New generalized unit distributions based on order statistics

New generalized unit distributions based on order statistics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article New generalized unit distributions based on order statistics Iman Mohammed Attia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7611111/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In the present paper, the author discusses the derivation of unit distributions and the derivation of the generalized form using the order statistics. The author discusses the Kumaraswamy as the smallest order statistic of the unit power distribution derived from the inverse Weibull distribution. The author discusses the unit Rayleigh distribution and how it can be generalized using the smallest, largest, and kth order statistics. Using the order statistics to generalize a distribution differs from other techniques like the power transformation and T-X family (transformed-transformer) method. For the discussed distribution, the author demonstrates the basic functions and properties with real data analysis. Applied Mathematics Applied Statistics Kumaraswamy distribution Median based unit Rayleigh distribution Unit distributions order statistics. T-X family Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7611111","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":514756849,"identity":"4d7e3892-3a9b-4152-aabf-495123db73b4","order_by":0,"name":"Iman Mohammed Attia","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0002-7333-9713","institution":"Faculty of Graduate Studies for Statistical Research","correspondingAuthor":true,"prefix":"","firstName":"Iman","middleName":"Mohammed","lastName":"Attia","suffix":""}],"badges":[],"createdAt":"2025-09-14 07:38:27","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-7611111/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7611111/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":91399744,"identity":"e96bfb5e-2638-4c75-95a6-8146918f895d","added_by":"auto","created_at":"2025-09-16 06:40:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1000443,"visible":true,"origin":"","legend":"","description":"","filename":"unitdistributions.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7611111/v1_covered_cb398c9b-8210-4e2e-9723-4577f69f5107.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eNew generalized unit distributions based on order statistics\u003c/strong\u003e\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Cairo University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Kumaraswamy distribution, Median based unit Rayleigh distribution, Unit distributions, order statistics. 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