{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:10:44Z","timestamp":1760238644387,"version":"build-2065373602"},"reference-count":64,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T00:00:00Z","timestamp":1598918400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["ECO2017-85577-P"],"award-info":[{"award-number":["ECO2017-85577-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero\/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero\/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.<\/jats:p>","DOI":"10.3390\/sym12091439","type":"journal-article","created":{"date-parts":[[2020,9,1]],"date-time":"2020-09-01T14:21:10Z","timestamp":1598970070000},"page":"1439","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Family of Skew-Normal Distributions for Modeling Proportions and Rates with Zeros\/Ones Excess"],"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 14014, Colombia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4755-3270","authenticated-orcid":false,"given":"V\u00edctor","family":"Leiva","sequence":"additional","affiliation":[{"name":"Escuela de Ingenier\u00eda Industrial, Pontificia Universidad Cat\u00f3lica de Valpara\u00edso, 2362807 Valpara\u00edso, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-7908","authenticated-orcid":false,"given":"Emilio","family":"G\u00f3mez-D\u00e9niz","sequence":"additional","affiliation":[{"name":"Facultad de Econom\u00eda, Empresa y Turismo, Universidad de Las Palmas de Gran Canaria and TIDES Institute, 35001 Canarias, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1832-4444","authenticated-orcid":false,"given":"Carolina","family":"Marchant","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias B\u00e1sicas, Universidad Cat\u00f3lica del Maule, 3466706 Talca, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,1]]},"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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