A Three-Parameter Generalized Topp-Leone ArcTan Exponential Distribution: Inference and Applications to Lifetime Data

A Three-Parameter Generalized Topp-Leone ArcTan Exponential Distribution: Inference and Applications to Lifetime Data | 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 Three-Parameter Generalized Topp-Leone ArcTan Exponential Distribution: Inference and Applications to Lifetime Data AASHUTOSH KUMAR AASHUTOSH KUMAR, Abhimanyu Singh Yadav Abhimanyu Singh Yadav This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7509321/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 01 Apr, 2026 Read the published version in Quality & Quantity → Version 1 posted You are reading this latest preprint version Abstract This paper introduces a new transformation technique based on the cumulative distribution function and inverse trigonometric function, aimed to propose a new generalized family of lifetime distribution which is parsimonious in parameter and flexibility in baseline distribution that can produce four different classes of distributions as an special case. The proposed transformation technique is applied using the exponential distribution as a baseline, and its various statistical properties are thoroughly examined. Further, the analytical, graphical, and numerical approaches are employed to study the characteristics of the resulting distribution, which is found to be positively skewed with a heavy tailed while the hazard function displays increasing, decreasing, and constant patterns. The maximum likelihood method of estimation is used to estimate the model parameters, and their performance is evaluated through a detailed Monte Carlo simulation study. The flexibility and practical utility of the proposed Generalized Topp-Leone Arctan Exponential (GTLATE) distribution is thoroughly demonstrated through the analysis of two real-world data sets. By comparing its performance against a range of existing lifetime distribution models, the study evaluates the effectiveness of the GTLATE model using various goodness-of-fit measures. These comparisons reveal that the GTLATE model consistently performs better in compare to the several competing models that exhibit similar hazard rate patterns, particularly in handling data sets with increasing, decreasing, or constant hazard rate patterns. This superior performance highlights the GTLATE model enhanced flexibility in fitting diverse types of real-world data, making it a valuable tool for practical applications in fields such as reliability analysis, survival studies. AMS Classification: 62E05, 62B10, 62F15. Generalized Topp-Leone ArcTan Exponential distribution Characterizations based on moments and hazard function Maximum likelihood estimation Montecarlo simulation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 01 Apr, 2026 Read the published version in Quality & Quantity → 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-7509321","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":516504613,"identity":"c47a02be-66ca-4ca6-874c-583fdb0d5870","order_by":0,"name":"AASHUTOSH KUMAR AASHUTOSH KUMAR","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA50lEQVRIiWNgGAWjYHACNjBpwMPY+ABI8/ARpyUBpIX5sAFICxsJWtjSJBCW4gH87cefPeb9YWNvznPGrPJrjp0MGwPzw0c38GiROJNjbsyTkJa4s7fH7LbstmSgw9iMjXPwWXMgh02aJ+FwgsF5HrPbktuYgVp42KTxaZE///wZSIs9SEux5LZ6wloMbiSYgbQwbjjblsb4cdthwloMb7wxk5yTlpa44czhw9KM247zsDET8Ivc+fRnEm9sbOwNziQ2fvy5rdqen7354WO83kcGzDxgkljlIMD4gxTVo2AUjIJRMGIAAMGZRKwGCT3xAAAAAElFTkSuQmCC","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":true,"prefix":"","firstName":"AASHUTOSH","middleName":"KUMAR AASHUTOSH","lastName":"KUMAR","suffix":""},{"id":516504614,"identity":"7bf5c44a-7489-44cf-8ce8-c249421cbba3","order_by":1,"name":"Abhimanyu Singh Yadav Abhimanyu Singh Yadav","email":"","orcid":"","institution":"Banaras Hindu University","correspondingAuthor":false,"prefix":"","firstName":"Abhimanyu","middleName":"Singh Yadav Abhimanyu Singh","lastName":"Yadav","suffix":""}],"badges":[],"createdAt":"2025-09-01 14:08:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7509321/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7509321/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11135-026-02639-8","type":"published","date":"2026-04-02T00:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":91715181,"identity":"a433d8f1-2003-4c97-8336-3c59aef4cc65","added_by":"auto","created_at":"2025-09-19 13:12:45","extension":"json","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":5393,"visible":true,"origin":"","legend":"","description":"","filename":"76c7eaa315de4364bdab63d7795e223c.json","url":"https://assets-eu.researchsquare.com/files/rs-7509321/v1/db2e0505b15bb09822309218.json"},{"id":106248304,"identity":"9d90c0da-aa3f-4c97-a0bd-0105744f0fa0","added_by":"auto","created_at":"2026-04-06 16:31:51","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":379679,"visible":true,"origin":"","legend":"","description":"","filename":"BlindedManuscriptd1.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7509321/v1_covered_c91d37d7-7a03-4adb-861f-9f1e7c212dc7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Three-Parameter Generalized Topp-Leone ArcTan Exponential Distribution: Inference and Applications to Lifetime Data","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"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":"Generalized Topp-Leone ArcTan Exponential distribution, Characterizations based on moments and hazard function, Maximum likelihood estimation, Montecarlo simulation","lastPublishedDoi":"10.21203/rs.3.rs-7509321/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7509321/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a new transformation technique based on the cumulative distribution function and inverse trigonometric function, aimed to propose a new generalized family of lifetime distribution which is parsimonious in parameter and flexibility in baseline distribution that can produce four different classes of distributions as an special case. The proposed transformation technique is applied using the exponential distribution as a baseline, and its various statistical properties are thoroughly examined. Further, the analytical, graphical, and numerical approaches are employed to study the characteristics of the resulting distribution, which is found to be positively skewed with a heavy tailed while the hazard function displays increasing, decreasing, and constant patterns. The maximum likelihood method of estimation is used to estimate the model parameters, and their performance is evaluated through a detailed Monte Carlo simulation study. The flexibility and practical utility of the proposed Generalized Topp-Leone Arctan Exponential (GTLATE) distribution is thoroughly demonstrated through the analysis of two real-world data sets. By comparing its performance against a range of existing lifetime distribution models, the study evaluates the effectiveness of the GTLATE model using various goodness-of-fit measures. 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