rmpareto {graphicalExtremes}

Sampling of a multivariate Pareto distribution

Description

Simulates exact samples of a multivariate Pareto distribution.

Usage

rmpareto(
  n,
  model = c("HR", "logistic", "neglogistic", "dirichlet"),
  d = NULL,
  par
)

Arguments

n

Number of simulations.

model

The parametric model type; one of:

• HR (default),

• logistic,

• neglogistic,

• dirichlet.

d

Dimension of the multivariate Pareto distribution. In some cases this can be NULL and will be inferred from par.

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 algorithm in Engelke and Hitz (2020). For details on the parameters of the Huesler-Reiss, logistic and negative logistic distributions see Dombry et al. (2016), and for the Dirichlet distribution see Coles and Tawn (1991).

Value

Numeric n \times d matrix of simulations of the multivariate Pareto distribution.

References

Coles S, Tawn JA (1991). “Modelling extreme multivariate events.” J. R. Stat. Soc. Ser. B Stat. Methodol., 53, 377–392.

Dombry C, Engelke S, Oesting M (2016). “Exact simulation of max-stable processes.” Biometrika, 103, 303–317.

Engelke S, Hitz AS (2020). “Graphical models for extremes (with discussion).” J. R. Stat. Soc. Ser. B Stat. Methodol., 82, 871–932.

See Also

Other sampling functions: rmpareto_tree(), rmstable_tree(), rmstable()

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)
)

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

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

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

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