基于Copula函数的洞庭湖流域水沙丰枯遭遇频率分析

周念清, 赵露, 沈新平

Copula-based Probability Evaluation of Rich-Poor Runoff and Sediment Encounter in Dongting Lake Basin

Nian-qing ZHOU, Lu ZHAO, Xin-ping SHEN

表1 3种常用的Archimedean型Copula函数

Table 1 Three types of popular Archimedean Copula

名称	C_q(u,v)的形式	t与q的关系
Clayton Copula	$\begin{matrix} C (u, v) = {(u^{- θ} + v^{- θ} - 1)}^{- 1 / θ} \end{matrix}$	$\begin{matrix} τ = \frac{θ}{2 + θ}, θ \in (0, \infty) \end{matrix}$
Frank Copula	$\begin{matrix} C (u, v) = - \frac{1}{θ} [1 + \frac{(e^{- θu} - 1) (e^{- θv} - 1)}{(e^{- θ} - 1)}] \end{matrix}$	$\begin{matrix} τ = 1 - \frac{4}{θ} [- \frac{1}{θ} \overset{0}{\int_{- θ}} \frac{t}{\exp (t) - 1} dt - 1], θ \in R \end{matrix}$
Gumbel-Hougaard Copula	$\begin{matrix} C (u, v) = \exp \{- {[{(- lnu)}^{θ} + {(- lnv)}^{θ}]}^{\frac{1}{θ}}\} \end{matrix}$	$\begin{matrix} τ = 1 - \frac{1}{θ}, θ \in [1, \infty) \end{matrix}$