The g-EV copula (Joe, 2014, p. 105) is a limiting form of the Gaussian copula: $$ \mathbf{C}_{\rho}(u,v) = \mathbf{gEV}(u,v; \rho) = \mathrm{exp}\bigl(-A(x,y; \rho)\bigr)\mbox{,} $$ where \(x = -\log(u)\), \(y = -\log(v)\), and $$ A(x,y; \rho) = y\mbox{,} $$ for \(0 \le x/(x+y) \le \rho^2/(1+\rho^2)\), $$ A(x,y; \rho) = (x+y - 2\rho\sqrt{xy})/(1-\rho^2)\mbox{,} $$ for \(\rho^2/(1+\rho^2) \le x/(x+y) \le 1/(1+\rho^2)\), $$ A(x,y; \rho) = x\mbox{,} $$ for \(1/(1+\rho^2) \le x/(x+y) \le 1\) and where \(\rho \in [0,1]\). A somewhat curious observation is that this copula has relative hard boundaries into the upper-left and lower-right corners when compared to the other copulas supported by the copBasic package. In other words, the hull defined by the copula has a near hard (not fuzzy) curvilinear boundaries that adjust with the parameter \(\rho\).
gEVcop(u, v, para=NULL, ...)Value(s) for the copula are returned.
Nonexceedance probability \(u\) in the \(X\) direction;
Nonexceedance probability \(v\) in the \(Y\) direction;
The parameter \(\rho\); and
Additional arguments to pass.
W.H. Asquith
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.
tEVcop