A New Lifetime Model: The Gamma Extended Fréchet Distribution
For the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliabilit...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Springer
2013-05-01
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| Series: | Journal of Statistical Theory and Applications (JSTA) |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/6642.pdf |
| _version_ | 1818039851437522944 |
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| author | Ronaldo V. da Silva Thiago A.N. de Andrade Diego B.M. Maciel Renilma P. S. Campos Gauss M. Cordeiro |
| author_facet | Ronaldo V. da Silva Thiago A.N. de Andrade Diego B.M. Maciel Renilma P. S. Campos Gauss M. Cordeiro |
| author_sort | Ronaldo V. da Silva |
| collection | DOAJ |
| description | For the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliability are provided. The order statistics and their moments are derived. The method of maximum likelihood is used for estimating the model parameters.We determine the observed information matrix. An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis. |
| first_indexed | 2024-12-10T08:05:12Z |
| format | Article |
| id | doaj.art-2b07de8a16bf495da05be949395eef1a |
| institution | Directory Open Access Journal |
| issn | 1538-7887 |
| language | English |
| last_indexed | 2024-12-10T08:05:12Z |
| publishDate | 2013-05-01 |
| publisher | Springer |
| record_format | Article |
| series | Journal of Statistical Theory and Applications (JSTA) |
| spelling | doaj.art-2b07de8a16bf495da05be949395eef1a2022-12-22T01:56:42ZengSpringerJournal of Statistical Theory and Applications (JSTA)1538-78872013-05-0112110.2991/jsta.2013.12.1.4A New Lifetime Model: The Gamma Extended Fréchet DistributionRonaldo V. da SilvaThiago A.N. de AndradeDiego B.M. MacielRenilma P. S. CamposGauss M. CordeiroFor the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliability are provided. The order statistics and their moments are derived. The method of maximum likelihood is used for estimating the model parameters.We determine the observed information matrix. An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models. We hope that this generalization may attract wider applications in reliability, biology and survival analysis.https://www.atlantis-press.com/article/6642.pdfFréchet distribution; gamma extended Fr´echet distribution; maximum likelihood; observed information matrix; Weibull distribution.Keywords: Extreme values theory; Asymptotic distribution; Functional Gaussian and nongaussian laws; Uniform entropy numbers; Asymptotic tightnessStochastic process of |
| spellingShingle | Ronaldo V. da Silva Thiago A.N. de Andrade Diego B.M. Maciel Renilma P. S. Campos Gauss M. Cordeiro A New Lifetime Model: The Gamma Extended Fréchet Distribution Journal of Statistical Theory and Applications (JSTA) Fréchet distribution; gamma extended Fr´echet distribution; maximum likelihood; observed information matrix; Weibull distribution.Keywords: Extreme values theory; Asymptotic distribution; Functional Gaussian and nongaussian laws; Uniform entropy numbers; Asymptotic tightness Stochastic process of |
| title | A New Lifetime Model: The Gamma Extended Fréchet Distribution |
| title_full | A New Lifetime Model: The Gamma Extended Fréchet Distribution |
| title_fullStr | A New Lifetime Model: The Gamma Extended Fréchet Distribution |
| title_full_unstemmed | A New Lifetime Model: The Gamma Extended Fréchet Distribution |
| title_short | A New Lifetime Model: The Gamma Extended Fréchet Distribution |
| title_sort | new lifetime model the gamma extended frechet distribution |
| topic | Fréchet distribution; gamma extended Fr´echet distribution; maximum likelihood; observed information matrix; Weibull distribution.Keywords: Extreme values theory; Asymptotic distribution; Functional Gaussian and nongaussian laws; Uniform entropy numbers; Asymptotic tightness Stochastic process of |
| url | https://www.atlantis-press.com/article/6642.pdf |
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