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.
Cite
@article{arxiv.2104.14071,
title = {On Rapid Variation of Multivariate Probability Densities},
author = {Haijun Li},
journal= {arXiv preprint arXiv:2104.14071},
year = {2021}
}