Compute the survival copula from a copula (Nelsen, 2006, pp. 32--34), which is defined as
$$\hat{\mathbf{C}}(1-u,1-v) = \hat{\mathbf{C}}(u',v') = \mathrm{Pr}[U > u, V > v] = u' + v' - 1 + \mathbf{C}(1-u', 1-v')\mbox{,}$$
where \(u'\) and \(v'\) are exceedance probabilities and \(\mathbf{C}(u,v)\) is the copula (COP). The survivial copula is a reflection of both \(U\) and \(V\).
The survival copula is an expression of the joint probability that both \(U > v\) and \(U > v\) when the arguments \(a\) and \(b\) to \(\hat{\mathbf{C}}(a,b)\) are exceedance probabilities as shown. This is unlike a copula that has \(U \le u\) and \(V \le v\) for nonexceedance probabilities \(u\) and \(v\). Alternatively, the joint probability that both \(U > u\) and \(V > v\) can be solved using just the copula \(1 - u - v + \mathbf{C}(u,v)\), as shown below where the arguments to \(\mathbf{C}(u,v)\) are nonexceedance probabilities. The later formula is the joint survival function \(\overline{\mathbf{C}}(u,v)\) (surfuncCOP) defined for a copula (Nelsen, 2006, p. 33) as
$$\overline{\mathbf{C}}(u,v) = \mathrm{Pr}[U > u, V > v] = 1 - u - v + \mathbf{C}(u,v)\mbox{.}$$
Users are directed to the collective documentation in COP and simCOPmicro for more details on copula reflection.
surCOP(u, v, cop=NULL, para=NULL, exceedance=TRUE, ...)Value(s) for the survival copula are returned.
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
COP, coCOP, duCOP, surfuncCOP, simCOPmicro