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Multivariate distribution models with generalized hyperbolic margins. (English) Zbl 1445.62108

Summary: Multivariate generalized hyperbolic distributions represent an attractive family of distributions (with exponentially decreasing tails) for multivariate data modelling. However, in a limited data environment, robust and fast estimation procedures are rare. An alternative class of multivariate distributions (with exponentially decreasing tails) is proposed which comprises affine-linearly transformed random vectors with stochastically independent and generalized hyperbolic marginals. The latter distributions possess good estimation properties and have attractive dependence structures which are explored in detail. In particular, dependencies of extreme events (tail dependence) can be modelled within this class of multivariate distributions. In addition the necessary estimation and random-number generation procedures are provided. Various advantages and disadvantages of both types of distributions are discussed and illustrated via a simulation study.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
62H10 Multivariate distribution of statistics
62P05 Applications of statistics to actuarial sciences and financial mathematics
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