{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:12:14Z","timestamp":1760235134340,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T00:00:00Z","timestamp":1626652800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Proyecto DIUDA de inserci\u00f3n","award":["22367"],"award-info":[{"award-number":["22367"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum\u2013Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum\u2013Saunders and skewed log-linear Birnbaum\u2013Saunders distributions. As shown, it is able to surpass the ordinary sinh-normal models when fitting data sets with high (above the expected with the sinh-normal) degrees of asymmetry. Maximum likelihood estimation is developed with the inverse of the observed information matrix used for standard error estimation. Large sample properties of the maximum likelihood estimators such as consistency and asymptotic normality are established. An application is reported for the data set previously analyzed in the literature, where performance of the new distribution is shown when compared with other proposed alternative models.<\/jats:p>","DOI":"10.3390\/sym13071297","type":"journal-article","created":{"date-parts":[[2021,7,19]],"date-time":"2021-07-19T10:07:37Z","timestamp":1626689257000},"page":"1297","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The Skewed-Elliptical Log-Linear Birnbaum\u2013Saunders Alpha-Power Model"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6441-5377","authenticated-orcid":false,"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica y Estad\u00edstica, Facultad de Ciencias B\u00e1sicas, Universidad de C\u00f3rdoba, Monter\u00eda 230027, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heleno","family":"Bolfarine","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edtica, IME, Universidade de S\u00e3o Paulo, S\u00e3o Paulo 13565-905, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8092-9666","authenticated-orcid":false,"given":"Yolanda M.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ingenieria, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,19]]},"reference":[{"key":"ref_1","unstructured":"Fang, K.T., and Zhang, Y.T. 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