R: Covariance models valid for max-stable random fields

Tail Correlation Funtioncs {RandomFields}

R Documentation

Covariance models valid for max-stable random fields

Description

This page summarizes the models that can be use for tail correlation functions

Details

The following models are available

Completely monotone function allowing for arbitray 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 arbitray 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

`RMmult`, `*`	product of covariance models
`RMplus`, `+`	sum of covariance models or variograms

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.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

References

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

Examples

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)