{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T09:21:04Z","timestamp":1781169664030,"version":"3.54.1"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T00:00:00Z","timestamp":1613088000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research","award":["G- 123-363-1440"],"award-info":[{"award-number":["G- 123-363-1440"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The last years have revealed the importance of the inverse Lomax distribution in the understanding of lifetime heavy-tailed phenomena. However, the inverse Lomax modeling capabilities have certain limits that researchers aim to overcome. These limits include a certain stiffness in the modulation of the peak and tail properties of the related probability density function. In this paper, a solution is given by using the functionalities of the half logistic family. We introduce a new three-parameter extended inverse Lomax distribution called the half logistic inverse Lomax distribution. We highlight its superiority over the inverse Lomax distribution through various theoretical and practical approaches. The derived properties include the stochastic orders, quantiles, moments, incomplete moments, entropy (R\u00e9nyi and q) and order statistics. Then, an emphasis is put on the corresponding parametric model. The parameters estimation is performed by six well-established methods. Numerical results are presented to compare the performance of the obtained estimates. Also, a simulation study on the estimation of the R\u00e9nyi entropy is proposed. Finally, we consider three practical data sets, one containing environmental data, another dealing with engineering data and the last containing insurance data, to show how the practitioner can take advantage of the new half logistic inverse Lomax model.<\/jats:p>","DOI":"10.3390\/sym13020309","type":"journal-article","created":{"date-parts":[[2021,2,12]],"date-time":"2021-02-12T18:46:31Z","timestamp":1613155591000},"page":"309","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Half Logistic Inverse Lomax Distribution with Applications"],"prefix":"10.3390","volume":"13","author":[{"given":"Sanaa","family":"Al-Marzouki","sequence":"first","affiliation":[{"name":"Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah 21551, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christophe","family":"Chesneau","sequence":"additional","affiliation":[{"name":"Department of Mathematics, LMNO, Universit\u00e9 de Caen-Normandie, Campus II, Science 3, 14032 Caen, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"The Higher Institute of Commercial Sciences, Al mahalla Al kubra, Algarbia 31951, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/0304-4076(94)01612-4","article-title":"A generalization of the beta distribution with applications","volume":"66","author":"McDonald","year":"1995","journal-title":"J. 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