The New Generalized Odd Median Based Unit Rayleigh with a New Shape Oscillating Hazard Rate Function

The New Generalized Odd Median Based Unit Rayleigh with a New Shape Oscillating Hazard Rate Function | 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 The New Generalized Odd Median Based Unit Rayleigh with a New Shape Oscillating Hazard Rate Function Iman Mohammed Attia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6096356/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 this paper, the author presents the generalized form of the Median-Based Unit Rayleigh (MBUR) distribution, a novel statistical distribution that is specifically defined within the interval (0, 1) expressing oscillating hazard rate function. This generalization adds a new parameter to the MBUR distribution that significantly addresses the unique characteristics of data represented as ratios and proportions, which are commonly encountered in various fields of research. The establishment of this generalization aims to deepen our understanding of these phenomena by providing a robust framework for analysis. The paper offers a thorough and meticulous derivation of the probability density function (PDF) for the MBUR distribution, illuminating each phase of the process with clarity and precision. It delves deep into the intricacies of the MBUR distribution's properties, presenting a rigorous examination of the accompanying functions that are vital for robust statistical evaluation. These functions—comprising the cumulative distribution function (CDF), survival function, hazard rate and reversed hazard rate function. The paper discusses real data analysis and how the generalization improves such analysis. Applied Mathematics Applied Statistics Generalized odd MBUR Median Based Unit Rayleigh maximum likelihood estimator oscillating hazard rate function 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-6096356","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":420098347,"identity":"1881e07e-773a-4a84-9768-1e52543330d3","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":"2025-02-24 11:28:17","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-6096356/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6096356/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77188509,"identity":"9253c54a-27c9-45f9-bc2c-b394e4716cd6","added_by":"auto","created_at":"2025-02-26 04:36:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":19396193,"visible":true,"origin":"","legend":"","description":"","filename":"GeneralizedOddMBUR.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6096356/v1_covered_358ed523-4669-4cce-b2bd-017327b94871.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eThe New Generalized Odd Median Based Unit Rayleigh with a New Shape Oscillating Hazard Rate Function\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":"Generalized odd MBUR, Median Based Unit Rayleigh, maximum likelihood estimator , oscillating hazard rate function","lastPublishedDoi":"10.21203/rs.3.rs-6096356/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6096356/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, the author presents the generalized form of the Median-Based Unit Rayleigh (MBUR) distribution, a novel statistical distribution that is specifically defined within the interval (0, 1) expressing oscillating hazard rate function. 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