satdad (version 1.1)

rMevlog: 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)

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.

Arguments

n

The number of observations.

ds

An object of class ds.

mar

A vector of length 3 or a (d times 3) matrix. See details.

x

A vector of size d or a matrix with d columns.

Author

Cécile Mercadier ([e-mail])

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).

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

gen.ds, tsic, ec, graphs

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)