Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data
In this paper, we develop two fully parametric quantile regression models, based on the power Johnson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>B</mi></msub&g...
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2249 |
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| author | Diego I. Gallardo Marcelo Bourguignon Yolanda M. Gómez Christian Caamaño-Carrillo Osvaldo Venegas |
| author_facet | Diego I. Gallardo Marcelo Bourguignon Yolanda M. Gómez Christian Caamaño-Carrillo Osvaldo Venegas |
| author_sort | Diego I. Gallardo |
| collection | DOAJ |
| description | In this paper, we develop two fully parametric quantile regression models, based on the power Johnson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>B</mi></msub></semantics></math></inline-formula> distribution for modeling unit interval response in different quantiles. In particular, the conditional distribution is modeled by the power Johnson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>B</mi></msub></semantics></math></inline-formula> distribution. The maximum likelihood (ML) estimation method is employed to estimate the model parameters. Simulation studies are conducted to evaluate the performance of the ML estimators in finite samples. Furthermore, we discuss influence diagnostic tools and residuals. The effectiveness of our proposals is illustrated with a data set of the mortality rate of COVID-19 in different countries. The results of our models with this data set show the potential of using the new methodology. Thus, we conclude that the results are favorable to the use of proposed quantile regression models for fitting double bounded data. |
| first_indexed | 2024-03-09T10:26:57Z |
| format | Article |
| id | doaj.art-2fd08ed94ea3426bacc2a72cb9ae370a |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:26:57Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-2fd08ed94ea3426bacc2a72cb9ae370a2023-12-01T21:35:17ZengMDPI AGMathematics2227-73902022-06-011013224910.3390/math10132249Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate DataDiego I. Gallardo0Marcelo Bourguignon1Yolanda M. Gómez2Christian Caamaño-Carrillo3Osvaldo Venegas4Departament of Mathematics, Faculty of Engineering, University of Atacama, Copiapó 1530000, ChileDepartament of Statistics, Federal University of Rio Grande do Norte, Natal 59078-970, BrazilDepartament of Mathematics, Faculty of Engineering, University of Atacama, Copiapó 1530000, ChileDepartament of Statistics, Faculty of Science, University of Bío-Bío, Concepción 4081112, ChileDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingenieía, Universidad Católica de Temuco, Temuco 4780000, ChileIn this paper, we develop two fully parametric quantile regression models, based on the power Johnson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>B</mi></msub></semantics></math></inline-formula> distribution for modeling unit interval response in different quantiles. In particular, the conditional distribution is modeled by the power Johnson <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>B</mi></msub></semantics></math></inline-formula> distribution. The maximum likelihood (ML) estimation method is employed to estimate the model parameters. Simulation studies are conducted to evaluate the performance of the ML estimators in finite samples. Furthermore, we discuss influence diagnostic tools and residuals. The effectiveness of our proposals is illustrated with a data set of the mortality rate of COVID-19 in different countries. The results of our models with this data set show the potential of using the new methodology. Thus, we conclude that the results are favorable to the use of proposed quantile regression models for fitting double bounded data.https://www.mdpi.com/2227-7390/10/13/2249COVID-19parametric quantile regressionpower Johnson SB distributionproportion |
| spellingShingle | Diego I. Gallardo Marcelo Bourguignon Yolanda M. Gómez Christian Caamaño-Carrillo Osvaldo Venegas Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data Mathematics COVID-19 parametric quantile regression power Johnson SB distribution proportion |
| title | Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data |
| title_full | Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data |
| title_fullStr | Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data |
| title_full_unstemmed | Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data |
| title_short | Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data |
| title_sort | parametric quantile regression models for fitting double bounded response with application to covid 19 mortality rate data |
| topic | COVID-19 parametric quantile regression power Johnson SB distribution proportion |
| url | https://www.mdpi.com/2227-7390/10/13/2249 |
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