{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T04:09:49Z","timestamp":1777435789221,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2020,10,14]],"date-time":"2020-10-14T00:00:00Z","timestamp":1602633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Researchers Supporting Project","award":["RSP-2020\/156"],"award-info":[{"award-number":["RSP-2020\/156"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model.<\/jats:p>","DOI":"10.3390\/sym12101677","type":"journal-article","created":{"date-parts":[[2020,10,17]],"date-time":"2020-10-17T07:23:22Z","timestamp":1602919402000},"page":"1677","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["The Transmuted Muth Generated Class of Distributions with Applications"],"prefix":"10.3390","volume":"12","author":[{"given":"Abdulhakim A.","family":"Al-Babtain","sequence":"first","affiliation":[{"name":"Department of Statistics and Operations Research, King Saud University, Riyadh 11362, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibrahim","family":"Elbatal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Universit\u00e9 de Caen, LMNO, Campus II, Science 3, 14032 Caen, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6192-9890","authenticated-orcid":false,"given":"Farrukh","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,14]]},"reference":[{"key":"ref_1","first-page":"401","article-title":"Reliability models with positive memory derived from the mean residual life function","volume":"Volume 2","author":"Tsokos","year":"1977","journal-title":"The Theory and Applications of Reliability"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"291","DOI":"10.3846\/13926292.2015.1048540","article-title":"On the Muth distribution","volume":"20","year":"2015","journal-title":"Math. 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