{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T16:41:11Z","timestamp":1769186471437,"version":"3.49.0"},"reference-count":48,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T00:00:00Z","timestamp":1635724800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Digiteknologian TKI-ymparisto project (ERDF, 357 Regional Council of Pohjois-Savo","award":["A74338"],"award-info":[{"award-number":["A74338"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we use Lehmann alternative-II to extend the odd generalized exponential family. The uniqueness of this family lies in the fact that this transformation has resulted in a multitude of inverted distribution families with important applications in actuarial field. We can characterize the density of the new family as a linear combination of generalised exponential distributions, which is useful for studying some of the family\u2019s properties. Among the structural characteristics of this family that are being identified are explicit expressions for numerous types of moments, the quantile function, stress-strength reliability, generating function, R\u00e9nyi entropy, stochastic ordering, and order statistics. The maximum likelihood methodology is often used to compute the new family\u2019s parameters. To confirm that our results are converging with reduced mean square error and biases, we perform a simulation analysis of one of the special model, namely OGE2-Fr\u00e9chet. Furthermore, its application using two actuarial data sets is achieved, favoring its superiority over other competitive models, especially in risk theory.<\/jats:p>","DOI":"10.3390\/sym13112064","type":"journal-article","created":{"date-parts":[[2021,11,2]],"date-time":"2021-11-02T22:14:52Z","timestamp":1635891292000},"page":"2064","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An Alternate Generalized Odd Generalized Exponential Family with Applications to Premium Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0258-5124","authenticated-orcid":false,"given":"Sadaf","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8870-9692","authenticated-orcid":false,"given":"Oluwafemi Samson","family":"Balogun","sequence":"additional","affiliation":[{"name":"School of Computing, University of Eastern Finland, 70211 Kuopio, Northern Europe, Finland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2157-3997","authenticated-orcid":false,"given":"Muhammad Hussain","family":"Tahir","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4497-1362","authenticated-orcid":false,"given":"Waleed","family":"Almutiry","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts in Ar Rass, Qassim University, Buryadah 52571, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5359-1340","authenticated-orcid":false,"given":"Amani Abdullah","family":"Alahmadi","sequence":"additional","affiliation":[{"name":"College of Science and Humanities, Shaqra University, Shaqra 15572, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,1]]},"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 parameters to a family of distributions with application to the exponential and Weibull families","volume":"10","author":"Marshall","year":"1997","journal-title":"Biometrika"},{"key":"ref_2","first-page":"51","article-title":"Properties of generalized log-logistic families of lifetime distributions","volume":"4","author":"Gleaton","year":"2006","journal-title":"J. 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