rmpareto: Sampling of a multivariate Pareto distribution

In sebastian-engelke/graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models

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, \eGamma , numeric \dxd 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 \insertCiteeng2019;textualgraphicalExtremes. For details on the parameters of the Huesler-Reiss, logistic and negative logistic distributions see \insertCitedom2016;textualgraphicalExtremes, and for the Dirichlet distribution see \insertCitecoles1991modelling;textualgraphicalExtremes.

Value

Numeric \nxd matrix of simulations of the multivariate Pareto distribution.

References

\insertAllCited

See Also

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

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)

sebastian-engelke/graphicalExtremes documentation built on Jan. 10, 2025, 10:02 a.m.