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

Description

Compute the inverse of a copula for $V$ with respect to $U$ given $t$ or $t = C (u = U, v) \to C^{(- 1)} (u = U, t) = v,$ and solving for $v$ . Nelsen (2006, p. 12) does not so name this function as an “inverse.” The COPinv function is internally used by level.curvesCOP and 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:


  COPinv(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 COPinv is functioning properly. One can not invert a copula for $u < t$ and for $u = t$ the $v = 1$ because of fundamental copula properties.

Usage

COPinv(cop=NULL, u, t, para=NULL, silent=TRUE, ...)

Value

Value(s) for $v$ are returned.

Arguments

cop: A copula function;
u: Nonexceedance probability $u$ in the $X$ direction;
t: Nonexceedance probability level $t$ ;
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.

Author

W.H. Asquith

References

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

Examples

Run this code

COPinv(cop=N4212cop, para=2, u=0.5, t=0.2)

Run the code above in your browser using DataLab

State of Data and AI Literacy Report 2025