Compute the (numerical) inverse \(F^{(-1)}_K(z) \equiv z(F_K)\) of the Kendall Function \(F_K(z; \mathbf{C})\) (kfuncCOP) of a copula \(\mathbf{C}(u,v)\) given nonexceedance probability \(F_K\). The \(z\) is the joint probability of the random variables \(U\) and \(V\) coupled to each other through the copula \(\mathbf{C}(u,v)\) and the nonexceedance probability of the probability \(z\) is \(F_K\)---statements such as “probabilities of probabilities” are rhetorically complex so pursuit of word precision is made herein.
kfuncCOPinv(f, cop=NULL, para=NULL, subdivisions=100L,
rel.tol=.Machine$double.eps^0.25, abs.tol=rel.tol, ...)The value(s) for \(z(F_K)\) are returned.
Nonexceedance probability \((0 \le F_K \le 1)\);
A copula function;
Vector of parameters or other data structure, if needed, to pass to the copula;
Argument of same name passed to integrate() through kfuncCOP,
Argument of same name passed to integrate() through kfuncCOP,
Argument of same name passed to integrate() through kfuncCOP, and
Additional arguments to pass.
W.H. Asquith
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.
Joe, H., 2014, Dependence modeling with copulas: Boca Raton, CRC Press, 462 p.
kfuncCOP