**7. Conclusions**

In this work we introduce a new distribution for positive data named the GTPN model. This new distribution includes as particular cases three models well-known in the literature: the TPN, GHN, and HN models. The basic properties of the model and ML estimation were studied. We performed a simulation study in finite samples and two real data applications, showing the good performance of the model compared with other usual models in the literature.

**Author Contributions:** All of the authors contributed significantly to this research article.

**Funding:** The research of H.J.G. was supported by Proyecto de Investigación de Facultad de Ingeniería. Universidad Católica de Temuco. UCT-FDI012019. The research of O.V. was supported by Vicerrectoría de Investigación y Postgrado de la Universidad Católica de Temuco, Projecto FEQUIP 2019-INRN-03.

**Conflicts of Interest:** The authors declare no conflict of interest.
