Copulas with Truncation-Invariance Property

Abstract

For a truncation-invariant copula, truncation does not change the dependence structure as well as all nonparametric measures of association such as Kendall's tau and Spearman's rho. In this article, we show that the products of algebraically independent Archimedean multivariate Clayton copulas and standard uniform distributions are the only truncation-invariant copulas.

Keywords:

• Ahmadi–Clayton copulas
• Clayton equation
• Lack of memory property
• Multivariate copulas
• Nonparametric measures of association
• Preservation under truncation
• Truncation-invariance property

Mathematics Subject Classification:

• Primary 60E05, 62E10
• Secondary 62H05, 62N99, 39B22

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