Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution
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| Format: | Artículo científico |
| Sprache: | en |
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Universidad Nacional de Colombia
2017
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| _version_ | 1876434120827994112 |
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| author | Paulino Pérez-Rodríguez |
| author_facet | Paulino Pérez-Rodríguez |
| contents | Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution Paulino Pérez-Rodríguez José A. Villaseñor Sergio Pérez Javier Suárez Física, Astronomía y Matemáticas Prior Dis tribution Metropolis Point Estimation Hastings Algorithm The skew-normal (SN) distribution is a generalization of the normal dis- tribution, where a shape parameter is added to adopt skewed forms. The SN distribution has some of the properties of a univariate normal distribu- tion, which makes it very attractive from a practical standpoint; however, it presents some inference problems. Specifically, the maximum likelihood es- timator for the shape parameter tends to infinity with a positive probability. A new Bayesian approach is proposed in this paper which allows to draw inferences on the parameters of this distribution by using improper prior distributions in the “centered parametrization” for the location and scale pa- rameter and a Beta-type for the shape parameter. Samples from posterior distributions are obtained by using the Metropolis-Hastings algorithm. A simulation study shows that the mode of the posterior distribution appears to be a good estimator in terms of bias and mean squared error. A com- parative study with similar proposals for the SN estimation problem was undertaken. Simulation results provide evidence that the proposed method is easier to implement than previous ones. Some applications and compar- isons are also included. 2017 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89949526008 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.40 |
| format | Artículo científico |
| id | redalyc_89949526008 |
| institution | Redalyc |
| language | en |
| publishDate | 2017 |
| publisher | Universidad Nacional de Colombia |
| spellingShingle | Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution Paulino Pérez-Rodríguez Física, Astronomía y Matemáticas Prior Dis tribution Metropolis Point Estimation Hastings Algorithm Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution Paulino Pérez-Rodríguez José A. Villaseñor Sergio Pérez Javier Suárez Física, Astronomía y Matemáticas Prior Dis tribution Metropolis Point Estimation Hastings Algorithm The skew-normal (SN) distribution is a generalization of the normal dis- tribution, where a shape parameter is added to adopt skewed forms. The SN distribution has some of the properties of a univariate normal distribu- tion, which makes it very attractive from a practical standpoint; however, it presents some inference problems. Specifically, the maximum likelihood es- timator for the shape parameter tends to infinity with a positive probability. A new Bayesian approach is proposed in this paper which allows to draw inferences on the parameters of this distribution by using improper prior distributions in the “centered parametrization” for the location and scale pa- rameter and a Beta-type for the shape parameter. Samples from posterior distributions are obtained by using the Metropolis-Hastings algorithm. A simulation study shows that the mode of the posterior distribution appears to be a good estimator in terms of bias and mean squared error. A com- parative study with similar proposals for the SN estimation problem was undertaken. Simulation results provide evidence that the proposed method is easier to implement than previous ones. Some applications and compar- isons are also included. 2017 artículo científico 0120-1751 https://www.redalyc.org/articulo.oa?id=89949526008 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.40 |
| title | Bayesian Estimation for the Centered Parameterization of the Skew-Normal Distribution |
| topic | Física, Astronomía y Matemáticas Prior Dis tribution Metropolis Point Estimation Hastings Algorithm |
| url | https://www.redalyc.org/articulo.oa?id=89949526008 |