copBasic (version 1.5.1)

derCOPinv: The Inverse of a Numeric Derivative for V with respect to U of a Copula

Description

Compute the inverse of a numeric derivative for $V$ with respect to $U$ of a copula or $$t = c_u(v) = \frac{\delta \mathbf{C}(u,v)}{\delta u}\mbox{,}$$ and solving for $v$.

Usage

derCOPinv(cop=NULL, u, t, delu=.Machine$double.eps^0.50,
          para=NULL, ...)

Arguments

cop

A copula function,

u

A nonexceedance probability in $X$ direction,

t

A nonexceedance probability in $t$ direction,

delu

The $\delta u$ interval for the derivative,

para

Vector of parameters or other data structure, if needed, to pass to the copula, and

...

Additional arguments to pass.

Value

• The value for the copula is returned.

References

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

See Also

derCOP, W, P, M, PSP

Examples

u <- runif(1)
t <- runif(1)
derCOPinv(cop=W,u,t)
derCOPinv(cop=P,u,t)
derCOPinv(cop=M,u,t)
derCOPinv(cop=PSP,u,t)

# Simulate 1000 values from product (independent)
# copula
plot(c(0,1),c(0,1),type="n")
for(i in 1:1000) {
  u <- runif(1); t <- runif(1)
  v <- derCOPinv(cop=P,u,t)
  points(u,v,cex=0.5,pch=16)
}
# Now simulate 1000 from the PSP copula and note
# the lower tail dependence, but absence of upper
# tail dependence.
for(i in 1:1000) {
  u <- runif(1); t <- runif(1)
  v <- derCOPinv(cop=PSP,u,t)
  points(u,v,cex=0.5,pch=16,col=2)
}