*Article* **Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution**

### **Barry C. Arnold 1, Héctor W. Gómez 2, Héctor Varela 2,\* and Ignacio Vidal 3**


Received: 8 May 2019; Accepted: 10 June 2019; Published: 14 June 2019

**Abstract:** In this paper, we consider a stochastic representation of the epsilon–skew–Cauchy distribution, viewed as a member of the family of skewed distributions discussed in Arellano-Valle et al. (2005). The stochastic representation facilitates derivation of distributional properties of the model. In addition, we introduce symmetric and asymmetric extensions of the Cauchy distribution, together with an extension of the epsilon–skew–Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.

**Keywords:** Epsilon-skew-Normal; Epsilon-skew-Cauchy; bivariate densities; generalized Cauchy distributions
