copula (version 0.999-14)

cCopula: Conditional Copula Function

Description

Compute the conditional distribution aka conditional copula function, $C(u[d] | u[1],..., u[d-1])$ of $u[d]$ given $u[1],..., u[d-1]$.

Usage

cCopula(u, copula, j.ind=ncol(u), n.MC=0, log=FALSE)
## Deprecated, for Archimedean copulas only:
cacopula(u, cop, n.MC=0, log=FALSE)

Arguments

u

$n x d$-matrix; the conditioning is done on the values in the first $d-1$ columns.

copula

any "copula" with specified parameters; currently only Archimedean and elliptical copulas provided.

j.ind

indices $j>=2$ for which $C(u[j]|u[1],...,u[j-1])$ is computed.

cop

"outer_nacopula" with specified parameters (only Archimedean copulas are currently provided).

n.MC

Monte Carlo sample size; for Archimedean copulas only, used if positive.

log

if TRUE the logarithm of the conditional copula function is returned.

Value

numeric vector of length $n$ containing the conditional copula function of $u[d]$ given $u[1],...,u[d-1]$.

Details

cCopula() can be seen as a special case of the Rosenblatt transform which by default computes all conditional distributions. Conseqently, cCopula() simply calls rtrafo().

Note that sampling aka random number generation from the conditional distribution can be achieved by rtrafo(*, inverse=TRUE).

See Also

rtrafo; acopula-families.

Examples

tau <- 0.5
(theta <- copGumbel@iTau(tau)) # 2
d <- 2
# two ways to specify a Gumbel copula:
cop  <- onacopulaL("Gumbel", list(theta,1:d))
gCop <- gumbelCopula(theta, dim=d) #

n <- 1000
set.seed(1)
U <- rCopula(n, cop)

U. <- cbind(U[,1], cCopula(U, cop=cop)) # should be ~ U[0,1]^2
plot(U.[,1],U.[,2])

stopifnot(all.equal(cacopula(U, cop),# with deprecation warning
                    cCopula (U, cop)))

## more examples:  -->  ?rtrafo