{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T05:46:50Z","timestamp":1771652810768,"version":"3.50.1"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T00:00:00Z","timestamp":1731456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSP2024R392"],"award-info":[{"award-number":["RSP2024R392"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This study introduces the DUS Topp\u2013Leone family of distributions, a novel extension of the Topp\u2013Leone distribution enhanced by the DUS transformer. We derive the cumulative distribution function (CDF) and probability density function (PDF), demonstrating the distribution\u2019s flexibility in modeling various lifetime phenomena. The DUS-TL exponential distribution was studied as a sub-model, with analytical and graphical evidence revealing that it exhibits a unique unimodal shape, along with fat-tail characteristics, making it suitable for time-to-event data analysis. We evaluate parameter estimation methods, revealing that non-Bayesian approaches, particularly Maximum Likelihood and Least Squares, outperform Bayesian techniques in terms of bias and root mean square error. Additionally, the distribution effectively models datasets with varying skewness and kurtosis values, as illustrated by its application to total factor productivity data across African countries and the mortality rate of people who injected drugs. Overall, the DUS Topp\u2013Leone family represents a significant advancement in statistical modeling, offering robust tools for researchers in diverse fields.<\/jats:p>","DOI":"10.3390\/e26110973","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T08:09:28Z","timestamp":1731485368000},"page":"973","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["DUS Topp\u2013Leone-G Family of Distributions: Baseline Extension, Properties, Estimation, Simulation and Useful Applications"],"prefix":"10.3390","volume":"26","author":[{"given":"Divine-Favour N.","family":"Ekemezie","sequence":"first","affiliation":[{"name":"Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, P.O. Box 5025, Awka 420007, Nigeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9335-3398","authenticated-orcid":false,"given":"Kizito E.","family":"Anyiam","sequence":"additional","affiliation":[{"name":"Department of Statistics, College of Physical Sciences, Federal University of Technology, Owerri 460114, Nigeria"}]},{"given":"Mohammed","family":"Kayid","sequence":"additional","affiliation":[{"name":"Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-9692","authenticated-orcid":false,"given":"Oluwafemi Samson","family":"Balogun","sequence":"additional","affiliation":[{"name":"Department of Computing, University of Eastern Finland, FI-70211 Kuopio, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7753-1868","authenticated-orcid":false,"given":"Okechukwu J.","family":"Obulezi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, P.O. Box 5025, Awka 420007, Nigeria"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,13]]},"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","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1081\/STA-120003130","article-title":"Beta-normal distribution and its applications","volume":"31","author":"Eugene","year":"2002","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1080\/00949650903530745","article-title":"A new family of generalized distributions","volume":"81","author":"Cordeiro","year":"2011","journal-title":"J. Stat. Comput. 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