On computing the number of distinct values occurring in generalized Dirichlet process samples

On computing the number of distinct values occurring in generalized Dirichlet process samples | 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 On computing the number of distinct values occurring in generalized Dirichlet process samples Hassan Akell, Farkhondeh-Alsadat Sajadi, Iraj Kazemi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4168279/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 This paper studies the generalized Dirichlet process ( \(\mathcal{GDP}\) ) with its main properties, including moments of random weights and tail moments. We present the truncated \(\mathcal{GDP}\ as a finite mixture distribution and assess the error bounds caused by the truncation. This tactic provides more practicable stick-breaking priors in nonparametric Bayesian settings and facilitates computation. We obtain the joint density of random weights, show that the number of distinct values varies on raising the $\mathcal{GDP}$ samples, and present the impact of the precision parameter on this number. We also show that our results coincide with the Dirichlet process \((\mathcal{DP})\) . MSC Classification: 62E15 , 60C05 , 97K60 Almost sure truncation Precision parameter Random weights Stick-breaking construction Tail moments 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-4168279","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":287346203,"identity":"e92ab50a-6d88-418d-849b-50d8aedd859c","order_by":0,"name":"Hassan Akell","email":"","orcid":"","institution":"University of Isfahan","correspondingAuthor":false,"prefix":"","firstName":"Hassan","middleName":"","lastName":"Akell","suffix":""},{"id":287346204,"identity":"31730eca-1816-445f-817d-eb600d5a08ff","order_by":1,"name":"Farkhondeh-Alsadat Sajadi","email":"","orcid":"","institution":"University of Isfahan","correspondingAuthor":false,"prefix":"","firstName":"Farkhondeh-Alsadat","middleName":"","lastName":"Sajadi","suffix":""},{"id":287346205,"identity":"b53bc032-9120-4f63-8c4f-a28797be8c39","order_by":2,"name":"Iraj Kazemi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYBACNiAEAR5+qAAPmEwgRotkAzMDwwFitDBAtTAYHIBoIQz4GNgSP/6o2CZjfP78wc8fGA7LMLAffsDwcA9ehx2WkDhzm8fsRjKzxAGGwzwMPGkGDAnP8Glhb5AwbANpYWaAaGHIAfoFjxOBWpp/JP67zWPcf5j5B1gL/xtCWtiOSRxsuM1jwJDMBrFFgpAtzGxplg3HbvNI3Eg2szhjkM7DJvHM4AA+LfLtbcY3f9TctufvP/j4RkWFtT0/f/LDhz/waGFgRuEZQOIJn4ZRMApGwSgYBUQAADB6RveYl4FWAAAAAElFTkSuQmCC","orcid":"","institution":"University of Isfahan","correspondingAuthor":true,"prefix":"","firstName":"Iraj","middleName":"","lastName":"Kazemi","suffix":""}],"badges":[],"createdAt":"2024-03-26 08:31:13","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4168279/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4168279/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55678505,"identity":"11d1c593-17c8-4b79-8039-a9aa70be99b8","added_by":"auto","created_at":"2024-05-01 15:51:32","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1423324,"visible":true,"origin":"","legend":"","description":"","filename":"3Akelletal.2024OncomputingMCAP.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4168279/v1_covered_a609d2bc-1725-431f-afa0-c2dd91e11526.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"On computing the number of distinct values occurring in generalized Dirichlet process samples","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"Almost sure truncation, Precision parameter, Random weights, Stick-breaking construction, Tail moments","lastPublishedDoi":"10.21203/rs.3.rs-4168279/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4168279/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper studies the generalized Dirichlet process ( \\(\\mathcal{GDP}\\) ) with its main properties, including moments of random weights and tail moments. 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