R: Transformation from Brown-Resnick to Gauss

RMbr2eg {RandomFields} | R Documentation

## Transformation from Brown-Resnick to Gauss

### Description

This function can be used to model a max-stable process based on the a binary field, with the same extremal correlation function as a Brown-Resnick process

C_{eg}(h) = 1 - 2 (1 - 2 Φ(√{γ(h) / 2}) )^2

Here, Φ is the standard normal distribution function, and γ is a semi-variogram with sill

4(erf^{-1}(1/√ 2))^2 = 2 * [Φ^{-1}( [1 + 1/√ 2] / 2)]^2 = 4.425098 / 2 = 2.212549

### Usage

    RMbr2eg(phi, var, scale, Aniso, proj)

### Arguments

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

### Details

`RMbr2eg`
The extremal Gaussian model `RPschlather` simulated with `RMbr2eg(RMmodel())` has tail correlation function that equals the tail correlation function of Brown-Resnick process with variogram `RMmodel`.

Note that the reference paper is based on the notion of the (genuine) variogram, whereas the package RandomFields is based on the notion of semi-variogram. So formulae differ by factor 2.

### Value

object of class `RMmodel`

### 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. (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

maxstableAdvanced, `RMbr2bg`, `RMmodel`, `RMm2r`, `RPbernoulli`, `RPbrownresnick`, `RPschlather`,

### Examples

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

    model <- RMexp(var=1.62 / 2)
    binary.model <- RPbernoulli(RMbr2bg(model))
    x <- seq(0, 10, 0.05)

    z <- RFsimulate(RPschlather(binary.model), x, x)
    plot(z)

[Package RandomFields version 3.1.50 Index]