{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:00:21Z","timestamp":1760234421526,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,20]],"date-time":"2021-05-20T00:00:00Z","timestamp":1621468800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Agency for Research and Development (ANID)","award":["FONDECYT grant number 1181662 & Anillo ACT\u201387 project"],"award-info":[{"award-number":["FONDECYT grant number 1181662 & Anillo ACT\u201387 project"]}]},{"DOI":"10.13039\/501100012655","name":"Universidad de Antofagasta","doi-asserted-by":"publisher","award":["grant SEMILLERO UA-2021"],"award-info":[{"award-number":["grant SEMILLERO UA-2021"]}],"id":[{"id":"10.13039\/501100012655","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We introduce a new class of distributions called the epsilon\u2013positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon\u2013positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log\u2013normal, log\u2013logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon\u2013positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM\u2013type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.<\/jats:p>","DOI":"10.3390\/sym13050908","type":"journal-article","created":{"date-parts":[[2021,5,20]],"date-time":"2021-05-20T06:13:45Z","timestamp":1621491225000},"page":"908","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6547-6179","authenticated-orcid":false,"given":"Perla","family":"Celis","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda y Ciencias, Universidad Adolfo Ib\u00e1\u00f1ez, Diagonal Las Torres 2640, Pe\u00f1alol\u00e9n, Santiago 7941169, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1415-1809","authenticated-orcid":false,"given":"Rolando","family":"de la Cruz","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda y Ciencias, Universidad Adolfo Ib\u00e1\u00f1ez, Diagonal Las Torres 2640, Pe\u00f1alol\u00e9n, Santiago 7941169, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Claudio","family":"Fuentes","sequence":"additional","affiliation":[{"name":"Department of Statistics, Oregon State University, 217 Weniger Hall, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3726-5507","authenticated-orcid":false,"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1080\/01621459.1996.10476725","article-title":"A generalization of the weibull distribution with application to the analysis of survival data","volume":"91","author":"Mudholkar","year":"1996","journal-title":"J. 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