A Novel Unit Distribution Named As Median Based Unit Rayleigh (MBUR): Properties and Estimations

A Novel Unit Distribution Named As Median Based Unit Rayleigh (MBUR): Properties and Estimations | 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 Systematic Review A Novel Unit Distribution Named As Median Based Unit Rayleigh (MBUR): Properties and Estimations Iman Mohammed Attia This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5206619/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract Background and aim In this paper, the author introduces the Median-Based Unit Rayleigh (MBUR) distribution, a newly formulated statistical distribution defined exclusively on the interval (0, 1). The development of such distributions is essential for enhancing our comprehension of phenomena modeled through ratios and proportions. Methods The paper provides a detailed derivation of the probability density function (PDF) for the MBUR distribution, thoroughly articulating each phase of the derivation process. The analysis extends to a rigorous examination of the MBUR distribution's properties, encompassing related functions crucial for statistical evaluation, including the cumulative distribution function (CDF), survival function, hazard rate function, and quantile function. These functions are integral to elucidating the distribution's behavior and characteristics.In addition to theoretical insights, the author examines various methodologies for parameter estimation relevant to the MBUR distribution. A detailed overview of the statistical techniques used for parameter estimation is provided, highlighting their respective strengths and weaknesses. Results To underpin these methodologies, extensive simulation studies will be conducted, demonstrating the efficacy and robustness of the proposed estimation techniques. These simulations will facilitate a comparative analysis to evaluate the fit of the MBUR distribution across diverse datasets. Discussion Additionally, the paper incorporates real data analyses to showcase the empirical utility of the MBUR distribution. This will involve a systematic comparison of the MBUR distribution's performance against wellestablished unit distributions, such as the beta and Kumaraswamy distributions, highlighting its advantages and adaptability in modeling practical scenarios. This thorough exploration aims to provide significant contributions to the expanding domain of statistical distributions. Conclusion: MBUR is an advanced statistical model designed to effectively manage a wide variety of skewed data distributions. It has been shown to outperform traditional distributions, such as the beta and Kumaraswamy distributions, in the analysis of certain real-world datasets. One of the main advantages of MBUR is its capability to estimate parameters using just a single parameter, which offers both flexibility and efficiency in modeling complex data patterns. This characteristic not only simplifies the estimation process but also enhances its applicability across different fields where skewed data is prevalent. Applied Statistics Median Based Unit Rayleigh (MBUR) new distribution unit distribution maximum product of spacing MLE Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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. 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The development of such distributions is\u003c/p\u003e\n\u003cp\u003eessential for enhancing our comprehension of phenomena modeled through ratios and proportions.\u003c/p\u003e\n\u003cp\u003eMethods\u003c/p\u003e\n\u003cp\u003eThe paper provides a detailed derivation of the probability density function (PDF) for the MBUR distribution,\u003c/p\u003e\n\u003cp\u003ethoroughly articulating each phase of the derivation process. The analysis extends to a rigorous examination\u003c/p\u003e\n\u003cp\u003eof the MBUR distribution's properties, encompassing related functions crucial for statistical evaluation,\u003c/p\u003e\n\u003cp\u003eincluding the cumulative distribution function (CDF), survival function, hazard rate function, and quantile\u003c/p\u003e\n\u003cp\u003efunction. These functions are integral to elucidating the distribution's behavior and characteristics.In addition\u003c/p\u003e\n\u003cp\u003eto theoretical insights, the author examines various methodologies for parameter estimation relevant to the\u003c/p\u003e\n\u003cp\u003eMBUR distribution. A detailed overview of the statistical techniques used for parameter estimation is\u003c/p\u003e\n\u003cp\u003eprovided, highlighting their respective strengths and weaknesses.\u003c/p\u003e\n\u003cp\u003eResults\u003c/p\u003e\n\u003cp\u003eTo underpin these methodologies, extensive simulation studies will be conducted, demonstrating the efficacy\u003c/p\u003e\n\u003cp\u003eand robustness of the proposed estimation techniques. These simulations will facilitate a comparative\u003c/p\u003e\n\u003cp\u003eanalysis to evaluate the fit of the MBUR distribution across diverse datasets.\u003c/p\u003e\n\u003cp\u003eDiscussion\u003c/p\u003e\n\u003cp\u003eAdditionally, the paper incorporates real data analyses to showcase the empirical utility of the MBUR\u003c/p\u003e\n\u003cp\u003edistribution. This will involve a systematic comparison of the MBUR distribution's performance against wellestablished\u003c/p\u003e\n\u003cp\u003eunit distributions, such as the beta and Kumaraswamy distributions, highlighting its advantages\u003c/p\u003e\n\u003cp\u003eand adaptability in modeling practical scenarios. This thorough exploration aims to provide significant\u003c/p\u003e\n\u003cp\u003econtributions to the expanding domain of statistical distributions.\u003c/p\u003e\n\u003cp\u003eConclusion:\u003c/p\u003e\n\u003cp\u003eMBUR is an advanced statistical model designed to effectively manage a wide variety of skewed data\u003c/p\u003e\n\u003cp\u003edistributions. It has been shown to outperform traditional distributions, such as the beta and Kumaraswamy distributions, in the analysis of certain real-world datasets. One of the main advantages of MBUR is its\u003c/p\u003e\n\u003cp\u003ecapability to estimate parameters using just a single parameter, which offers both flexibility and efficiency in\u003c/p\u003e\n\u003cp\u003emodeling complex data patterns. This characteristic not only simplifies the estimation process but also\u003c/p\u003e\n\u003cp\u003eenhances its applicability across different fields where skewed data is prevalent.\u003c/p\u003e","manuscriptTitle":"A Novel Unit Distribution Named As Median Based Unit Rayleigh (MBUR): Properties and Estimations","msid":"","msnumber":"","nonDraftVersions":[{"code":2,"date":"2025-09-24 15:06:11","doi":"10.21203/rs.3.rs-5206619/v2","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}},{"code":1,"date":"2024-10-09 04:08:50","doi":"10.21203/rs.3.rs-5206619/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"c2407869-20e0-4f2a-8ac3-5d3c357e720b","owner":[],"postedDate":"September 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":38712574,"name":"Applied Statistics"}],"tags":[],"updatedAt":"2024-10-09T04:08:50+00:00","versionOfRecord":[],"versionCreatedAt":"2025-09-24 15:06:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v2","identity":"rs-5206619","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5206619","identity":"rs-5206619","version":["v2"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}