A multivariate version of Williamson's theorem, \(\ell^1\)-symmetric survival functions, and generalized Archimedean copulas

DOI10.1515/demo-2018-0020zbMath1434.62085OpenAlexW2907228157MaRDI QIDQ2283655

Paul Ressel

Publication date: 13 January 2020

Published in: Dependence Modeling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/demo-2018-0020

zbMATH Keywords

Archimedean copulamultivariate survival functionWilliamson's theoremhigher order monotonicitymonotone composition theorem

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Probability distributions: general theory (60E05) Monotonic functions, generalizations (26A48) Reliability and life testing (62N05) Representation and superposition of functions (26B40)

Related Items (4)

Stable tail dependence functions -- some basic properties ⋮ Simulation algorithms for hierarchical Archimedean copulas beyond the completely monotone case ⋮ Abel-Gontcharoff polynomials, parking trajectories and ruin probabilities ⋮ On partially Schur-constant models and their associated copulas

Cites Work

• Hierarchical Archimedean copulas through multivariate compound distributions
• Homogeneous distributions -- and a spectral representation of classical mean values and stable tail dependence functions
• Monotonicity properties of multivariate distribution and survival functions -- with an application to Lévy-frailty copulas
• Higher order monotonic functions of several variables
• Functions operating on multivariate distribution and survival functions - With applications to classical mean-values and to copulas
• Multiply monotone functions and their Laplace transforms
• Multivariate Archimedean copulas, \(d\)-monotone functions and \(\ell _{1}\)-norm symmetric distributions
• Copulas, stable tail dependence functions, and multivariate monotonicity

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