Two Precision-controlled Numerical Algorithms forthe CDF of Doubly Non-central Beta DistributionBased on the Segmentation of the Infinite DoubleSeries Matrix

Two Precision-controlled Numerical Algorithms forthe CDF of Doubly Non-central Beta DistributionBased on the Segmentation of the Infinite DoubleSeries Matrix | 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 Article Two Precision-controlled Numerical Algorithms forthe CDF of Doubly Non-central Beta DistributionBased on the Segmentation of the Infinite DoubleSeries Matrix han li, baoli dai, fangfang ma, yinhua tian, tianyan dong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7760016/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 The cumulative distribution function (CDF) of the doubly non-central beta distribution can be expressed as an infinite doubleseries. By truncating the sum of this series, one can obtain an approximate value of the CDF. Although numerous methodsexist for calculating the non-central beta distribution, which allow for the control of the truncation range and estimation of thecomputational error, no such methods have been developed for the doubly non-central beta distribution. In this paper, wepropose two new numerical computation methods based on the segmentation of the infinite double series, termed DIV1 andDIV2. Both methods enable automated calculations once the error control parameters are set; there is no need to predeterminethe truncation range, and their computational times are comparable. Following detailed derivations, we have established theupper bounds of the errors for both methods, thus ensuring the determinability of the precision. Physical sciences/Mathematics and computing Physical sciences/Physics 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-7760016","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":534832279,"identity":"fe3ca381-7cb8-41b6-9558-6e49ac2156da","order_by":0,"name":"han li","email":"","orcid":"","institution":"Shandong University of Science and Technology Taian Campus","correspondingAuthor":false,"prefix":"","firstName":"han","middleName":"","lastName":"li","suffix":""},{"id":534832280,"identity":"ea13b47b-23bb-4992-af1e-7bedb302b230","order_by":1,"name":"baoli dai","email":"","orcid":"","institution":"Shandong University of Science and Technology Taian 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By truncating the sum of this series, one can obtain an approximate value of the CDF. Although numerous methodsexist for calculating the non-central beta distribution, which allow for the control of the truncation range and estimation of thecomputational error, no such methods have been developed for the doubly non-central beta distribution. In this paper, wepropose two new numerical computation methods based on the segmentation of the infinite double series, termed DIV1 andDIV2. Both methods enable automated calculations once the error control parameters are set; there is no need to predeterminethe truncation range, and their computational times are comparable. 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