Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions

Ressel, Paul

doi:10.1016/j.jmva.2013.02.013

Cited by 46 publications

(22 citation statements)

References 7 publications

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“…in terms of a function : [12,15,19] whose analytical characterization is given in [3,34]. The stable tail dependence function of the Gumbel copula with parameter ρ ∈ (0, 1) is given, for all…”

Section: Gumbel and Galambos Brought Togethermentioning

confidence: 99%

When Gumbel met Galambos

Genest

Nešlehová

2017

Copulas and Dependence Models With Applications

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Section: Gumbel and Galambos Brought Togethermentioning

confidence: 99%

When Gumbel met Galambos

Genest

Nešlehová

2017

Copulas and Dependence Models With Applications

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“…One of the major ndings in multivariate extreme-value theory, at least known since [9] and many times rediscovered and re-formulated since then, is a one-to-one relationship between d-dimensional MSMVEs and certain measures on a subspace of R d + , which is somehow comparable with the one-to-one relationship between in nitely divisible distributions and their associated Lévy measures. A quite recent, purely analytical derivation of this result can be retrieved from [36]. Additionally, the latter reference shows that a d-variate…”

Section: Mathematical Prerequisites and Notationmentioning

confidence: 86%

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Bernhart

Mai²,

Scherer

2015

Dependence Modeling

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Min-stable multivariate exponential (MSMVE) distributions constitute an important family of distributions, among others due to their relation to extreme-value distributions. Being true multivariate exponential models, they also represent a natural choice when modeling default times in credit portfolios. Despite being well-studied on an abstract level, the number of known parametric families is small. Furthermore, for most families only implicit stochastic representations are known. The present paper develops new parametric families of MSMVE distributions in arbitrary dimensions. Furthermore, a convenient stochastic representation is stated for such models, which is helpful with regard to sampling strategies.

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“…For later use we mention the fact that ℓ necessarily satisfies the following properties (Drees and Huang, 1998;Ressel, 2013):…”

Section: Basicsmentioning

confidence: 99%

Multivariate generalized Pareto distributions: Parametrizations, representations, and properties

Rootzén

Segers

Wadsworth

2018

Journal of Multivariate Analysis

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Multivariate generalized Pareto distributions arise as the limit distributions of exceedances over multivariate thresholds of random vectors in the domain of attraction of a max-stable distribution. These distributions can be parametrized and represented in a number of different ways. Moreover, generalized Pareto distributions enjoy a number of interesting stability properties. An overview of the main features of such distributions are given, expressed compactly in several parametrizations, giving the potential user of these distributions a convenient catalogue of ways to handle and work with generalized Pareto distributions.

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Homogeneous distributions—And a spectral representation of classical mean values and stable tail dependence functions

Cited by 46 publications

References 7 publications

When Gumbel met Galambos

When Gumbel met Galambos

On the construction of low-parametric families of min-stable multivariate exponential distributions in large dimensions

Multivariate generalized Pareto distributions: Parametrizations, representations, and properties

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