{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T23:01:18Z","timestamp":1775602878703,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2021,3,14]],"date-time":"2021-03-14T00:00:00Z","timestamp":1615680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson\u2013Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.<\/jats:p>","DOI":"10.3390\/sym13030474","type":"journal-article","created":{"date-parts":[[2021,3,15]],"date-time":"2021-03-15T02:51:48Z","timestamp":1615776708000},"page":"474","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science"],"prefix":"10.3390","volume":"13","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3430-2464","authenticated-orcid":false,"given":"Hazem","family":"Al-Mofleh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6767-4016","authenticated-orcid":false,"given":"Ahmed M.","family":"Gemeay","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6723-6785","authenticated-orcid":false,"given":"Ahmed Z.","family":"Afify","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdullah M.","family":"Sarg","sequence":"additional","affiliation":[{"name":"Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1093\/biomet\/84.3.641","article-title":"A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families","volume":"84","author":"Marshall","year":"1997","journal-title":"Biometrika"},{"key":"ref_2","unstructured":"Shaw, W.T., and Buckley, I.R. 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