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

Abstract

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