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

### See Also

coordinate systems, RM, `RMmodels`, `RMtrafo`

### 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)

[Package RandomFields version 3.1.50 Index]