Bernoulli

  • Bernoulli
  • Volume 24, Number 4B (2018), 3751-3790.

The class of multivariate max-id copulas with $\ell_{1}$-norm symmetric exponent measure

Christian Genest, Johanna G. Nešlehová, and Louis-Paul Rivest

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Abstract

Members of the well-known family of bivariate Galambos copulas can be expressed in a closed form in terms of the univariate Fréchet distribution. This formula extends to any dimension and can be used to define a whole new class of tractable multivariate copulas that are generated by suitable univariate distributions. This paper gives necessary and sufficient conditions on the underlying univariate distribution which ensure that the resulting copula exists. It is also shown that these new copulas are in fact dependence structures of certain max-id distributions with $\ell_{1}$-norm symmetric exponent measure. The basic dependence properties of this new class of multivariate exchangeable copulas is investigated, and an efficient algorithm is provided for generating observations from distributions in this class.

Article information

Source
Bernoulli, Volume 24, Number 4B (2018), 3751-3790.

Dates
Received: October 2016
Revised: May 2017
First available in Project Euclid: 18 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.bj/1524038769

Digital Object Identifier
doi:10.3150/17-BEJ977

Mathematical Reviews number (MathSciNet)
MR3788188

Zentralblatt MATH identifier
06869891

Keywords
Clayton copula completely monotone function exponent measure Galambos copula Laplace transform $\ell_{1}$-norm symmetric max-id distributions

Citation

Genest, Christian; Nešlehová, Johanna G.; Rivest, Louis-Paul. The class of multivariate max-id copulas with $\ell_{1}$-norm symmetric exponent measure. Bernoulli 24 (2018), no. 4B, 3751--3790. doi:10.3150/17-BEJ977. https://projecteuclid.org/euclid.bj/1524038769


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