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Open AccessArticle

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

1
Statistics Department, University of California Riverside, Riverside, CA 92521, USA
2
Departamento de Matemática, Universidad de Antofagasta, Antofagasta 1240000, Chile
3
Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(6), 794; https://doi.org/10.3390/sym11060794
Received: 8 May 2019 / Revised: 27 May 2019 / Accepted: 10 June 2019 / Published: 14 June 2019
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. View Full-Text
Keywords: Epsilon-skew-Normal; Epsilon-skew-Cauchy; bivariate densities; generalized Cauchy distributions Epsilon-skew-Normal; Epsilon-skew-Cauchy; bivariate densities; generalized Cauchy distributions
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Arnold, B.C.; Gómez, H.W.; Varela, H.; Vidal, I. Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution. Symmetry 2019, 11, 794.

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