Power Truncated Positive Normal Distribution: A Quantile Regression Approach Applied to Health Databases

In this paper we present a new extension of the truncated positive normal (TPN) model, called power truncated positive normal. This extension incorporates a shape parameter that provides more flexibility to the model. In addition, this new extension was reparameterized based on the p-th quantile of the distribution in order to perform quantile regression. The initial values were calculated from a modification of the moment estimators, which allowed the maximum likelihood estimators to be obtained. A simulation study was carried out which suggests good behavior of the maximum likelihood estimators in finite samples. Finally, two applications using health databases are presented.