{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T18:23:48Z","timestamp":1767205428368,"version":"build-2238731810"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Symmetry"],"abstract":"<jats:p>The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal\/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recently introduced Lambert transformation when considering a generalized bimodal baseline distribution. The bimodal-normal and generalized bimodal distributions can be derived as special cases of the new distribution. The main structural properties are derived and the parameter estimation is carried out under the maximum likelihood method. The behavior of the estimators is assessed through simulation experiments. Finally, two applications are presented in order to illustrate the utility of the proposed distribution in data modeling in different real settings.<\/jats:p>","DOI":"10.3390\/sym13020269","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T08:33:48Z","timestamp":1612514028000},"page":"269","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Unimodal\/Bimodal Skew\/Symmetric Distribution Generated from Lambert\u2019s Transformation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9847-1497","authenticated-orcid":false,"given":"Yuri A.","family":"Iriarte","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8685-9470","authenticated-orcid":false,"given":"M\u00e1rio","family":"de Castro","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancias Matem\u00e1ticas e de Computa\u00e7\u00e3o, Universidade de S\u00e3o Paulo, S\u00e3o Carlos 13560-095, SP, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1093\/aesa\/39.1.7","article-title":"Dimorphism in the African Oecophylla worker Nd an anomaly (Hym.: Formicidae)","volume":"39","author":"Weber","year":"1946","journal-title":"Ann. 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