{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T05:14:26Z","timestamp":1787030066283,"version":"build-2736575974"},"reference-count":22,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T00:00:00Z","timestamp":1586736000000},"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>This paper introduces a new family of asymmetric distributions that allows to fit unimodal as well as bimodal and trimodal data sets. The model extends the normal model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new distribution are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrix is derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. Finally, two data set are considered to illustrate the developed methodology.<\/jats:p>","DOI":"10.3390\/sym12040613","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T03:10:01Z","timestamp":1586833801000},"page":"613","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Likelihood-Based Inference for the Asymmetric Beta-Skew Alpha-Power Distribution"],"prefix":"10.3390","volume":"12","author":[{"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, Monter\u00eda 230027, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5649-532X","authenticated-orcid":false,"given":"Roger","family":"Tovar-Fal\u00f3n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, Monter\u00eda 230027, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marvin","family":"Jim\u00e9mez-Narv\u00e1ez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Industrial, Facultad de Ciencias e Ingenier\u00edas, Universidad del Sin\u00fa, Monter\u00eda 230027, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,13]]},"reference":[{"key":"ref_1","first-page":"171","article-title":"A class of distributions which includes the normal ones","volume":"12","author":"Azzalini","year":"1985","journal-title":"Scand. 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