copArchimaxMevlog {satdad} | R Documentation |
cop-ell-psi-psiinv- functions for Archimax Mevlog models.
Description
Copula function, stable tail dependence function, psi function, psi inverse function for Archimax Mevlog models.
Usage
copArchimaxMevlog(x, ds, dist = "exp", dist.param = 1)
ellArchimaxMevlog(x, ds)
psiArchimaxMevlog(t, dist = "exp", dist.param = 1)
psiinvArchimaxMevlog(t, dist = "exp", dist.param = 1)
Arguments
x |
A vector of size |
ds |
An object of class |
dist |
The underlying distribution. A character string among |
dist.param |
The parameter associated with the choice |
t |
A non negative scalar or vector. |
Details
The tail dependence structure is set by a ds
object. See Section Value in gen.ds
.
Turning to Archimax structures, we follow Charpentier et al. (2014). Their algorithm (4.1 of p. 124) has been applied in rArchimaxMevlog
to generate observations sampled from the copula
when is here the stable tail dependence function of a Mevlog model. In this package, the stdf function
is completely characterized by the
ds
object. See ellMevlog
.
Value
When the underlying distribution dist
is
"exp" ; For a positive
given by
dist.param
,and
.
"gamma" ; For positive scale
and shape
given by
dist.param
,and
.
"ext" ;
and
.
copArchimaxMevlog
returns the copula function .
ellArchimaxMevlog
returns the stable tail dependence function .
psiArchimaxMevlog
returns the psi function .
psiinvArchimaxMevlog
returns the psi inverse function .
Author(s)
Cécile Mercadier (mercadier@math.univ-lyon1.fr
)
References
Charpentier, A., Fougères, A.-L., Genest, C. and Nešlehová, J.G. (2014) Multivariate Archimax copulas. Journal of Multivariate Analysis, 126, 118–136.
See Also
rArchimaxMevlog
, gen.ds
, ellMevlog
Examples
## Fix a 7-dimensional tail dependence structure
ds7 <- gen.ds(d = 7)
## Fix the parameters for the underlying distribution
(lambda <- runif(1, 0.01, 5))
(shape <- runif(1, 0.01, 5))
(scale <- runif(1, 0.01, 5))
## Fix x and t
x <- c(0.8, 0.9, 0.5, 0.8, 0.4, 0.9, 0.9)
t <- 2
## Evaluate the functions under the underlying exponential construction
copArchimaxMevlog(x = x, ds = ds7, dist = "exp", dist.param = lambda)
ellArchimaxMevlog(x = x, ds = ds7)
psiArchimaxMevlog(t = t, dist = "exp", dist.param = lambda)
psiinvArchimaxMevlog(t = t, dist = "exp", dist.param = lambda)
## Evaluate the functions under the underlying gamma construction
copArchimaxMevlog(x = x, ds = ds7, dist = "gamma", dist.param = c(shape, scale))
ellArchimaxMevlog(x = x, ds = ds7)
psiArchimaxMevlog(t = t, dist = "gamma", dist.param = c(shape, scale))
psiinvArchimaxMevlog(t = t, dist = "gamma", dist.param = c(shape, scale))