A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propos...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/3/528 |
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| author | Marcelo Bourguignon Diego I. Gallardo Héctor J. Gómez |
| author_facet | Marcelo Bourguignon Diego I. Gallardo Héctor J. Gómez |
| author_sort | Marcelo Bourguignon |
| collection | DOAJ |
| description | Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression models where the response variable is Pareto-type distributed using new parameterizations that are indexed by mean and precision parameters. The main motivation for these new parametrizations is the useful interpretation of the regression coefficients in terms of the mean and precision, as is usual in the context of regression models. The parameter estimation of these new models is performed, based on the maximum likelihood paradigm. Some numerical illustrations of the estimators are presented with a discussion of the obtained results. Finally, we illustrate the practicality of the new models by means of two applications to real data sets. |
| first_indexed | 2024-03-09T23:30:55Z |
| format | Article |
| id | doaj.art-1abc24ccfc2649a381ae2b7e7963f4ae |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:30:55Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-1abc24ccfc2649a381ae2b7e7963f4ae2023-11-23T17:09:01ZengMDPI AGMathematics2227-73902022-02-0110352810.3390/math10030528A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision ParametersMarcelo Bourguignon0Diego I. Gallardo1Héctor J. Gómez2Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, RN, BrazilDepartamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, ChileDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChilePareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression models where the response variable is Pareto-type distributed using new parameterizations that are indexed by mean and precision parameters. The main motivation for these new parametrizations is the useful interpretation of the regression coefficients in terms of the mean and precision, as is usual in the context of regression models. The parameter estimation of these new models is performed, based on the maximum likelihood paradigm. Some numerical illustrations of the estimators are presented with a discussion of the obtained results. Finally, we illustrate the practicality of the new models by means of two applications to real data sets.https://www.mdpi.com/2227-7390/10/3/528pareto-type distributionsmodelingparameterizationvarying precision |
| spellingShingle | Marcelo Bourguignon Diego I. Gallardo Héctor J. Gómez A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters Mathematics pareto-type distributions modeling parameterization varying precision |
| title | A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters |
| title_full | A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters |
| title_fullStr | A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters |
| title_full_unstemmed | A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters |
| title_short | A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters |
| title_sort | note on pareto type distributions parameterized by its mean and precision parameters |
| topic | pareto-type distributions modeling parameterization varying precision |
| url | https://www.mdpi.com/2227-7390/10/3/528 |
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