The Beta-Gompertz Distribution
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| Natura: | Artículo científico |
| Lingua: | en |
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Universidad Nacional de Colombia
2014
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| _version_ | 1876453835013095424 |
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| author | Ali Akbar Jafari |
| author_facet | Ali Akbar Jafari |
| contents | The Beta-Gompertz Distribution Ali Akbar Jafari Saeid Tahmasebi Morad Alizadeh Física, Astronomía y Matemáticas Beta generator Gompertz distribution Maximum likelihood estimation In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher’s information matrix. A simulation study is performed in order to investigate the properties of the proposed estimator. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327010 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| format | Artículo científico |
| id | redalyc_89931327010 |
| institution | Redalyc |
| language | en |
| publishDate | 2014 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | The Beta-Gompertz Distribution Ali Akbar Jafari Física, Astronomía y Matemáticas Beta generator Gompertz distribution Maximum likelihood estimation The Beta-Gompertz Distribution Ali Akbar Jafari Saeid Tahmasebi Morad Alizadeh Física, Astronomía y Matemáticas Beta generator Gompertz distribution Maximum likelihood estimation In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as Beta-exponential and generalized Gompertz distributions as special sub-models. This new distribution is quite flexible and can be used effectively in modeling survival data and reliability problems. It can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the new distribution, such as closed-form expressions for the density, cumulative distribution, hazard rate function, the kth order moment, moment generating function, Shannon entropy, and the quantile measure are provided. We discuss maximum likelihood estimation of the BG parameters from one observed sample and derive the observed Fisher’s information matrix. A simulation study is performed in order to investigate the properties of the proposed estimator. At the end, in order to show the BG distribution flexibility, an application using a real data set is presented. 2014 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89931327010 en http://www.redalyc.org/revista.oa?id=899 Revista Colombiana de Estadística application/pdf Universidad Nacional de Colombia Revista Colombiana de Estadística (Colombia) Num.1 Vol.37 |
| title | The Beta-Gompertz Distribution |
| topic | Física, Astronomía y Matemáticas Beta generator Gompertz distribution Maximum likelihood estimation |
| url | https://www.redalyc.org/articulo.oa?id=89931327010 |