rparpcs: Simulation from Pareto processes (max) using composition...

In mev: Modelling of Extreme Values

Simulation from Pareto processes (max) using composition sampling

Description

The algorithm performs forward sampling by simulating first from a mixture, then sample angles conditional on them being less than one. The resulting sample from the angular distribution is then multiplied by Pareto variates with tail index shape.

Usage

rparpcs(
  n,
  Lambda = NULL,
  Sigma = NULL,
  df = NULL,
  model = c("br", "xstud"),
  riskf = c("max", "min"),
  shape = 1
)

Arguments

n	sample size.
Lambda	parameter matrix for the Brown–Resnick model. See Details.
Sigma	correlation matrix if model = 'xstud', otherwise the covariance matrix formed from the stationary Brown-Resnick process.
df	degrees of freedom for extremal Student process.
model	string indicating the model family.
riskf	string indicating the risk functional. Only max and min are currently supported.
shape	tail index of the Pareto variates (reciprocal shape parameter). Must be strictly positive.

Details

Only extreme value models based on elliptical processes are handled. The Lambda matrix is formed by evaluating the semivariogram \gamma at sites s_i, s_j, meaning that \Lambda_{i,j} = \gamma(s_i, s_j)/2.

The argument Sigma is ignored for the Brown-Resnick model if Lambda is provided by the user.

Value

an n by d matrix of samples, where d = ncol(Sigma), with attributes mixt.weights.

Author(s)

Leo Belzile

See Also

rparp for general simulation of Pareto processes based on an accept-reject algorithm.

Examples

## Not run: 
#Brown-Resnick, Wadsworth and Tawn (2014) parametrization
D <- 20L
coord <- cbind(runif(D), runif(D))
semivario <- function(d, alpha = 1.5, lambda = 1){0.5 * (d/lambda)^alpha}
Lambda <- semivario(as.matrix(dist(coord))) / 2
rparpcs(n = 10, Lambda = Lambda, model = 'br', shape = 0.1)
#Extremal Student
Sigma <- stats::rWishart(n = 1, df = 20, Sigma = diag(10))[,,1]
rparpcs(n = 10, Sigma = cov2cor(Sigma), df = 3, model = 'xstud')

## End(Not run)

mev documentation built on April 20, 2023, 5:10 p.m.