A note on the undercover relationship between the Chotikapanich Lorenz curve and the Pareto distribution.

A note on the undercover relationship between the Chotikapanich Lorenz curve and the Pareto distribution. | 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 A note on the undercover relationship between the Chotikapanich Lorenz curve and the Pareto distribution. Javier Cortés-Orihuela, Pablo Gutiérrez Cubillos This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4391558/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 We study the relationship between the Chotikapanich (1993) Lorenz curve and the Pareto distribution. First, we show that the Chotikapanich Lorenz curve is generated by a log-uniform distribution. Second, we show that the log-uniform distribution is a limiting case of a truncated Pareto distribution. Given this, we propose a mixture Lorenz curve model to estimate the scale parameter of the Pareto distribution, thus allowing us to identify at which point of the distribution incomes become Pareto-distributed. This model assumes that the bottom part of the income distribution is drawn from a log-uniform distribution, and the upper part as a classical Pareto distribution. Using Montecarlo simulations, we show that our model can accurately recover the threshold. With this, we estimate this model for 181 countries using data from the World Income Inequality Database. We find a negative relationship between the aggregate level of inequality (measured through the Gini coefficient) and the point where the Pareto distribution starts. JEL Classification: D3, H8. Pareto distribution Chotikapanich distribution Lorenz curves Top incomes measurement Income inequality 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. 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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-4391558","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":302095501,"identity":"68876a63-5be7-4d2b-9b1d-7c90ba3e1aea","order_by":0,"name":"Javier Cortés-Orihuela","email":"","orcid":"","institution":"University of Chile","correspondingAuthor":false,"prefix":"","firstName":"Javier","middleName":"","lastName":"Cortés-Orihuela","suffix":""},{"id":302095502,"identity":"9a846f5c-f0c8-457c-a485-c0c4a11623b8","order_by":1,"name":"Pablo Gutiérrez Cubillos","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYLCCBCDmZz4AYbOxg6gCvBoYG0BaJNsSoFqYQZQBAS1gNcegWhgIaTHnX2P+4EGFXeLmY8zHHjC22eXxMQOd+AOPFssZbwwbEs4kJ247xpZuwNiWXMzGzJbA2INHi8GNM4YNiW0HErfd7zGTYAQy2ph5DJjxOQyi5d+BxM1t/N+gWvg/4NdyvgeopeFA4gY2HjaYLQx4tVjOYCuckXAs2XjGMTYziYRzyUAtbAYH8fnFnP/who8/auxk+9uYn0l8KLNLnN/e/PDBjwo8DpNIQOLB2AdwawBq4ccrPQpGwSgYBaMACAAsqU/dCuiMBwAAAABJRU5ErkJggg==","orcid":"","institution":"University of Chile","correspondingAuthor":true,"prefix":"","firstName":"Pablo","middleName":"Gutiérrez","lastName":"Cubillos","suffix":""}],"badges":[],"createdAt":"2024-05-08 22:23:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4391558/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4391558/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58071363,"identity":"b687d780-7fb5-4582-9da9-ce50ceb18acf","added_by":"auto","created_at":"2024-06-10 18:50:14","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":337324,"visible":true,"origin":"","legend":"","description":"","filename":"Choti.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4391558/v1_covered_e8d9ab32-d04f-49af-9ac2-225b90f172b5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eA note on the undercover relationship between the Chotikapanich Lorenz curve and the Pareto distribution.\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","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":"Pareto distribution, Chotikapanich distribution, Lorenz curves, Top incomes measurement, Income inequality","lastPublishedDoi":"10.21203/rs.3.rs-4391558/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4391558/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe study the relationship between the Chotikapanich (1993) Lorenz curve and the Pareto distribution. 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