{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:34:36Z","timestamp":1760236476979,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T00:00:00Z","timestamp":1638230400000},"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 introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented.<\/jats:p>","DOI":"10.3390\/sym13122279","type":"journal-article","created":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T03:12:40Z","timestamp":1638328360000},"page":"2279","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Asymmetric Bimodal Double Regression Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8184-7403","authenticated-orcid":false,"given":"Diego I.","family":"Gallardo","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6643-6972","authenticated-orcid":false,"given":"Osvaldo","family":"Venegas","sequence":"additional","affiliation":[{"name":"Departamento de Ciencias Matem\u00e1ticas y F\u00edsicas, Facultad de Ingenier\u00eda, Universidad Cat\u00f3lica de Temuco, Temuco 4780000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3814-9532","authenticated-orcid":false,"given":"Tiago M.","family":"Magalh\u00e3es","sequence":"additional","affiliation":[{"name":"Department of Statistics, Institute of Exact Sciences, Federal University of Juiz de Fora, Juiz de Fora 36036-900, MG, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2348","DOI":"10.1086\/117248","article-title":"Detecting bimodality in astronomical datasets","volume":"108","author":"Ashman","year":"1994","journal-title":"Astron. 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