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On Rapid Variation of Multivariate Probability Densities

Statistics Theory 2021-04-30 v1 Probability Statistics Theory

Abstract

Multivariate rapid variation describes decay rates of joint light tails of a multivariate distribution. We impose a local uniformity condition to control decay variation of distribution tails along different directions, and using higher-order tail dependence of copulas, we prove that a rapidly varying multivariate density implies rapid variation of the joint distribution tails. As a corollary, rapid variation of skew-elliptical distributions is established under the assumption that the underlying density generators belong to the max-domain of attraction of the Gumbel distribution.

Keywords

Cite

@article{arxiv.2104.14071,
  title  = {On Rapid Variation of Multivariate Probability Densities},
  author = {Haijun Li},
  journal= {arXiv preprint arXiv:2104.14071},
  year   = {2021}
}
R2 v1 2026-06-24T01:37:04.094Z