Compute the inverse of a numerical partial derivative for \(U\) with respect to \(V\) of a copula, which is a conditional quantile function for nonexceedance probability \(t\), or $$t = c_v(u) = \mathbf{C}^{(-1)}_{1 \mid 2}(u \mid v) = \frac{\delta \mathbf{C}(u,v)}{\delta v}\mbox{,}$$ and solving for \(u\). Nelsen (2006, pp. 13, 40--41) shows that this inverse is quite important for random variable generation using the conditional distribution method. This function is not vectorized and will not be so.
derCOPinv2(cop=NULL, v, t, trace=FALSE,
delv=.Machine$double.eps^0.50, para=NULL, ...)Value(s) for the derivative inverse are returned.
A copula function;
A single nonexceedance probability \(v\) in the \(Y\) direction;
A single nonexceedance probability level \(t\);
A logical controlling a message on whether the signs on the uniroot are the same---this is helpful in exploring the numerical derivative limits of a given implementation of a copula.
The \(\Delta v\) interval for the derivative;
Vector of parameters or other data structure, if needed, to pass to cop; and
Additional arguments to pass to the copula.
W.H. Asquith
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
derCOP2