{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T01:59:23Z","timestamp":1785376763198,"version":"3.55.0"},"reference-count":35,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T00:00:00Z","timestamp":1785283200000},"content-version":"vor","delay-in-days":209,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["The Scientific World Journal"],"published-print":{"date-parts":[[2026,1]]},"abstract":"<jats:p>The Pareto distribution is a fundamental model for heavy\u2010tailed data, but its rigid structure often fails to capture the diverse tail behaviors and hazard rate patterns observed in real\u2010world applications. To address this limitation, we propose a new extended Pareto (EP) distribution, obtained by applying the modified Fr\u00e9chet generator to the classical Pareto baseline. This novel construction introduces an additional shape parameter that enhances tail flexibility and accommodates a wide range of hazard rate shapes, including decreasing, increasing, bathtub, and upside\u2010down bathtub forms. We derive several key distributional properties, including the probability density and cumulative distribution functions, quantile function, and moments. Parameter estimation is carried out using the method of maximum likelihood, and the asymptotic properties of the estimators are established. Monte Carlo simulations confirm the consistency and efficiency of the estimators. The practical utility of the EP model is demonstrated through applications to diverse real datasets, where it consistently outperforms classical Pareto and other Pareto\u2010type competitors based on likelihood\u2010based criteria and goodness\u2010of\u2010fit tests. The proposed distribution provides a powerful new tool for modeling heavy\u2010tailed phenomena in economics, finance, reliability, hydrology, and environmental sciences.<\/jats:p>","DOI":"10.1155\/tswj\/6572559","type":"journal-article","created":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T01:37:28Z","timestamp":1785375448000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Extended Pareto Distribution: Statistical Properties, Estimation, and Applications"],"prefix":"10.1155","volume":"2026","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4291-6247","authenticated-orcid":false,"given":"Merga Abdissa","family":"Aga","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,7,29]]},"reference":[{"key":"e_1_2_9_1_2","volume-title":"Cours d\u2032\u00c9conomie Politique","author":"Pareto V.","year":"1897"},{"key":"e_1_2_9_2_2","doi-asserted-by":"crossref","DOI":"10.1002\/0471457175","volume-title":"Statistical Size Distributions in Economics and Actuarial Sciences","author":"Kleiber C.","year":"2003"},{"key":"e_1_2_9_3_2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-33483-2","volume-title":"Modelling Extremal Events for Insurance and Finance","author":"Embrechts P.","year":"1997"},{"key":"e_1_2_9_4_2","doi-asserted-by":"crossref","DOI":"10.1201\/b18141","volume-title":"Pareto Distributions","author":"Arnold B. 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