Gluing copulas. (English) Zbl 1292.60025

Summary: We present a new way of constructing \(n\)-copulas, by scaling and gluing finitely many \(n\)-copulas. Gluing for bivariate copulas produces a copula that coincides with the independence copula on some grid of horizontal and vertical sections. Examples illustrate how gluing can be applied to build complicated copulas from simple ones. Finally, we investigate the analytical as well as statistical properties of the copulas obtained by gluing, in particular, the behavior of Spearman’s \(\rho\) and Kendall’s \(\tau\).


60E05 Probability distributions: general theory
62H05 Characterization and structure theory for multivariate probability distributions; copulas
Full Text: DOI


[1] DOI: 10.1081/STA-200063351 · Zbl 1071.62047
[2] DOI: 10.1109/TFUZZ.2006.890681 · Zbl 05516334
[3] Durante F., Kybernetika 43 pp 209– (2007)
[4] DOI: 10.1080/03610920500498758 · Zbl 1098.60017
[5] DOI: 10.1080/03610920701386976 · Zbl 1130.60017
[6] Nelsen R. B., An Introduction to Copulas., 2. ed. (2006) · Zbl 1152.62030
[7] Schweizer B., Probabilistic Metric Spaces (2005)
[8] DOI: 10.1214/lnms/1215452606
[9] Sklar M., Publ. Inst. Statist. Univ. Paris 8 pp 229– (1959)
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