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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Diego I. Gallardo & Marcelo Bourguignon & Yolanda M. Gómez & Christian Caamaño-Carrillo & Osvaldo Venegas, 2022. "Parametric Quantile Regression Models for Fitting Double Bounded Response with Application to COVID-19 Mortality Rate Data," Mathematics, MDPI, vol. 10(13), pages 1-21, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2249-:d:848957
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    References listed on IDEAS

    as
    1. J. Mazucheli & A. F. B. Menezes & L. B. Fernandes & R. P. de Oliveira & M. E. Ghitany, 2020. "The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(6), pages 954-974, April.
    2. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
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