A Family of Truncated Positive Distributions
In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients,...
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| Format: | Article |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/21/4431 |
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| author | Héctor J. Gómez Karol I. Santoro Inmaculada Barranco-Chamorro Osvaldo Venegas Diego I. Gallardo Héctor W. Gómez |
| author_facet | Héctor J. Gómez Karol I. Santoro Inmaculada Barranco-Chamorro Osvaldo Venegas Diego I. Gallardo Héctor W. Gómez |
| author_sort | Héctor J. Gómez |
| collection | DOAJ |
| description | In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called “tpn”, has been implemented, which includes the relevant cases of interest in this family. |
| first_indexed | 2024-03-11T11:25:48Z |
| format | Article |
| id | doaj.art-ebf396cd20c049b688fae677905a0e1a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T11:25:48Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ebf396cd20c049b688fae677905a0e1a2023-11-10T15:07:52ZengMDPI AGMathematics2227-73902023-10-011121443110.3390/math11214431A Family of Truncated Positive DistributionsHéctor J. Gómez0Karol I. Santoro1Inmaculada Barranco-Chamorro2Osvaldo Venegas3Diego I. Gallardo4Héctor W. Gómez5Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileDepartamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileDepartamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, SpainDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileDepartamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, ChileDepartamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called “tpn”, has been implemented, which includes the relevant cases of interest in this family.https://www.mdpi.com/2227-7390/11/21/4431positive truncationlikelihoodsymmetric distributionstpn package |
| spellingShingle | Héctor J. Gómez Karol I. Santoro Inmaculada Barranco-Chamorro Osvaldo Venegas Diego I. Gallardo Héctor W. Gómez A Family of Truncated Positive Distributions Mathematics positive truncation likelihood symmetric distributions tpn package |
| title | A Family of Truncated Positive Distributions |
| title_full | A Family of Truncated Positive Distributions |
| title_fullStr | A Family of Truncated Positive Distributions |
| title_full_unstemmed | A Family of Truncated Positive Distributions |
| title_short | A Family of Truncated Positive Distributions |
| title_sort | family of truncated positive distributions |
| topic | positive truncation likelihood symmetric distributions tpn package |
| url | https://www.mdpi.com/2227-7390/11/21/4431 |
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