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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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
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spelling doaj-3bce6ba83ca94112a210f4bc555897a82020-11-24T23:55:37ZengMDPI AGSymmetry2073-89942019-06-0111679410.3390/sym11060794sym11060794Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy DistributionBarry C. Arnold0Héctor W. Gómez1Héctor Varela2Ignacio Vidal3Statistics Department, University of California Riverside, Riverside, CA 92521, USADepartamento de Matemática, Universidad de Antofagasta, Antofagasta 1240000, ChileDepartamento de Matemática, Universidad de Antofagasta, Antofagasta 1240000, ChileInstituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, ChileIn 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.https://www.mdpi.com/2073-8994/11/6/794Epsilon-skew-NormalEpsilon-skew-Cauchybivariate densitiesgeneralized Cauchy distributions
collection DOAJ
language English
format Article
sources DOAJ
author Barry C. Arnold
Héctor W. Gómez
Héctor Varela
Ignacio Vidal
spellingShingle Barry C. Arnold
Héctor W. Gómez
Héctor Varela
Ignacio Vidal
Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
Symmetry
Epsilon-skew-Normal
Epsilon-skew-Cauchy
bivariate densities
generalized Cauchy distributions
author_facet Barry C. Arnold
Héctor W. Gómez
Héctor Varela
Ignacio Vidal
author_sort Barry C. Arnold
title Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
title_short Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
title_full Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
title_fullStr Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
title_full_unstemmed Univariate and Bivariate Models Related to the Generalized Epsilon–Skew–Cauchy Distribution
title_sort univariate and bivariate models related to the generalized epsilon–skew–cauchy distribution
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2019-06-01
description 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.
topic Epsilon-skew-Normal
Epsilon-skew-Cauchy
bivariate densities
generalized Cauchy distributions
url https://www.mdpi.com/2073-8994/11/6/794
work_keys_str_mv AT barrycarnold univariateandbivariatemodelsrelatedtothegeneralizedepsilonskewcauchydistribution
AT hectorwgomez univariateandbivariatemodelsrelatedtothegeneralizedepsilonskewcauchydistribution
AT hectorvarela univariateandbivariatemodelsrelatedtothegeneralizedepsilonskewcauchydistribution
AT ignaciovidal univariateandbivariatemodelsrelatedtothegeneralizedepsilonskewcauchydistribution
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