  In this paper, we develop two fully parametric quantile regression models,
based on power Johnson SB distribution Cancho et al. (2020), for modeling unit
interval response at different quantiles. In particular, the conditional
distribution is modelled by the power Johnson SB distribution. The maximum
likelihood method is employed to estimate the model parameters. Simulation
studies are conducted to evaluate the performance of the maximum likelihood
estimators in finite samples. Furthermore, we discuss residuals and influence
diagnostic tools. The effectiveness of our proposals is illustrated with two
data set given by the mortality rate of COVID-19 in different countries.
