Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions

Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions | 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 Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions Jonathan El Methni, Stéphane Girard This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7773261/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract Most of extrapolation methods dedicated to the estimation of extreme risk measures rely on the approximation of the excesses distribution above a high threshold by a Generalized Pareto Distribution (GPD). We propose an alternative to the GPD, called the Refined Pareto Distribution (RPD), which allows for a second-order approximation of the excesses distribution. The parameters of the RPD are estimated using an Approximate Bayesian Computation (ABC) method, and reduced-bias estimators of extreme risk measures are then derived together with the associated credible intervals. The ABC estimator demonstrates good performance over a wide range of heavy-tailed distributions. Its usefulness is also illustrated on two data sets of insurance claims. Extreme-value statistics Generalized Pareto Distribution Heavy-tailed distributions Risk measures Full Text Additional Declarations No competing interests reported. Supplementary Files STCOsubmissionsupplement.pdf Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 30 Mar, 2026 Reviews received at journal 28 Mar, 2026 Reviewers agreed at journal 16 Feb, 2026 Reviewers agreed at journal 15 Oct, 2025 Reviewers agreed at journal 09 Oct, 2025 Reviewers invited by journal 09 Oct, 2025 Editor assigned by journal 07 Oct, 2025 Submission checks completed at journal 07 Oct, 2025 First submitted to journal 03 Oct, 2025 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. 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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-7773261","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":530190990,"identity":"955e4e63-0dcb-438f-8cda-fe0f62b91b2b","order_by":0,"name":"Jonathan El Methni","email":"","orcid":"","institution":"Grenoble Alpes University","correspondingAuthor":false,"prefix":"","firstName":"Jonathan","middleName":"El","lastName":"Methni","suffix":""},{"id":530190992,"identity":"37f48e41-b4a5-4010-8226-d70c2961e383","order_by":1,"name":"Stéphane 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We propose an alternative to the GPD, called the Refined Pareto Distribution (RPD), which allows for a second-order approximation of the excesses distribution. The parameters of the RPD are estimated using an Approximate Bayesian Computation (ABC) method, and reduced-bias estimators of extreme risk measures are then derived together with the associated credible intervals. The ABC estimator \ndemonstrates good performance over a wide range of heavy-tailed distributions. Its usefulness is also illustrated on two data sets of insurance claims.","manuscriptTitle":"Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-23 19:54:37","doi":"10.21203/rs.3.rs-7773261/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-30T08:31:43+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-28T12:03:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"110027638615857509114931975060099666285","date":"2026-02-16T14:14:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"9374124322572079511410582651280078195","date":"2025-10-15T16:14:43+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"131402166793947410416862127890356012781","date":"2025-10-09T16:46:05+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-09T13:40:54+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-07T07:09:48+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-07T05:07:34+00:00","index":"","fulltext":""},{"type":"submitted","content":"Statistics and Computing","date":"2025-10-03T11:48:58+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"statistics-and-computing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"stco","sideBox":"Learn more about [Statistics and Computing](http://link.springer.com/journal/11222)","snPcode":"11222","submissionUrl":"https://submission.nature.com/new-submission/11222/3","title":"Statistics and Computing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"f7a4daa3-d0aa-4d75-9190-bd932c0a4776","owner":[],"postedDate":"October 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-30T11:55:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-23 19:54:37","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7773261","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7773261","identity":"rs-7773261","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}