf1063380https://repositorio.unal.edu.co/bitstream/unal/66545/1/48806-239245-1-PB.pdf48a901a45c0a69ec648e9346d0a48a56MD51THUMBNAIL48806-239245-1-PB.pdf.jpg48806-239245-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg5229https://repositorio.unal.edu.co/bitstream/unal/66545/2/48806-239245-1-PB.pdf.jpg8870949def7bb85832bb60367fab8811MD52unal/66545oai:repositorio.unal.edu.co:unal/665452024-05-16 23:09:43.6Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
The Exponentiated Generalized Gumbel Distribution |
| title |
The Exponentiated Generalized Gumbel Distribution |
| spellingShingle |
The Exponentiated Generalized Gumbel Distribution 51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Gumbel Distribution Maximum Likelihood Moment Rényi Entropy Distribución Gumbel Entropía de Rényi Máxima verosimilitud Momentos. |
| 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 |
| dc.creator.fl_str_mv |
Andrade, Thiago Rodrigues, Heloisa Bourguignon, Marcelo Cordeiro, Gauss |
| dc.contributor.author.spa.fl_str_mv |
Andrade, Thiago Rodrigues, Heloisa Bourguignon, Marcelo Cordeiro, Gauss |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics |
| topic |
51 Matemáticas / Mathematics 31 Colecciones de estadística general / Statistics Gumbel Distribution Maximum Likelihood Moment Rényi Entropy Distribución Gumbel Entropía de Rényi Máxima verosimilitud Momentos. |
| dc.subject.proposal.spa.fl_str_mv |
Gumbel Distribution Maximum Likelihood Moment Rényi Entropy Distribución Gumbel Entropía de Rényi Máxima verosimilitud Momentos. |
| 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. |
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2015 |
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2015-01-01 |
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2019-07-03T02:20:36Z |
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2019-07-03T02:20:36Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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Text |
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publishedVersion |
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ISSN: 2389-8976 |
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https://repositorio.unal.edu.co/handle/unal/66545 |
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http://bdigital.unal.edu.co/67573/ |
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ISSN: 2389-8976 |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/estad/article/view/48806 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Estadística Revista Colombiana de Estadística |
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Andrade, Thiago and Rodrigues, Heloisa and Bourguignon, Marcelo and Cordeiro, Gauss (2015) The Exponentiated Generalized Gumbel Distribution. Revista Colombiana de Estadística, 38 (1). pp. 123-143. ISSN 2389-8976 |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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