{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,12]],"date-time":"2025-11-12T03:27:36Z","timestamp":1762918056939,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003593","name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["301808\/2016-3"],"award-info":[{"award-number":["301808\/2016-3"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.<\/jats:p>","DOI":"10.3390\/sym11121509","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T11:06:41Z","timestamp":1576148801000},"page":"1509","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference"],"prefix":"10.3390","volume":"11","author":[{"given":"Guillermo","family":"Mart\u00ednez-Fl\u00f3rez","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Estad\u00edstica, Universidad de C\u00f3rdoba, Monter\u00eda 230002, Colombia"}]},{"given":"Artur J.","family":"Lemonte","sequence":"additional","affiliation":[{"name":"Departamento de Estat\u00edstica, Universidade Federal do Rio Grande do Norte, Natal 59078970, RN, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7302-7461","authenticated-orcid":false,"given":"Hugo S.","family":"Salinas","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,12]]},"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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