 On the length of copula level curvesMaximilian Coblenz, Oliver Grothe, Manuela Schreyer and Wolfgang Trutschnig Journal of Multivariate Analysis, 2018, vol. 167, issue C, 347-365 Abstract: Motivated by the well-known fact that the surface of copulas is closely related to common dependence measures such as Spearman’s rho, we investigate level curves of bivariate copulas and study their lengths. To this end, we establish the length profile LC(t) which maps each level t∈[0,1] to the length of the respective level curve. Some basic properties of the length profile, such as continuity and differentiability with respect to t, are examined. Based on the length profile, a measure ℓC is defined, which can be interpreted as the average level curve length. ℓC is a measure of association, it is, however, not a concordance measure in general. Some further, partially surprising properties, such as closed-form formulas of ℓC for completely dependent copulas, conclude the paper. Keywords: Complete dependence; Copulas; Level curves; Measure of association (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:167:y:2018:i:c:p:347-365 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2018.06.001 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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