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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Universidad Nacional de Colombia
2015-01-01
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| Series: | Revista Colombiana de Estadística |
| Subjects: | |
| Online Access: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=en&tlng=en |
| _version_ | 1818689190536151040 |
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| author | THIAGO ANDRADE HELOISA RODRIGUES MARCELO BOURGUIGNON GAUSS CORDEIRO |
| author_facet | THIAGO ANDRADE HELOISA RODRIGUES MARCELO BOURGUIGNON GAUSS CORDEIRO |
| author_sort | THIAGO ANDRADE |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-17T12:06:10Z |
| format | Article |
| id | doaj.art-0bfe34d6600346cf8b835bfb217cad39 |
| institution | Directory Open Access Journal |
| issn | 0120-1751 |
| language | English |
| last_indexed | 2024-12-17T12:06:10Z |
| publishDate | 2015-01-01 |
| publisher | Universidad Nacional de Colombia |
| record_format | Article |
| series | Revista Colombiana de Estadística |
| spelling | doaj.art-0bfe34d6600346cf8b835bfb217cad392022-12-21T21:49:36ZengUniversidad Nacional de ColombiaRevista Colombiana de Estadística0120-17512015-01-0138112314310.15446/rce.v38n1.48806S0120-17512015000100007The Exponentiated Generalized Gumbel DistributionTHIAGO ANDRADE0HELOISA RODRIGUES1MARCELO BOURGUIGNON2GAUSS CORDEIRO3Universidade Federal de PernambucoUniversidade Federal de PernambucoUniversidade Federal do PiauíUniversidade Federal de PernambucoA 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.http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=en&tlng=endistribución Gumbelentropía de Rényimáxima verosimilitudmomentos |
| spellingShingle | THIAGO ANDRADE HELOISA RODRIGUES MARCELO BOURGUIGNON GAUSS CORDEIRO The Exponentiated Generalized Gumbel Distribution Revista Colombiana de Estadística distribución Gumbel entropía de Rényi máxima verosimilitud momentos |
| title | 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_short | The Exponentiated Generalized Gumbel Distribution |
| title_sort | exponentiated generalized gumbel distribution |
| topic | distribución Gumbel entropía de Rényi máxima verosimilitud momentos |
| url | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0120-17512015000100007&lng=en&tlng=en |
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