基于Copula函数的暴雨要素三维联合分布—

基于Copula函数的暴雨要素三维联合分布——以宽甸县为例

张野, 王康, 刘欣铭, 张苏辰, 周嘉, 王菜林

The Three-dimensional Joint Distributions of Rainstorm Factors Based on Copula Function: A Case in Kuandian County, Liaoning Province

Ye Zhang, Kang Wang, Xinming Liu, Suchen Zhang, Jia Zhou, Cailin Wang

表1 4种三维Copula分布函数及参数范围

Table 1 Four kinds of three-dimensional Copula distribution function and parameter range

	分布函数	参数范围
Frank	$\begin{matrix} - \frac{1}{θ} \ln \end{matrix}$ {1+ $\begin{matrix} \frac{[\exp (- θ_{u 1}) - 1] [\exp (- θ_{u 2}) - 1] [\exp (- θ_{u 3}) - 1]}{{[\exp (- θ_{}) - 1]}^{2}} \end{matrix}$ }	（–∞,∞）\{0}
Clayton	$\begin{matrix} \max {({u_{\overset{?}{1}}}^{θ} + {u_{\overset{?}{2}}}^{θ} + {u_{\overset{?}{3}}}^{θ} - 2)}^{- (\frac{1}{θ})} \end{matrix}$	[-1,∞]\{0}
Gumbel	$\begin{matrix} \exp {[{(- \ln u_{1})}^{θ} + {(- \ln u_{2})}^{θ} + {(- \ln u_{3})}^{θ}]}^{(1 / θ)} \end{matrix}$	[1,∞]
AMH	$\begin{matrix} \frac{uvw}{1 - θ (1 - u) (1 - v) (1 - w)} \end{matrix}$	[-1,1]