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Concordance, symmetrization and non-exchangeability for bivariate copulas
[Submitted on 6 May 2026 (v1), last revised 30 Jun 2026 (this ve · 2026-05-07 · via math.ST updates on arXiv.org

This paper has been withdrawn by Manuel Úbeda-Flores

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Abstract:We study the relationship between measures of non-exchangeability $\mu_p$ ($p\in[1,+\infty]$), in the sense of Durante et al. (2010), and classical dependence functionals for bivariate copulas. We show that the symmetrization $C\mapsto(C+C^t)/2$ preserves Spearman's $\rho$ while annihilating $\mu_p$, and that Blomqvist's $\beta$ carries no information about the degree of non-exchangeability. We also establish the sharp lower bound $\sigma(C)\ge 6\,\mu_1(C)$, where $\sigma$ is the Schweizer-Wolff dependence measure, showing that asymmetry implies dependence. Closed-form expressions for $\tau$, $\rho$, and the tail-dependence coefficients of the maximally non-exchangeable family $\{M_\theta\}$ are derived as illustrations.

Submission history

From: Manuel Úbeda-Flores [view email]
[v1] Wed, 6 May 2026 17:40:26 UTC (9 KB)
[v2] Tue, 30 Jun 2026 08:10:47 UTC (1 KB) (withdrawn)

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