copBasic (version 2.1.5)

kfuncCOPinv: The Inverse Kendall Function of a Copula

Description

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.

Usage

kfuncCOPinv(f, cop=NULL, para=NULL, ...)

Arguments

f

Nonexceedance probability \((0 \le F_K \le 1)\);

cop

A copula function;

para

Vector of parameters or other data structure, if needed, to pass to the copula; and

...

Additional arguments to pass.

Value

The value(s) for \(z(F_K)\) are returned.

References

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.

See Also

kfuncCOP

Examples

# NOT RUN {
Z <- c(0,0.25,0.50,0.75,1) # Joint probabilities of a N412cop
kfuncCOPinv(kfuncCOP(Z, cop=N4212cop, para=4.3), cop=N4212cop, para=4.3)
# [1] 0.0000000 0.2499984 0.5000224 0.7500112 1.0000000
# }