{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T02:08:55Z","timestamp":1773886135957,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T00:00:00Z","timestamp":1626998400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012655","name":"Universidad de Antofagasta","doi-asserted-by":"publisher","award":["SEMILLERO UA-2021"],"award-info":[{"award-number":["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>In this paper, the inverse gamma power series (IGPS) class of distributions asymmetric is introduced. This family is obtained by compounding inverse gamma and power series distributions. We present the density, survival and hazard functions, moments and the order statistics of the IGPS. Estimation is first discussed by means of the quantile method. Then, an EM algorithm is implemented to compute the maximum likelihood estimates of the parameters. Moreover, a simulation study is carried out to examine the effectiveness of these estimates. Finally, the performance of the new class is analyzed by means of two asymmetric real data sets.<\/jats:p>","DOI":"10.3390\/sym13081328","type":"journal-article","created":{"date-parts":[[2021,7,23]],"date-time":"2021-07-23T10:31:44Z","timestamp":1627036304000},"page":"1328","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Compound Class of the Inverse Gamma and Power Series Distributions"],"prefix":"10.3390","volume":"13","author":[{"given":"Pilar A.","family":"Rivera","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\/0000-0001-6364-627X","authenticated-orcid":false,"given":"Enrique","family":"Calder\u00edn-Ojeda","sequence":"additional","affiliation":[{"name":"Centre for Actuarial Studies, Department of Economics, The University of Melbourne, Melbourne, VIC 3010, Australia"}],"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"}]},{"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\u00e1ticas, Facultad de Ciencias B\u00e1sicas, Universidad de Antofagasta, Antofagasta 1240000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0167-7152(98)00012-1","article-title":"A Lifetime Distribution with Decreasing Failure Rate","volume":"39","author":"Adamidis","year":"1998","journal-title":"Stat. 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