The Galambos copula (Joe, 2014, p. 174) is
$$\mathbf{C}_{\Theta}(u,v) = \mathbf{GL}(u,v) = uv\,\mathrm{exp}{[x^{-\Theta} + y^{-\Theta}]^{-1/\Theta}}\mbox{,}$$
where $\Theta \in [0, \infty)$, $x = -\log(u)$, and $y = -\log(v)$. As $\Theta \rightarrow 0^{+}$, the copula limits to independence ($\mathbf{\Pi}$; P) and as $\Theta \rightarrow \infty$, the copula limits to perfect association ($\mathbf{M}$; M).
The copula here is a bivariate extreme value copula ($BEV$), and the parameter $\Theta$ requires numerical methods.
Usage
GLcop(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
Galambos extreme value copula
References
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.