Covariance models valid for max-stable random fields
This page summarizes the models that can be used for tail correlation functions.
The following models are available:
Completely monotone functions allowing for arbitrary scale
RMbcw |
Model bridging stationary and
intrinsically stationary processes for alpha <= 1
and beta < 0
|
RMdagum |
Dagum model with β < γ and γ ≤ 1 |
RMexp |
exponential model |
RMgencauchy |
generalized Cauchy family with α ≤ 1 (and arbitrary β> 0) |
RMmatern |
Whittle-Matern model with ν ≤ 1/2 |
RMstable |
symmetric stable family or powered exponential model with α ≤ 1 |
RMwhittle |
Whittle-Matern model, alternative parametrization with ν ≤ 1/2 |
Other isotropic models with arbitrary scale
RMnugget |
nugget effect model |
Compactly supported covariance functions
RMaskey |
Askey's model |
RMcircular |
circular model |
RMconstant
|
identically constant |
RMcubic |
cubic model |
RMgengneiting |
Wendland-Gneiting model; differentiable models with compact support |
RMgneiting |
differentiable model with compact support |
RMspheric |
spherical model |
Anisotropic models
| None up to now. |
Basic Operators
Operators related to process constructions
RMbernoulli |
correlation of binary fields |
RMbrownresnick
|
tcf of a Brown-Resnick process |
RMschlather
|
tcf of an extremal Gaussian process / Schlather process |
RMm2r
|
M2 process with monotone shape function |
RMm3b
|
M3 process with balls of random radius |
RMmps
|
M3 process with hyperplane polygons |
See RMmodels for cartesian models.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Strokorb, K., Ballani, F., and Schlather, M. (2015) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, 18, 241-271
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again RFgetModelNames(type="tail") ## an example of a simple model model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget plot(model)
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