
The survival copula is an expression of the probability that both $U > v$ and $U > v$ when the arguments to $\hat{\mathbf{C}}(u,v)$ are exceedance probabilities, which is obviously unlike a copula that has $U \le u$ and $V \le v$.
Alternatively, the probability that both $U > u$ and $V > v$ can be solved using just a copula: $1 - u - v + \mathbf{C}(u,v)$ when the arguments to $\mathbf{C}(u,v)$ are nonexceedance probabilities.
surCOP(cop=NULL, u, v, exceedance=TRUE, ...)
u
and v
really in exceedance probability? If FALSE
, then the complements of the two are made internally and the nonexceedances can thus be passed, andCOP
, coCOP
, duCOP
, W
, P
, M
, PSP
u <- 1 - runif(1) # make exceedance
v <- 1 - runif(1) # make exceedance
cat(c("u and v are",
round(u,digits=4),"and",
round(v,digits=4),"exceedance probabilities
"))
surCOP(cop=W,u,v)
surCOP(cop=P,u,v)
surCOP(cop=M,u,v)
surCOP(cop=PSP,u,v)
# computation using manual manipulation to nonexceedance probability
1 - (1-u) - (1-v) + COP(cop=PSP,(1-u),(1-v))
# computation using manual manipulation to nonexceedance probability
surCOP(cop=PSP,u,v, exceedance=FALSE)
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