Estimation of the Generalized Exponential Distribution Parameters Based on Picard’s Method

Estimation of the Generalized Exponential Distribution Parameters Based on Picard’s Method | 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 Estimation of the Generalized Exponential Distribution Parameters Based on Picard’s Method Mohamed Sadek Maswadah This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4298772/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 In statistical inference, Bayes’ method is the most commonly applicable in reliability analysis, despite its subjectivity to prior information other than data. Therefore, the main objective of this work is to introduce an efficient numerical method, Picard’s method, as a tool for estimation in statistical inference and compatible with Bayes’ method. The proposed method has been applied to the generalized exponential distribution parameters and compared to Bayes’ method based on different priors via Monte Carlo simulation. The simulation results indicated that Picard’s method provides better estimates and outperforms Bayes’ method based on the generalized progressive hybrid censoring scheme. Finally, two real datasets have been analyzed for illustrations and comparison of the proposed methods. Applied Statistics Bayesian estimation Characteristic prior Informative prior Kernel prior Picard’s Full Text Additional Declarations The authors declare no competing interests. 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-4298772","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":293568192,"identity":"0e605328-4943-4599-b9c6-8dffe91f1411","order_by":0,"name":"Mohamed Sadek Maswadah","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1ElEQVRIiWNgGAWjYNACNoYEfgkwS0KGeC2SMxgYG4BaeIjXYnADrIWBsBbd9uPPJH6U2eUZ324+/uhGjQUPA/vhoxvwaTE7k2Mm2XMuudjszrHE5pxjQIfxpKXdwKvlQA7bDd425sRtN3IMm3PYgFokeMzwazn//NnNv231iZtngLT8I0bLjQSz27xthxM3SAC15LYRpeWN+W+Zc8cTZ9xIS5yd2yfBw0bQL+fTHxu+KatO7J+RfOBzzrc6OX72w8fwasEEbKQpHwWjYBSMglGADQAAw6ZMdKc9hWYAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0002-2296-931X","institution":"Aswan University","correspondingAuthor":true,"prefix":"","firstName":"Mohamed","middleName":"Sadek","lastName":"Maswadah","suffix":""}],"badges":[],"createdAt":"2024-04-20 20:59:43","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-4298772/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4298772/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":55128422,"identity":"8d0df97d-74fd-459e-9fb4-1c2bc586c8d6","added_by":"auto","created_at":"2024-04-23 03:37:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":429623,"visible":true,"origin":"","legend":"","description":"","filename":"PICARDGEXPD.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4298772/v1_covered_237bd0b4-290e-42c0-a57b-ff499674527d.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEstimation of the Generalized Exponential Distribution Parameters Based on Picard’s Method\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Aswan University","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":"Bayesian estimation, Characteristic prior, Informative prior, Kernel prior, Picard’s","lastPublishedDoi":"10.21203/rs.3.rs-4298772/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4298772/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn statistical inference, Bayes\u0026rsquo; method is the most commonly applicable in reliability analysis, despite its subjectivity to prior information other than data. 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