Compute the inverse of a numerical partial derivative for \(V\) with respect to \(U\) of a copula, which is a conditional quantile function for nonexceedance probability \(t\), or $$t = c_u(v) = \mathbf{C}^{(-1)}_{2 \mid 1}(v \mid u) = \frac{\delta \mathbf{C}(u,v)}{\delta u}\mbox{,}$$ and solving for \(v\). 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.
derCOPinv(cop=NULL, u, t, trace=FALSE,
delu=.Machine$double.eps^0.50, para=NULL, ...)Value(s) for the derivative inverse are returned.
A copula function;
A single nonexceedance probability \(u\) in the \(X\) 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 \(\Delta u\) interval for the derivative;
Vector of parameters or other data structures, if needed, to pass to cop; and
Additional arguments to pass to the copula.
W.H. Asquith
Durante, F., 2007, Families of copulas, Appendix C, in Salvadori, G., De Michele, C., Kottegoda, N.T., and Rosso, R., 2007, Extremes in Nature---An approach using copulas: Springer, 289 p.
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.
Johnson, M.E., 1987, Multivariate statistical simulation: New York, John Wiley, 230 p.
Nelsen, R.B., 2006, An introduction to copulas: New York, Springer, 269 p.
Zhang, L., and Singh, V.P., 2019, Copulas and their applications in water resources engineering: Cambridge University Press, ISBN 978--1--108--47425--2.
derCOP