{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:27:34Z","timestamp":1771673254840,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,20]],"date-time":"2023-08-20T00:00:00Z","timestamp":1692489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"SEMILLERO UA-2023 project, Chile"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, a more flexible extension of the Fr\u00e9chet distribution is introduced. The new distribution is defined by means of the stochastic representation as the quotient of two independent random variables, a Fr\u00e9chet distribution and the power of a random variable, with uniform distribution in the interval (0, 1). We will call this new extension the slash Fr\u00e9chet distribution and one of its main characteristics is that its tails are heavier than the Fr\u00e9chet distribution. The general density of this distribution and some basic properties are determined. Its moments, skewness coefficients, and kurtosis are calculated. In addition, the estimation of the model parameters is obtained by the method of moments and maximum likelihood. Finally, three applications with real data are performed by fitting the new model and comparing it with the Fr\u00e9chet distribution.<\/jats:p>","DOI":"10.3390\/sym15081608","type":"journal-article","created":{"date-parts":[[2023,8,21]],"date-time":"2023-08-21T01:33:11Z","timestamp":1692581591000},"page":"1608","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A More Flexible Extension of the Fr\u00e9chet Distribution Based on the Incomplete Gamma Function and Applications"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-5247-8308","authenticated-orcid":false,"given":"Jaime S.","family":"Castillo","sequence":"first","affiliation":[{"name":"Escuela de Postgrado, Vicerrector\u00eda de Investigaci\u00f3n, Innovaci\u00f3n y Postgrado, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mario A.","family":"Rojas","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencia de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2921-3056","authenticated-orcid":false,"given":"Jimmy","family":"Reyes","sequence":"additional","affiliation":[{"name":"Departamento de Estad\u00edstica y Ciencia de Datos, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,20]]},"reference":[{"key":"ref_1","first-page":"93","article-title":"Sur la loi de Probabilit\u00e9 de l\u2019\u00e9cart Maximum","volume":"6","year":"1927","journal-title":"Ann. 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