R: Tail correlation function of the Brown-Resnick process

RMbrownresnick {RandomFields} | R Documentation

## Tail correlation function of the Brown-Resnick process

### Description

`RMbrownresnick` defines the tail correlation function of the Brown-Resnick process.

C(h) = 2 - 2Φ(√{γ(h)} / 2)

where φ is the standard normal distribution function and γ is the semi-variogram.

### Usage

    RMbrownresnick(phi, var, scale, Aniso, proj);

### Arguments

`phi` | variogram of class `RMmodel`.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

For a given `RMmodel` the function `RMbrownresnick(RMmodel())` 'returns' the tail correlation function of a Brown-Resnick process with variogram `RMmodel`.

### Value

object of class `RMmodel`

### Note

In the paper Kabluchko et al (2009) the variogram instead of the semi-variogram is considered, so the formulae differ slightly.

In Version 3.0.33 a typo has been corrected.

Here, a definition is used that is consistend with the rest of the package.

### Author(s)

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

### References

- Kabluchko, Z., Schlather, M. & de Haan, L (2009) Stationary max-stable random fields associated to negative definite functions Ann. Probab. 37, 2042-2065.

- Strokorb, K., Ballani, F., and Schlather, M. (2014) Tail correlation functions of max-stable processes: Construction principles, recovery and diversity of some mixing max-stable processes with identical TCF. Extremes, Submitted.

### See Also

`RFsimulate`, `RMm2r`, `RMm3b`, `RMmps`, `RMmodel`.

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again

    #plot covariance model of type RMbrownresnick
    RMmodel <- RMfbm(alpha=1.5, scale=0.2)
    plot(RMbrownresnick(RMmodel))

    #simulate and plot corresponding Gaussian random field
    x <- seq(-5, 5, 0.05)
    z <- RFsimulate(RMbrownresnick(RMmodel), x=x, y=x)
    plot(z)

[Package RandomFields version 3.1.50 Index]