*Article* **The Asymmetric Alpha-Power Skew***t* **Distribution**

#### **Roger Tovar-Falón 1,\*, Heleno Bolfarine 2 and Guillermo Martínez-Flórez 1**


Received: 13 November 2019; Accepted: 25 December 2019; Published: 2 January 2020

**Abstract:** In this paper, we propose a new asymmetric and heavy-tail model that generalizes both the skew-*t* and power-*t* models. Properties of the model are studied in detail. The score functions and the elements of the observed information matrix are given. The process to estimate the parameters in model is discussed by using the maximum likelihood approach. Also, the observed information matrix is shown to be non-singular at the whole parametric space. Two applications to real data sets are reported to demonstrate the usefulness of this new model.

**Keywords:** alpha-power skew-*t* distribution; skew-*t* distribution; power-*t* distribution; asymmetry; Fisher information matrix; maximum likelihood estimation
