论文标题
在一般情况下，双变量偏差正常
Tail asymptotics for the bivariate skew normal in the general case
论文作者
论文摘要
本文是Fung and Seneta（2016）的续集和概括，其主要结果给出了$ u \ to $ u \ to $ u \ to $λ_l（u）= p（x_1 \ leq f_1^{ - 1} { - 1}（ - 1}（x_1 \ leq f_1^{ - 1}（U） sn_2（\boldsymbolα，r）$，带有$α_1=α_2=α，$，即：对于equi-skew案例中的双变量偏斜的正态分布，其中$ r $是相关矩阵，具有偏高的矩阵，带有偏高的条目$ρ，$ρ，$ρ，$ρ，$ f_i（x），$ f_i（x） Beranger等人的论文。 （2017）阐述了不包含约束$α_1=α_2=α$的上限版本，但需要约束$ 0 <ρ<1 $。在他们的附录A.3中，证明非常凝结。当翻译成Fung and Seneta（2016）的下部尾部设置时，我们发现，当$α_1=α_2=α$ $ u $的指数定期变化的功能渐近表达式确实同意，但是缓慢变化的组件，始终是y rysyptic form $ const（y log u u u）^τ$，并非等于Asymptiondy arsmptent。我们的一般方法包括$ -1 <ρ<0 $的情况，并涵盖了所有可能性。
The present paper is a sequel to and generalization of Fung and Seneta (2016) whose main result gives the asymptotic behaviour as $ u \to 0^{+}$ of $λ_L(u) = P(X_1 \leq F_1^{-1}(u) | X_2 \leq F_2^{-1}(u)),$ when $\bf{X} \sim SN_2(\boldsymbolα, R)$ with $α_1 = α_2 = α,$ that is: for the bivariate skew normal distribution in the equi-skew case, where $R$ is the correlation matrix, with off-diagonal entries $ρ,$ and $F_i(x), i=1,2$ are the marginal cdf's of $\textbf{X}$. A paper of Beranger et al. (2017) enunciates an upper-tail version which does not contain the constraint $α_1=α_2= α$ but requires the constraint $0 <ρ<1$ in particular. The proof, in their Appendix A.3, is very condensed. When translated to the lower tail setting of Fung and Seneta (2016), we find that when $α_1=α_2= α$ the exponents of $u$ in the regularly varying function asymptotic expressions do agree, but the slowly varying components, always of asymptotic form $const (-\log u)^τ$, are not asymptotically equivalent. Our general approach encompasses the case $ -1 <ρ< 0$, and covers all possibilities.
