Limit Conditional Distributions for Bivariate Vectors with Polar Representation

DOI10.1080/15326340903291362zbMath1195.60025arXiv0904.0580OpenAlexW2018540650MaRDI QIDQ3562373

Anne-Laure Fougères, Philippe Soulier

Publication date: 21 May 2010

Published in: Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.0580

zbMATH Keywords

asymptotic independenceelliptic distributionbivariate random vector

Mathematics Subject Classification ID

Characterization and structure theory for multivariate probability distributions; copulas (62H05) Extreme value theory; extremal stochastic processes (60G70) Probability distributions: general theory (60E05)

Related Items (12)

Extreme value analysis of actuarial risks: estimation and model validation ⋮ Linking representations for multivariate extremes via a limit set ⋮ Unnamed Item ⋮ Extremes of randomly scaled Gumbel risks ⋮ Implicit extremes and implicit max-stable laws ⋮ Estimation of conditional laws given an extreme component ⋮ On conditional extreme values of random vectors with polar representation ⋮ A conditional limit theorem for a bivariate representation of a univariate random variable and conditional extreme values ⋮ Extremal dependence of random scale constructions ⋮ Asymptotic behaviour of multivariate default probabilities and default correlations under stress ⋮ Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions ⋮ Hidden Regular Variation and Detection of Hidden Risks

Cites Work

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• Conditioning on an extreme component: model consistency with regular variation on cones
• Estimation of conditional laws given an extreme component
• Estimation of bivariate excess probabilities for elliptical models
• Sojourns and extremes of Fourier sums and series with random coefficients
• Subexponentiality of the product of independent random variables
• Hidden regular variation, second order regular variation and asymptotic independence
• Limit laws for random vectors with an extreme component
• The convex hull of a spherically symmetric sample
• A Conditional Approach for Multivariate Extreme Values (with Discussion)
• Gaussian Approximation of Conditional Elliptical Random Vectors

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