rMevlog {satdad} | R Documentation |
r-p-d-ell- functions for Mevlog models.
Description
Random vectors generation (rMevlog
), cumulative distribution function (pMevlog
), probability density function (dMevlog
), stable tail dependence function (ellMevlog
) for Mevlog models. A Mevlog
model is a multivariate extreme value (symmetric or asymmetric) logistic model.
Usage
rMevlog(n, ds, mar = c(1,1,1))
pMevlog(x, ds, mar = c(1,1,1))
dMevlog(x, ds, mar = c(1,1,1))
ellMevlog(x, ds)
Arguments
n |
The number of observations. |
ds |
An object of class |
mar |
A vector of length 3 or a |
x |
A vector of size |
Details
The tail dependence structure is set by a ds
object. See Section Value in gen.ds
.
The marginal information mar
is given by a 3-dimensional vector (the order should be location, scale and shape) or a matrix with 3 columns depending on whether the components share the same characteristics or not. When the marginal parameters differ, mar
is a matrix containing d
locations in the first column, d
scales in the second column and d
shapes in the third column.
The (a)symmetric logistic models respectively are simulated in 'rMevlog' using Algorithms 2.1 and 2.2 in Stephenson(2003).
Value
rMevlog
returns a (n times d)
matrix containing n
realizations of a d
-variate Mevlog random vector with margins mar
and tail dependence structure ds
.
pMevlog
returns a scalar (when x
is a numeric vector) or a vector (when x
is a numeric matrix, in which case the evaluation is done across the rows). The margins are provided by mar
and the tail dependence structure through a ds
object.
dMevlog
returns a scalar (when x
is a numeric vector) or a vector (when x
is a numeric matrix, in which case the evaluation is done across the rows). The margins are provided by mar
and the tail dependence structure through a ds
object.
ellMevlog
returns a scalar (when x
is a numeric vector) or a vector (when x
is a numeric matrix, in which case the evaluation is done across the rows). The tail dependence structure is provided by a ds
object.
Author(s)
Cécile Mercadier (mercadier@math.univ-lyon1.fr
)
References
Gumbel, E. J. (1960) Distributions des valeurs extremes en plusieurs dimensions. Publ. Inst. Statist. Univ. Paris, 9, 171–173.
Stephenson, A. (2002) evd: Extreme Value Distributions. R News, 2(2):31–32.
Stephenson, A. (2003) Simulating Multivariate Extreme Value Distributions of Logistic Type. Extremes, 6, 49–59.
Tawn, J. A. (1990) Modelling multivariate extreme value distributions. Biometrika, 77, 245–253.
See Also
Examples
## Fix a 3-dimensional symmetric tail dependence structure
ds3 <- gen.ds(d = 3, type = "log")
## The dependence parameter is given by
ds3$dep
## Generate a 1000-sample of Mevlog random vectors associated with ds3
## The margins are kept as standard Frechet
sample3 <- rMevlog(n = 1000, ds = ds3)
## Fix a 10-dimensional asymmetric tail dependence structure
# The option \cdoe{mns = 4} produces a support involving subsets of cardinality 4 plus singletons.
ds10 <- gen.ds(d = 10, mnns = 4)
## Margins differ from one to another
mar10 <- matrix(runif(10*3), ncol = 3)
## Generate a 50-sample of Mevlog random vectors associated with ds10 and mar10
sample10 <- rMevlog(n = 50, ds = ds10, mar = mar10)
## Continuing with ds3 ; we compute other attributes
## The cumulative distribution function
pMevlog(x = rep(1,3), ds = ds3)
# should be similar to :
# evd::pmvevd(q = rep(1,3), dep = ds3$dep, model = "log", d = 3, mar = c(1,1,1))
## The probability density function:
dMevlog(x = rep(1,3), ds = ds3, mar = c(1.2,1,0.5))
# should be similar to :
# evd::dmvevd(x = rep(1,3), dep = ds3$dep, model = "log", d = 3, mar = c(1.2,1,0.5))
## The stable tail dependence function:
ellMevlog(x = rep(1,3), ds = ds3)