A new quantile regression model for bounded responses with applications

This work proposes a new quantile regression model with a bounded response distribution that generalizes the L-logistic distribution. Following a Bayesian approach, estimation model comparison criteria and residual analysis are performed as well as a simulation study for prior sensitivity and parameter recovery, considering a computationally intensive approach. An application of the new distribution to model poverty vulnerability in Brazil and a regression analysis with poverty data from Peru is included. Comparison with the Beta and L-Logistic distributions are also performed showing the great flexibility of the new model.