A Novel Approach for Parameter Estimation of Mixture oftwo Weibull Distributions in Failure Data Modeling

A Novel Approach for Parameter Estimation of Mixture oftwo Weibull Distributions in Failure Data Modeling | 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 Novel Approach for Parameter Estimation of Mixture oftwo Weibull Distributions in Failure Data Modeling Tianyu Yan, Kai-Tai Fang, Hong Yin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4265084/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Nov, 2024 Read the published version in Statistics and Computing → Version 1 posted 7 You are reading this latest preprint version Abstract The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixtureof Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms ofreliability studies and survival analysis. A principal challenge in dealing with MixW lies in the estima-tion of parameters. Inspired by the exemplary efficacy of the quasi-Monte Carlo method in Quantileestimation, this paper introduces an innovative approach, which employs the Harrell-Davis and threeSfakianakis and Verginis quantile estimators to enhance the representativeness of the sample, therebyimproving the accuracy of parameter estimation. Given the difficulty in deriving analytical expres-sions for the parameters of MixW and their propensity for convergence to local maxima, this paperadopts the sequential number-theoretic (SNTO) algorithm for the numerical resolution of parameterestimation. The initial optimization region for SNTO is determined via the graphical method of theWeibull Probability Plot (WPP). Simulation studies have demonstrated that our proposed methodsignificantly enhances estimation precision and reduces dependence on the “quality” of the sample.Furthermore, this methodology has been applied to two real data sets, showcasing the effectiveness ofour proposed approach. Mixture of two Weibull distributions Parameter estimation Quasi-Monte Carlo Quantile estimation SNTO algorithm Weibull probability plot (WPP) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 14 Nov, 2024 Read the published version in Statistics and Computing → Version 1 posted Editorial decision: Revision requested 27 Oct, 2024 Reviews received at journal 05 May, 2024 Reviewers agreed at journal 24 Apr, 2024 Reviewers invited by journal 24 Apr, 2024 Editor assigned by journal 15 Apr, 2024 Submission checks completed at journal 15 Apr, 2024 First submitted to journal 14 Apr, 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-4265084","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":291610800,"identity":"749ff408-2108-40a7-8431-848d11d585ce","order_by":0,"name":"Tianyu Yan","email":"","orcid":"","institution":"School of Mathematics, Renmin University of China","correspondingAuthor":false,"prefix":"","firstName":"Tianyu","middleName":"","lastName":"Yan","suffix":""},{"id":291610801,"identity":"7a28ec93-bfc0-4c98-a6c4-24e7f170de14","order_by":1,"name":"Kai-Tai Fang","email":"","orcid":"","institution":"Division of Science and Technology, BNU-HKBU United International College","correspondingAuthor":false,"prefix":"","firstName":"Kai-Tai","middleName":"","lastName":"Fang","suffix":""},{"id":291610803,"identity":"35e6a7f8-32ea-4566-b176-0457ea7baa37","order_by":2,"name":"Hong Yin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwklEQVRIiWNgGAWjYDACZgY2ECUH4bGRoMWYBC1QZYkNRGsxOM577MHHHbXp22ckP2D4UHaYgX92AwEth/nSDWeeOZ4750aaAeOMc4cZJO4cIKSFx0yat+1Y7gyJHAZm3rbDDAYSCcRpSZcAaflLgpaaBLAWRmK0SAK1SM5sO2A4g+eZwcGec+k8EjcIaOE7f8ZM4mNbnbwEe/LDBz/KrOX4ZxDQonAATB0GkyA2D371QCDfAKbqCCocBaNgFIyCEQwAlHU+OvVt1egAAAAASUVORK5CYII=","orcid":"","institution":"School of Mathematics, Renmin University of China","correspondingAuthor":true,"prefix":"","firstName":"Hong","middleName":"","lastName":"Yin","suffix":""}],"badges":[],"createdAt":"2024-04-14 13:29:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4265084/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4265084/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11222-024-10534-1","type":"published","date":"2024-11-14T15:58:16+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":69285219,"identity":"08c38ddc-8c8e-44f0-a0fb-0e1a8f19e236","added_by":"auto","created_at":"2024-11-18 19:24:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1054746,"visible":true,"origin":"","legend":"","description":"","filename":"Papersubmission.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4265084/v1_covered_83476bbf-c5cc-4d15-9afd-fca6330a35be.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Approach for Parameter Estimation of Mixture oftwo Weibull Distributions in Failure Data Modeling","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":"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},"keywords":"Mixture of two Weibull distributions, Parameter estimation, Quasi-Monte Carlo, Quantile estimation, SNTO algorithm, Weibull probability plot (WPP)","lastPublishedDoi":"10.21203/rs.3.rs-4265084/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4265084/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The mixture of two 2-parameter Weibull distributions (MixW), as a specialized variant of the mixtureof Weibull distributions, serves as an ideal model for heterogeneous data sets within the realms ofreliability studies and survival analysis. 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