Modelling the proportions with excessive endpoints based on a generalized Lindley binomial model

Modelling the proportions with excessive endpoints based on a generalized Lindley binomial model | 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 Modelling the proportions with excessive endpoints based on a generalized Lindley binomial model Dianliang Deng, Xiaoqing Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4510950/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 This paper presents the generalized Lindley binomial (GLB) distribution, a novel probability distribution designed for the analysis of proportional data with excessive endpoints. The study delves into the probabilistic characteristics of the GLB distribution, including the probability mass function and the rth factorial moment function. Estimation of the distribution parameters in the GLB model, both with and without covariates, is addressed using the Fisher scoring algorithm and the EM algorithm. Furthermore, the paper explores techniques for model diagnosis and evaluates the goodness of fit for the proposed GLB model. To illustrate the performance of the derived EM algorithms in parameter estimation, a limited simulation study is conducted for both cases, with and without covariates, in the GLB model. The practical application of the proposed Lindley binomial regression model is demonstrated using the whitefly dataset. Binomial regression EM algorithm Endpoint inflation Lindley distribution Proportions Randomized quantile residuals Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Dec, 2025 Reviews received at journal 13 Aug, 2024 Reviewers agreed at journal 09 Aug, 2024 Reviewers agreed at journal 09 Aug, 2024 Reviewers agreed at journal 07 Aug, 2024 Reviewers invited by journal 07 Aug, 2024 Editor assigned by journal 03 Jun, 2024 Submission checks completed at journal 03 Jun, 2024 First submitted to journal 31 May, 2024 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-4510950","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":313373030,"identity":"c0496330-da00-4463-a7ad-f61934d19283","order_by":0,"name":"Dianliang Deng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYDCCA0D8AcRgJkUL4wyStTDzkOIsBr7jvYdf27bdk5N35z34gaHGjrAWyTPn0qxz24qNDQ/zJUswHEsmrMXgRo6ZcW5bQuLGZh4DCcYGInxkcP+NmbFlW0I9UIvxD8aGemJs4TF+zNiWkCDPzGMGtOUwMX7JMWPsOZdguAGoxSLh2HHCWviOnzH+8KMsQV6+/4zxjQ811YS1AAGbBNiFB4BEAlEagDEJTi/yDUQqHwWjYBSMgpEHAGmcNwRvsMvMAAAAAElFTkSuQmCC","orcid":"","institution":"University of Regina","correspondingAuthor":true,"prefix":"","firstName":"Dianliang","middleName":"","lastName":"Deng","suffix":""},{"id":313373032,"identity":"1930097e-8c26-4e76-a18d-f1746be450b5","order_by":1,"name":"Xiaoqing Zhang","email":"","orcid":"","institution":"University of Regina","correspondingAuthor":false,"prefix":"","firstName":"Xiaoqing","middleName":"","lastName":"Zhang","suffix":""}],"badges":[],"createdAt":"2024-05-31 20:23:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4510950/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4510950/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58471253,"identity":"c300ed84-86a8-4364-878a-13485b04cd56","added_by":"auto","created_at":"2024-06-17 05:47:34","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":675448,"visible":true,"origin":"","legend":"","description":"","filename":"journalofstatisticalTheoryandapplications.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4510950/v1_covered_71f7475f-e3fb-4960-a3f5-bfbf5e2ea0c5.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Modelling the proportions with excessive endpoints based on a generalized Lindley binomial model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-statistical-theory-and-applications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Journal of Statistical Theory and Applications](https://link.springer.com/journal/44199)","snPcode":"44199","submissionUrl":"https://submission.nature.com/new-submission/44199/3","title":"Journal of Statistical Theory and Applications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Open","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Binomial regression, EM algorithm, Endpoint inflation, Lindley distribution, Proportions, Randomized quantile residuals","lastPublishedDoi":"10.21203/rs.3.rs-4510950/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4510950/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper presents the generalized Lindley binomial (GLB) distribution, a novel probability distribution designed for the analysis of proportional data with excessive endpoints. 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