{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T16:53:27Z","timestamp":1775148807299,"version":"3.50.1"},"reference-count":41,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,12,10]],"date-time":"2021-12-10T00:00:00Z","timestamp":1639094400000},"content-version":"vor","delay-in-days":343,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>The purpose of this paper is to investigate a new family of distributions based on an inverse trigonometric function known as the arctangent function. In the context of actuarial science, heavy\u2010tailed probability distributions are immensely beneficial and play an important role in modelling data sets. Actuaries are committed to finding for such distributions in order to get an excellent fit to complex economic and actuarial data sets. The current research takes a look at a popular method for generating new distributions which are excellent candidates for dealing with heavy\u2010tailed data. The proposed family of distributions is known as the Arctan\u2010X family of distributions and is introduced using an inverse trigonometric function. For the specific purpose of the show of strength, we studied the Arctan\u2010Weibull distribution as a special case of the developed family. To estimate the parameters of the Arctan\u2010Weibull distribution, the frequentist approach, i.e., maximum likelihood estimation, is used. A rigorous Monte Carlo simulation analysis is used to determine the efficiency of the obtained estimators. The Arctan\u2010Weibull model is demonstrated using a real\u2010world insurance data set. The Arctan\u2010Weibull is compared to well\u2010known two\u2010, three\u2010, and four\u2010parameter competitors. Among the competing distributions are Weibull, Kappa, Burr\u2010XII, and beta\u2010Weibull. For model comparison, we used the most precise tests used to know whether the Arctan\u2010Weibull distribution is more useful than competing models.<\/jats:p>","DOI":"10.1155\/2021\/4689010","type":"journal-article","created":{"date-parts":[[2021,12,11]],"date-time":"2021-12-11T03:20:16Z","timestamp":1639192816000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":31,"title":["The Arctan\u2010<i>X<\/i> Family of Distributions: Properties, Simulation, and Applications to Actuarial Sciences"],"prefix":"10.1155","volume":"2021","author":[{"given":"Ibrahim","family":"Alkhairy","sequence":"first","affiliation":[]},{"given":"M.","family":"Nagy","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4139-7334","authenticated-orcid":false,"given":"Abdisalam Hassan","family":"Muse","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2527-5938","authenticated-orcid":false,"given":"Eslam","family":"Hussam","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,12,10]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.1080\/16583655.2020.1741942"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.32604\/cmc.2020.012420"},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/5580228"},{"key":"e_1_2_12_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/3058170"},{"key":"e_1_2_12_5_2","doi-asserted-by":"publisher","DOI":"10.3390\/math9121386"},{"key":"e_1_2_12_6_2","doi-asserted-by":"publisher","DOI":"10.1590\/0001-3765201520140299"},{"key":"e_1_2_12_7_2","article-title":"Compounding of distributions: a survey and new generalized classes","volume":"3","author":"Tahir M. 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