The Annals of Applied Probability

Bernoulli and tail-dependence compatibility

Paul Embrechts, Marius Hofert, and Ruodu Wang

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The tail-dependence compatibility problem is introduced. It raises the question whether a given $d\times d$-matrix of entries in the unit interval is the matrix of pairwise tail-dependence coefficients of a $d$-dimensional random vector. The problem is studied together with Bernoulli-compatible matrices, that is, matrices which are expectations of outer products of random vectors with Bernoulli margins. We show that a square matrix with diagonal entries being 1 is a tail-dependence matrix if and only if it is a Bernoulli-compatible matrix multiplied by a constant. We introduce new copula models to construct tail-dependence matrices, including commonly used matrices in statistics.

Article information

Ann. Appl. Probab., Volume 26, Number 3 (2016), 1636-1658.

Received: January 2015
First available in Project Euclid: 14 June 2016

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Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory 62H99: None of the above, but in this section 62H20: Measures of association (correlation, canonical correlation, etc.) 62E15: Exact distribution theory 62H86: Multivariate analysis and fuzziness

Tail dependence Bernoulli random vectors compatibility matrices copulas insurance application


Embrechts, Paul; Hofert, Marius; Wang, Ruodu. Bernoulli and tail-dependence compatibility. Ann. Appl. Probab. 26 (2016), no. 3, 1636--1658. doi:10.1214/15-AAP1128.

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