R: Transformation from Brown-Resnick to Bernoulli

RMbr2bg {RandomFields} | R Documentation

## Transformation from Brown-Resnick to Bernoulli

### 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_{bg}(h) = \cos(π (2Φ(√{γ(h) / 2}) -1) )

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}( 3 / 4 ) }^2 = 1.819746 / 2 = 0.9098728

### Usage

    RMbr2bg(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

`RMbr2bg`
binary random field `RPbernoulli` simulated with `RMbr2bg(RMmodel())` has a uncentered covariance function that equals

1. the tail correlation function of the max-stable process constructed with this binary random field

2. 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, `RMbr2eg`, `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)
    x <- seq(0, 10, 0.05)
    z <- RFsimulate(RPschlather(RMbr2eg(model)), x, x)
    plot(z)

[Package RandomFields version 3.1.50 Index]