Description Usage Arguments Value Note Author(s) References See Also Examples
View source: R/rExtremalStudentPar.R
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 κ so that the maximum of the sample is greater than κ.
1 2 3 4 5 6 7 8 | rExtremalStudentParetoProcess(
n,
Sigma,
nu,
normalize = FALSE,
matchol = NULL,
trunc = TRUE
)
|
n |
sample size |
Sigma |
a |
nu |
degrees of freedom parameter |
normalize |
logical; should unit Pareto samples above κ be returned? |
matchol |
Cholesky matrix A such that AA^t = Σ. Corresponds to |
trunc |
logical; should negative components be truncated at zero? Default to |
an n
by d
matrix of samples, with attributes
"accept.rate"
indicating
the fraction of samples accepted.
If ν>2, an accept-reject algorithm using simulations from the angular measure on the l1 is at least twice as efficient. The relative efficiency of the latter is much larger for larger ν. 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.
Emeric Thibaud, Leo Belzile
Thibaud, E. and T. Opitz (2015). Efficient inference and simulation for elliptical Pareto processes. Biometrika, 102(4), 855-870.
rparp
1 2 3 | loc <- expand.grid(1:4, 1:4)
Sigma <- exp(-as.matrix(dist(loc))^1.5)
rExtremalStudentParetoProcess(100, Sigma, nu = 2)
|
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