{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:40:31Z","timestamp":1760240431357,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider a stochastic representation of the epsilon\u2013skew\u2013Cauchy 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\u2013skew\u2013Cauchy distribution. Multivariate versions of these distributions can be envisioned. Bivariate examples are discussed in some detail.<\/jats:p>","DOI":"10.3390\/sym11060794","type":"journal-article","created":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T11:19:58Z","timestamp":1560511198000},"page":"794","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Univariate and Bivariate Models Related to the Generalized Epsilon\u2013Skew\u2013Cauchy Distribution"],"prefix":"10.3390","volume":"11","author":[{"given":"Barry C.","family":"Arnold","sequence":"first","affiliation":[{"name":"Statistics Department, University of California Riverside, Riverside, CA 92521, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1890-3438","authenticated-orcid":false,"given":"H\u00e9ctor","family":"Varela","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6654-652X","authenticated-orcid":false,"given":"Ignacio","family":"Vidal","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica y F\u00edsica, Universidad de Talca, Casilla 747, Talca, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0378-3758(99)00096-8","article-title":"The epsilon-skew-normal distribution for analyzing near-normal data","volume":"83","author":"Mudholkar","year":"2000","journal-title":"J. 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