Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data

Diego I. Gallardo, Marcelo Bourguignon, Yolanda M. Gómez, Christian Caamaño-Carrillo and Osvaldo Venegas
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Diego I. Gallardo: Departament of Mathematics, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile
Marcelo Bourguignon: Departament of Statistics, Federal University of Rio Grande do Norte, Natal 59078-970, Brazil
Yolanda M. Gómez: Departament of Mathematics, Faculty of Engineering, University of Atacama, Copiapó 1530000, Chile
Christian Caamaño-Carrillo: Departament of Statistics, Faculty of Science, University of Bío-Bío, Concepción 4081112, Chile
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingenieía, Universidad Católica de Temuco, Temuco 4780000, Chile

Mathematics, 2022, vol. 10, issue 13, 1-21

Abstract: In this paper, we develop two fully parametric quantile regression models, based on the power Johnson S B distribution for modeling unit interval response in different quantiles. In particular, the conditional distribution is modeled by the power Johnson S B 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.

Keywords: COVID-19; parametric quantile regression; power Johnson SB distribution; proportion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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