copBasic (version 2.0.1)

kfuncCOPinv: The Inverse Kendall Function of a Copula

Description

Compute the (numerical) inverse $z(F_K)$ of the Kendall Function $F_K(z; \mathbf{C}; \code{\link{kfuncCOP}})$ of a copula $\mathbf{C}$ 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 $\mathbf{C}$ 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.

encoding

utf8

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

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