graphicalExtremes (version 0.1.0)

rmstable: Sampling of a multivariate max-stable distribution

Description

Simulates exact samples of a multivariate max-stable distribution.

Usage

rmstable(n, model = c("HR", "logistic", "neglogistic", "dirichlet")[1],
  d, par)

Value

Numeric matrix of size \(n \times d\) of simulations of the multivariate max-stable distribution.

Arguments

n

Number of simulations.

model

The parametric model type; one of:

• HR (default),

• logistic,

• neglogistic,

• dirichlet.

d

Dimension of the multivariate Pareto distribution.

par

Respective parameter for the given model, that is,

• \(\Gamma\), numeric \(d \times d\) variogram matrix, if model = HR.

• \(\theta \in (0, 1)\), if model = logistic.

• \(\theta > 0\), if model = neglogistic.

• \(\alpha\), numeric vector of size d with positive entries, if model = dirichlet.

Details

The simulation follows the extremal function algorithm in dom2016;textualgraphicalExtremes. For details on the parameters of the Huesler--Reiss, logistic and negative logistic distributions see dom2016;textualgraphicalExtremes, and for the Dirichlet distribution see coles1991modelling;textualgraphicalExtremes.

References

Examples

## A 4-dimensional HR distribution
n <- 10
d <- 4
G <-  cbind(c(0, 1.5, 1.5, 2),
            c(1.5, 0, 2, 1.5),
            c(1.5, 2, 0, 1.5),
            c(2, 1.5, 1.5, 0))

rmstable(n, "HR", d = d, par = G)

## A 3-dimensional logistic distribution
n <- 10
d <- 3
theta <- .6
rmstable(n, "logistic", d, par = theta)

## A 5-dimensional negative logistic distribution
n <- 10
d <- 5
theta <- 1.5
rmstable(n, "neglogistic", d, par = theta)

## A 4-dimensional Dirichlet distribution
n <- 10
d <- 4
alpha <- c(.8, 1, .5, 2)
rmstable(n, "dirichlet", d, par = alpha)