A New Generalization of the Truncated Gumbel Distribution with Quantile Regression and Applications

Abstract

In this article, we introduce a new model with positive support. This model is an extension of the truncated Gumbel distribution, where a shape parameter is incorporated that provides greater flexibility to the new model. The model is parameterized in terms of the p-th quantile of the distribution to perform quantile regression in this model. An extensive simulation study demonstrates the good performance of the maximum likelihood estimators in finite samples. Finally, two applications to real datasets related to the level of beta-carotene and body mass index are presented.

Keywords

• Gumbel distribution
• maximum likelihood estimators
• quantile regression
• truncated distribution