Tail asymptotics for the bivariate equi-skew Variance-Gamma distribution

TL;DR

This paper derives the asymptotic tail dependence decay rate of the bivariate skew Variance-Gamma distribution, providing explicit regularly varying functions under equal-skewness, extending previous work on skew normal distributions.

Contribution

It introduces the tail asymptotics for the bivariate skew Variance-Gamma distribution, generalizing earlier results for skew normal distributions and connecting to the broader skew GH family.

Findings

Explicit tail decay rates derived for the bivariate skew VG distribution.

Reduction of the bivariate problem to a univariate analysis.

Extension of tail dependence analysis to the skew GH family.

Abstract

We derive the asymptotic rate of decay to zero of the tail dependence of the bivariate skew Variance Gamma (VG) distribution under the equal-skewness condition, as an explicit regularly varying function. Our development is in terms of a slightly more general bivariate skew Generalized Hyperbolic (GH) distribution. Our initial reduction of the bivariate problem to a univariate one is motivated by our earlier study of tail dependence rate for the bivariate skew normal distribution