copBasic (version 1.5.1)

coCOP: The Co-Copula

Description

Compute the co-copula from a copula

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

The co-copula is the expression for the probability that either $U > u$ or $V > v$ when the arguments to $\mathbf{C}^{\star}(u,v)$ are exceedance probabilities, which is obviously unlike a dual of a copula that has $U \le u$ or $V \le v$.

Alternatively, the probability that either $U > u$ or $V > v$ can be solved using just a copula: $1 - \mathbf{C}(u,v)$ when the arguments to $\mathbf{C}(u,v)$ are nonexceedance probabilities.

Usage

coCOP(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 dual of a copula is returned.

References

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

See Also

COP, surCOP, 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
"))

coCOP(cop=W,u,v)
coCOP(cop=P,u,v)
coCOP(cop=M,u,v)
coCOP(cop=PSP,u,v)

# computation using manual manipulation to nonexceedance probability
1 - COP(cop=PSP,(1-u),(1-v))

# computation using manual manipulation to nonexceedance probability
coCOP(cop=PSP,u,v, exceedance=FALSE)