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

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

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, ...)

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.

Value

Value(s) for u are returned.

Author(s)

W.H. Asquith

References

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

See Also

COP, COPinv, level.curvesCOP, level.curvesCOP2

Examples

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

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