COPinv2: The Inverse of a Copula for U with respect to V

Description

Compute the inverse of a copula for $U$ with respect to $V$ given $t$ or $$t = \mathbf{C}(u,v{=}V) \rightarrow \mathbf{C}^{(-1)}(v{=}V, t) = u\mbox{,}$$ and solving for $u$. Nelsen (2006, p. 12) does not so name this function as an “inverse.” The COPinv2 function is internally used by level.curvesCOP2. A common misapplication that will puzzle the user (including the developer after long breaks from package use) is that the following call and error message are often seen, if silent=FALSE:


  COPinv2(0.2, 0.25, cop=PSP)
  # Error in uniroot(func, interval = c(lo, 1), u = u, LHS = t, cop = cop,  :
  #  f() values at end points not of opposite sign
  # [1] NA

This is a harmless error in the sense that COPinv2 is functioning properly. One can not invert a copula for $v < t$ and for $v = t$ the $u = 1$ because of fundamental copula properties.

Usage

COPinv2(cop=NULL, v, t, para=NULL, silent=TRUE, ...)

Value

Value(s) for $u$ are returned.

Arguments

cop: A copula function;
v: Nonexceedance probability $v$ in the $Y$ direction;
t: Nonexceedance probability in $t$;
para: Vector of parameters or other data structures, if needed, to pass to the copula;
silent: The argument of the same name given over to try() wrapping the uniroot() operation; and
...: Additional arguments to pass to the copula.

Author

W.H. Asquith

References

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

Examples

Run this code

# See those for COPinv as they are the same by analogy.

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