{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T00:56:03Z","timestamp":1775696163675,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T00:00:00Z","timestamp":1346716800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The aim of this work is to provide the tools to compute the well-known Kullback\u2013Leibler divergence measure for the flexible family of multivariate skew-normal distributions. In particular, we use the Jeffreys divergence measure to compare the multivariate normal distribution with the skew-multivariate normal distribution, showing that this is equivalent to comparing univariate versions of these distributions. Finally, we applied our results on a seismological catalogue data set related to the 2010 Maule earthquake. Specifically, we compare the distributions of the local magnitudes of the regions formed by the aftershocks.<\/jats:p>","DOI":"10.3390\/e14091606","type":"journal-article","created":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T11:09:45Z","timestamp":1346756985000},"page":"1606-1626","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":67,"title":["Kullback\u2013Leibler Divergence Measure for Multivariate Skew-Normal Distributions"],"prefix":"10.3390","volume":"14","author":[{"given":"Javier E.","family":"Contreras-Reyes","sequence":"first","affiliation":[{"name":"Divisi\u00f3n de Investigaci\u00f3n Pesquera, Instituto de Fomento Pesquero, Almte, Manuel Blanco Encalada 839, Valpara\u00edso, 2361827, Chile"},{"name":"Departamento de Estad\u00edstica, Universidad de Valpara\u00edso, Gran Breta\u00f1a 1111, Playa Ancha, Valpara\u00edso, 2360102, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reinaldo B.","family":"Arellano-Valle","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica, Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Av. Vicu\u00f1a Mackenna 4860, Macul, Santiago, 7820436, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2012,9,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_3","first-page":"81","article-title":"Information theory and image understanding: An application to polarimetric SAR imagery","volume":"2","author":"Frery","year":"2011","journal-title":"Chil. J. 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