copBasic (version 1.5.1)

surCOP: The Survival Copula

Description

Compute the survival copula from a copula

$$\mathrm{Pr}[U > u, V > v] = \hat{\mathbf{C}}(u,v) = u + v - 1 + \mathbf{C}(1-u,1-v)$$

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.

Usage

surCOP(cop=NULL, u, v, exceedance=TRUE, ...)

Arguments

cop

A copula function,

u

An exceedance probability in X direction,

v

An exceedance probability in Y direction,

exceedance

Are 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, and

...

Additional arguments to pass (such as parameters, if needed, for the copula in the form of a list.

Value

• The value for the survival copula is returned.

References

Nelson, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.

See Also

COP, coCOP, duCOP, W, P, M, PSP

Examples

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)