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

In wasquith/copBasic: General Bivariate Copula Theory and Many Utility Functions

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 = \mathbf{C}(u{=}U,v) \rightarrow \mathbf{C}^{(-1)}(u{=}U, t) = v\mbox{,}

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, ...)

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.

Value

Value(s) for v are returned.

Author(s)

W.H. Asquith

References

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

See Also

COP, COPinv2, level.curvesCOP, level.curvesCOP2

Examples

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

wasquith/copBasic documentation built on Dec. 13, 2024, 6:39 p.m.