Norm-Based Measures of Inequality: A Property-Focused Evaluation

Norm-Based Measures of Inequality: A Property-Focused Evaluation | 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 Article Norm-Based Measures of Inequality: A Property-Focused Evaluation Muhammad Hamza, Beomsu Baek, Joongyang Park, Youngsoon Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7210061/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 Norm-based inequality measures are developed within the UD/RUD framework by applying L 1 and squared L 2 norms to the CDQF, QF, and their joint CDQF representations. All six indices satisfy scale, replication, and translation invariance, as well as anonymity, and their behavior under Pigou-Dalton transfers and subgroup decomposition is characterized analytically. CDQF-based indices combine the vertical and horizontal gaps, giving them representation decomposability and making L 1,cq and L 2 2,cq the most informative overall measures of inequality. A Monte Carlo study on six contrasting income distributions corroborates these theoretical advantages, confirming finite, stable values even for mixed-sign and heavy-tailed supports. JEL Classification: C43 , D31 , D63 Physical sciences/Mathematics and computing Physical sciences/Physics anonymity CDQF decomposability inequality Lorenz curve norm normalization population invariance RUD income replication invariance QF scale invariance transfer principle Full Text Additional Declarations No competing interests reported. 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-7210061","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":490612755,"identity":"a48aeb36-2eb7-4899-ad46-452cd47d43ed","order_by":0,"name":"Muhammad Hamza","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Hamza","suffix":""},{"id":490612756,"identity":"6d07a173-8b78-414a-b336-162263fffbce","order_by":1,"name":"Beomsu Baek","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Beomsu","middleName":"","lastName":"Baek","suffix":""},{"id":490612758,"identity":"330176cb-364d-40a8-bc82-405b56df2d88","order_by":2,"name":"Joongyang Park","email":"","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":false,"prefix":"","firstName":"Joongyang","middleName":"","lastName":"Park","suffix":""},{"id":490612759,"identity":"78d1e54c-efcf-4fef-84d7-e48d290071e0","order_by":3,"name":"Youngsoon Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA70lEQVRIiWNgGAWjYFADHsYGhg9QNpBJpBbGGSRqYWBg5iFGi8HxHrOHX/7YyJnzHG7dbPPrTmID++EHjDP34NFy5oy5sWxbmrFlb2Pb7dy+Z4kNPGkGjBue4dFyI8dMWrLhcOKG84xALT2HExsYchgYHxwgoEXiD1SLJUgL/xvCWiQ/sAG1nAU6jOEHUIsE0JYNeLRInjlWJs0I9IvBmYNtN3sbDhu3STwzODgDjxa+483bJH8AQ8zgTPqzGz/+HJbt509++LAHjxaFA0jRwcDYxsDABqTxaGBgkG8AKvwB5/7Bp3YUjIJRMApGKgAAb7pettdVycIAAAAASUVORK5CYII=","orcid":"","institution":"Gyeongsang National University","correspondingAuthor":true,"prefix":"","firstName":"Youngsoon","middleName":"","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2025-07-25 03:53:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7210061/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7210061/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":87686566,"identity":"68da2284-3b6d-4d90-8a49-f87c8f664324","added_by":"auto","created_at":"2025-07-28 02:48:52","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":967142,"visible":true,"origin":"","legend":"","description":"","filename":"Article.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7210061/v1_covered_2d20cc4f-6643-4bb3-9845-694aa2a2df9a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Norm-Based Measures of Inequality: A Property-Focused Evaluation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"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":"anonymity, CDQF, decomposability, inequality, Lorenz curve, norm, normalization, population invariance, RUD income, replication invariance, QF, scale invariance, transfer principle","lastPublishedDoi":"10.21203/rs.3.rs-7210061/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7210061/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNorm-based inequality measures are developed within the UD/RUD framework by applying L\u003csub\u003e1\u003c/sub\u003e and squared L\u003csub\u003e2\u003c/sub\u003e norms to the CDQF, QF, and their joint CDQF representations. 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