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

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

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...

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Bibliographic Details
Main Authors: Barry C. Arnold, Héctor W. Gómez, Héctor Varela, Ignacio Vidal
Format: Article
Language:English
Published: MDPI AG 2019-06-01
Series:Symmetry
Subjects:
Epsilon-skew-Normal
Epsilon-skew-Cauchy
bivariate densities
generalized Cauchy distributions
Online Access:https://www.mdpi.com/2073-8994/11/6/794
Description
Summary: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.
ISSN:2073-8994

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