mubz.copula: mu(B,z) for the copula model
In HiDimMaxStable: Inference on High Dimensional Max-Stable Distributions

Description Usage Arguments Details See Also Examples

Computes mu(B,z) for the copula model.

1	mubz.copula(details=FALSE,...)

`details`	get more details in the return value?
`...`	See details section.

mubz.copula uses integrate to compute the value of mu(B,z). If details is TRUE, mubz.copula returns the integrate return value. If details is FALSE, mubz.copula returns the value only.

The types of distributions (with scalar parameter p) in the 'margin' class are the following: marginUnif is for the Uniform distribution with support [1-p,1+p]; marginLnorm is for the Lognormal distribution whose the standard deviation of the normal distribution is equal to p; marginWeibull is for the Weibull distribution with shape parameter equal to p; marginFrechet is for the Frechet distribution with shape parameter equal to p; marginGamma is for the Gamma distribution with shape parameter equal to p; marginGPD is for the GPD distribution with shape parameter equal to p.

The types of Archimedean copulas are those implemented in the package copula: copAMH, copClayton, copFrank, copGumbel, copJoe.

Parameters of mubz.copula:

b: a vector of TRUE or FALSE, of length d where d=length(z), TRUE indicating the coordinates of B
z: a vector of positive constants
params: a vector of length 2*max(classes), giving successively the parameters of the archimedean copula and of the marginal distribution for each class
cop: a vector of 'acopula' objects from package copula of length max(classes) giving the archimedean copulas for each class
margins: a vector of objects of 'margin' class of length max(classes) giving the marginal distributions for each class
classes: a vector of integers indicating for each coordinate of z the number of its class (from 1 to max(classes))

mubz.normal, mubz.lnormal

# In this example, we compute mu(B,z) for the independent copula
# and Frechet margins.
z<-c(2,3)
kappa<-2
mu<-numeric(2)
mu[1]<-mubz.copula(b=c(TRUE,FALSE),z=z,params=c(1,kappa),
    cop=c(copGumbel),margins=c(marginFrechet),classes=c(1,1))
mu[2]<-mubz.copula(b=c(FALSE,TRUE),z=z,params=c(1,kappa),
    cop=c(copGumbel),margins=c(marginFrechet),classes=c(1,1))
# Compares mu({1},z)+mu({2},z) with the exact value:
t(mu) %*% z
(sum(1/z^kappa))^(1/kappa)

# For independent components with different distributions,
# one can use any "one-dimensional" copula:
mubz.copula(b=c(TRUE,FALSE),z=z,
    params=c(1,2,1,3),cop=c(copGumbel,copGumbel),
    margins=c(marginFrechet,marginGamma),classes=c(1,2))