HRcop: The Hüsler{Husler}-Reiss Extreme Value Copula
Description
The Hüsler{Husler}-Reiss copula (Joe, 2014, p. 176) is
$$\mathbf{C}_{\Theta}(u,v) = \mathbf{HR}(u,v) = \mathrm{exp}{-x \Phi(X) - y\Phi(Y)}\mbox{,}$$
where $\Theta \ge 0$, $x = - \log(u)$, $y = - \log(v)$, $\Phi(.)$ is the cumulative distribution function of the standard normal distribution, $X$ and $Y$ are defined as:
$$X = \frac{1}{\Theta} + \frac{\Theta}{2} \log[x/y]\mbox{\ and\ } Y = \frac{1}{\Theta} + \frac{\Theta}{2} \log[y/x]\mbox{.}$$
As $\Theta \rightarrow 0^{+}$, the copula limits to independence ($\mathbf{\Pi}$; P). The copula here is a bivariate extreme value copula ($BEV$), and the parameter $\Theta$ requires numerical methods.
Usage
HRcop(u, v, para=NULL, ...)
Arguments
u
Nonexceedance probability $u$ in the $X$ direction;
v
Nonexceedance probability $v$ in the $Y$ direction;
para
A vector (single element) of parameters---the $\Theta$ parameter of the copula; and
...
Additional arguments to pass.
Value
Value(s) for the copula are returned.
encoding
utf8
concept
Hüsler{Husler}-Reiss extreme value copula
References
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.