rArchimaxMevlog {satdad} | R Documentation |
r function for Archimax Mevlog models.
Description
Random vectors generation for some Archimax Mevlog models.
Usage
rArchimaxMevlog(n, ds, dist = "exp", dist.param = 1)
Arguments
n |
The number of observations. |
ds |
An object of class |
dist |
The underlying distribution. A character string among |
dist.param |
The parameter associated with the choice |
Details
We follow below Algorithm 4.1 of p. 124 in Charpentier et al. (2014). Let \psi
defined by \psi(x)=\int_0^\infty \exp(-x t) dF(t)
, the Laplace transform of a positive random variable with cumulative distribution function F
.
Define the random vector (U_1,...,U_d)
as U_i=\psi(-\log(Y_i)/V)
where
-
Z
has a multivariate extreme value distribution with stable tail dependence function\ell
; hereZ
has standard Frechet margins, -
(Y_1,...,Y_d)=(\exp(-1/Z_1),...,\exp(-1/Z_d))
the margin transform ofZ
so thatY
is sampled from the extreme value copula associated with\ell
, -
V
has the distribution functionF
, -
Y
andV
are independent.
Then, U
is sampled from the Archimax copula C(u_1,...,u_d) = \psi(\ell(\psi^{-1}(u_1),...,\psi^{-1}(u_d)))
.
We restrict here the function \ell
to those associated with Mevlog models. See ellMevlog
and gen.ds
.
We restrict also the distribution of V
to
exponential ; For a positive
\lambda
, setdF(t)=\lambda \exp(-\lambda t) 1_{t>0} dt
, then\psi(x)=\frac{\lambda}{x+\lambda}
and\psi^{-1}(x)=\lambda \frac{1-x}{x}
.gamma ; For positive scale
\sigma
and shapea
, setdF(t)= \frac{1}{\sigma^a \Gamma(a)}t^{a-1}\exp(-t/\sigma)1_{t>0}
, then\psi(x)=\frac{1}{(x+\sigma)^a}
and\psi^{-1}(x)=\frac{x^{-1/a}-1}{\sigma}
.
Value
returns a n x d
matrix containing n
realizations of a d
-variate Archimax Mevlog random vector.
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
rMevlog
, copArchimaxMevlog
, psiArchimaxMevlog
, psiinvArchimaxMevlog
, gen.ds
Examples
## Fix a 5-dimensional asymmetric tail dependence structure
(ds5 <- gen.ds(d = 5))
## Generate a 1000-sample of Archimax Mevlog random vectors
## associated with ds5 and underlying distribution gamma
(shape5 <- runif(1, 0.01, 5))
(scale5 <- runif(1, 0.01, 5))
sample5.gamma <- rArchimaxMevlog(n = 1000, ds = ds5, dist = "gamma", dist.param = c(shape5, scale5))
## Compare theoretical (left) and empirical (right) tail dependographs
oldpar <- par(mfrow = c(1,2))
graphs(ds = ds5)
graphsEmp(sample = sample5.gamma, k = 100)
par(oldpar)
## Generate a 1000-sample of Archimax Mevlog random vectors
## associated with ds5 and underlying distribution exp
(lambda <- runif(1, 0.01, 5))
sample5.exp <- rArchimaxMevlog(n = 1000, ds = ds5, dist = "exp", dist.param = lambda)
## Compare theoretical (left) and empirical (right) tail dependographs
graphs(ds = ds5)
graphsEmp(sample = sample5.exp, k = 100)