Tail dependence convergence rate for the bivariate skew normal under the equal-skewness condition

TL;DR

This paper investigates how quickly the tail dependence of the bivariate skew normal distribution converges under equal-skewness, revealing different rates depending on the skewness parameter's sign.

Contribution

It derives the convergence rates of tail dependence for the bivariate skew normal under equal-skewness, including the asymptotic behavior of the univariate skew normal's quantile function.

Findings

Rate depends on skewness sign

Asymptotic behavior matches the symmetric case when skewness is negative

Provides theoretical insights into tail dependence decay

Abstract

We derive the rate of decay of the tail dependence of the bivariate skew normal distribution under the equal-skewness condition {\theta}1 = {\theta}2,= {\theta}, say. The rate of convergence depends on whether {\theta} > 0 or {\theta} < 0. The latter case gives rate asymp- totically identical with the case {\theta} = 0. The asymptotic behaviour of the quantile function for the univariate skew normal is part of the theoretical development.