Multivariate distribution models with generalized hyperbolic margins

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. In this paper we propose an alternative class of multivariate distributions (with exponentially decreasing tails) belonging to affine-linear transformed random vectors with stochastically independent and generalized hyperbolic marginals. The latter distributions possess good estimation properties and have attractive dependence structures which we explore in detail. In particular, dependencies of extreme events (tail dependence) can be modelled within this class of multivariate distributions. In addition we introduce the necessary estimation and random-number generation procedures. Various advantages and disadvantages of both types of distributions are discussed and illustrated via a simulation study.