Application of the sample copula of order m in the estimation of cosmological parameters

Application of the sample copula of order m in the estimation of cosmological parameters | 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 Application of the sample copula of order m in the estimation of cosmological parameters Ricardo Hoyos-Argüelles This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7652269/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 02 Feb, 2026 Read the published version in Astrophysics and Space Science → Version 1 posted 8 You are reading this latest preprint version Abstract The sample copula of order m provides an approximation to the copula that characterizes the dependence structure of a set of random variables. In this work, we first derive the sample copula of order m for a random vector X = (X 1 , · · · , X d), with d ≥ 2, by extending previously established results for the bivariate case. Based on the definition of a parametric copula with piecewise constant density, we show that the maximum likelihood estimation of the density parameters coincides with the elements employed in the definition of the sample copula of order m, under the condition 2 ≤ m ≤ n, where m is an integer divisor of n, and n denotes the given sample size. In the second part, we present an application of the sample copula of order m as a complementary alternative for estimating the cosmological parameters H 0 and Ω m0 , the current values of the Hubble constant and the matter density, respectively. This is carried out using a sample of observations of the redshift z, the Hubble parameter H, and its measurement error. To this end, several probability distributions, in addition to the Gaussian distribution, are proposed to model the observed error in the variable H. Moreover, the applicability of this methodology is highlighted in the context of limited sample sizes. AMS Subject Classification (2020): 62H05 · 62F10 · 83C05 · 85A40. Copulas Parametric Inference Cosmological Parameters General Relativity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 02 Feb, 2026 Read the published version in Astrophysics and Space Science → Version 1 posted Editorial decision: Revision requested 15 Dec, 2025 Reviews received at journal 21 Oct, 2025 Reviewers agreed at journal 01 Oct, 2025 Reviewers agreed at journal 29 Sep, 2025 Reviewers invited by journal 28 Sep, 2025 Editor assigned by journal 27 Sep, 2025 Submission checks completed at journal 20 Sep, 2025 First submitted to journal 18 Sep, 2025 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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