An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations
In this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/22/4336 |
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| author | Jaime Arrué Reinaldo Boris Arellano-Valle Osvaldo Venegas Heleno Bolfarine Héctor W. Gómez |
| author_facet | Jaime Arrué Reinaldo Boris Arellano-Valle Osvaldo Venegas Heleno Bolfarine Héctor W. Gómez |
| author_sort | Jaime Arrué |
| collection | DOAJ |
| description | In this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such as the computation of its moments and the non-existence of the moment-generating function. Parameter estimation by the maximum likelihood approach is also studied. This approach presents an overestimation problem in the shape parameter, which in some cases, can even be infinite. However, as we demonstrate, this problem is solved by adapting bias reduction using Firth’s approach. We also show that the modified log-skew-normal model likewise inherits the non-singularity of the Fisher information matrix of the untransformed model, when the shape parameter is null. Finally, we apply the modified log-skew-normal model to a real example related to pollution data. |
| first_indexed | 2024-03-09T18:11:02Z |
| format | Article |
| id | doaj.art-95f6974bad4a4866886f333f260c3c29 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:11:02Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-95f6974bad4a4866886f333f260c3c292023-11-24T09:09:53ZengMDPI AGMathematics2227-73902022-11-011022433610.3390/math10224336An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant ConcentrationsJaime Arrué0Reinaldo Boris Arellano-Valle1Osvaldo Venegas2Heleno Bolfarine3Héctor W. Gómez4Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileDepartamento de Estadística, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago 7820436, ChileDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileDepartamento de Estatítica, IME, Universidade de São Paulo, São Paulo 05508-090, BrazilDepartamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such as the computation of its moments and the non-existence of the moment-generating function. Parameter estimation by the maximum likelihood approach is also studied. This approach presents an overestimation problem in the shape parameter, which in some cases, can even be infinite. However, as we demonstrate, this problem is solved by adapting bias reduction using Firth’s approach. We also show that the modified log-skew-normal model likewise inherits the non-singularity of the Fisher information matrix of the untransformed model, when the shape parameter is null. Finally, we apply the modified log-skew-normal model to a real example related to pollution data.https://www.mdpi.com/2227-7390/10/22/4336log-normal distributionnon-singular information matrixmodified likelihoodmodified scorebias prevention |
| spellingShingle | Jaime Arrué Reinaldo Boris Arellano-Valle Osvaldo Venegas Heleno Bolfarine Héctor W. Gómez An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations Mathematics log-normal distribution non-singular information matrix modified likelihood modified score bias prevention |
| title | An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations |
| title_full | An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations |
| title_fullStr | An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations |
| title_full_unstemmed | An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations |
| title_short | An Alternative to the Log-Skew-Normal Distribution: Properties, Inference, and an Application to Air Pollutant Concentrations |
| title_sort | alternative to the log skew normal distribution properties inference and an application to air pollutant concentrations |
| topic | log-normal distribution non-singular information matrix modified likelihood modified score bias prevention |
| url | https://www.mdpi.com/2227-7390/10/22/4336 |
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