rExtremalStudentParetoProcess {mvPot}

Simulation of extremal Student generalized Pareto vectors

Description

Simulation of Pareto processes associated to the max functional. The algorithm is described in section 4 of Thibaud and Opitz (2015). The Cholesky decomposition of the matrix Sigma leads to samples on the unit sphere with respect to the Mahalanobis distance. An accept-reject algorithm is then used to simulate samples from the Pareto process. If normalize = TRUE, the vector is scaled by the exponent measure \kappa so that the maximum of the sample is greater than \kappa.

Usage

rExtremalStudentParetoProcess(
  n,
  Sigma,
  nu,
  normalize = FALSE,
  matchol = NULL,
  trunc = TRUE
)

Arguments

n

sample size

Sigma

a d by d correlation matrix

nu

degrees of freedom parameter

normalize

logical; should unit Pareto samples above \kappa be returned?

matchol

Cholesky matrix \mathbf{A} such that \mathbf{A}\mathbf{A}^\top = \boldsymbol{\Sigma}. Corresponds to t(chol(Sigma)). Default to NULL, in which case the Cholesky root is computed within the function.

trunc

logical; should negative components be truncated at zero? Default to TRUE.

Value

an n by d matrix of samples, with attributes "accept.rate" indicating the fraction of samples accepted.

Note

If \nu>2, an accept-reject algorithm using simulations from the angular measure on the l_1 is at least twice as efficient. The relative efficiency of the latter is much larger for larger \nu. This algorithm should therefore not be used in high dimensions as its acceptance rate is several orders of magnitude smaller than that implemented in rparp.

Author(s)

Emeric Thibaud, Leo Belzile

References

Thibaud, E. and T. Opitz (2015). Efficient inference and simulation for elliptical Pareto processes. Biometrika, 102(4), 855-870.

See Also

rparp

Examples

loc <- expand.grid(1:4, 1:4)
Sigma <- exp(-as.matrix(dist(loc))^1.5)
rExtremalStudentParetoProcess(100, Sigma, nu = 2)