{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T16:10:56Z","timestamp":1760199056611,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,12,6]],"date-time":"2018-12-06T00:00:00Z","timestamp":1544054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SEMILLERO","award":["UA-2018"],"award-info":[{"award-number":["UA-2018"]}]},{"name":"CTM2015","award":["68276-R"],"award-info":[{"award-number":["68276-R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a generalization of the modified slash Birnbaum\u2013Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton\u2013Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.<\/jats:p>","DOI":"10.3390\/sym10120724","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T03:46:14Z","timestamp":1544154374000},"page":"724","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Generalized Modified Slash Birnbaum\u2013Saunders Distribution"],"prefix":"10.3390","volume":"10","author":[{"given":"Jimmy","family":"Reyes","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9064-2597","authenticated-orcid":false,"given":"Inmaculada","family":"Barranco-Chamorro","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica e Investigaci\u00f3n Operativa, Universidad de Sevilla, 41000 Sevilla, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8184-7403","authenticated-orcid":false,"given":"Diego I.","family":"Gallardo","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H\u00e9ctor W.","family":"G\u00f3mez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,12,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.2307\/3212003","article-title":"A New Family of Life Distributions","volume":"6","author":"Birnbaum","year":"1969","journal-title":"J. Appl. Probab."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"328","DOI":"10.2307\/3212004","article-title":"Estimation for a family of life distributions with applications to fatigue","volume":"6","author":"Birnbaum","year":"1969a","journal-title":"J. Appl. Probab."},{"key":"ref_3","first-page":"25","article-title":"A quantile alternative for kurtosis","volume":"37","author":"Moors","year":"1988","journal-title":"J. R. Stat. Soc. Ser. D"},{"key":"ref_4","unstructured":"Johnson, N.L., Kotz, S., and Balakrishnan, N. (1995). Continuous Univariate Distributions, Wiley. [2nd ed.]."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Leiva, V. (2016). The Birnbaum\u2013Saunders Distribution, Academic Press.","DOI":"10.1016\/B978-0-12-803769-0.00002-9"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.spl.2008.08.014","article-title":"An extension of the generalized Birnbaum\u2013Saunders distribution","volume":"79","author":"Bolfarine","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"ref_7","first-page":"929","article-title":"Modified slash distribution","volume":"47","author":"Reyes","year":"2013","journal-title":"Stat. J. Theor. App. Stat."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.1467-9574.1972.tb00191.x","article-title":"Understanding some long-tailed symmetrical distributions","volume":"26","author":"Rogers","year":"1972","journal-title":"Stat. Neerl."},{"key":"ref_9","unstructured":"Reyes, J., Barranco-Chamorro, I., and G\u00f3mez, H.W. (2018). Generalized modified slash distribution. 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[3rd ed.].","DOI":"10.1002\/9781118165676"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/724\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:31:34Z","timestamp":1760196694000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/12\/724"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,6]]},"references-count":17,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["sym10120724"],"URL":"https:\/\/doi.org\/10.3390\/sym10120724","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2018,12,6]]}}}