R: Simulation of Max-Stable Random Fields

Max-stable random fields {RandomFields} | R Documentation

## Simulation of Max-Stable Random Fields

### Description

Here, a list of models and methods for simulating max-stable random fields is given.

See also maxstableAdvanced for more advanced examples.

### Implemeted models and methods

Models

`RPbrownresnick` | Brown-Resnick process using an automatic choice of the below 3 `RPbr*` methods
`RPopitz` | extremal t process
`RPschlather` | extremal Gaussian process
`RPsmith` | M3 processes

Methods

`RPbrmixed` | simulation of Brown-Resnick processes using M3 representation
`RPbrorig` | simulation of Brown-Resnick processes using the original definition
`RPbrshifted` | simulation of Brown-Resnick processes using a random shift

### 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.

- Schlather, M. (2002) Models for stationary max-stable random fields. Extremes 5, 33-44.

- Smith, R.L. (1990) Max-stable processes and spatial extremes Unpublished Manuscript.

### See Also

RP, `RMmodel`, `RPgauss`, `RPbernoulli` `maxstableAdvanced`

### Examples

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

    ### currently not programmed

    ## Not run: \dontshow{
    ## to do : seq(0, 10, 0.02) oben ist furchtbar langsam. Warum?
    }
    ## End(Not run)

    ## Not run: \dontshow{
    model <- RMball()
    x <- seq(0, 10, 5) # nice for   x <- seq(0, 10, 0.02)
    z <- RFsimulate(RPsmith(model, xi=0), x, n=1000, every=1000)
    plot(z)
    hist(unlist(z@data), 150, freq=FALSE) #not correct; to do; sqrt(2) wrong
    curve(exp(-x) * exp(-exp(-x)), from=-3, to=8, add=TRUE, col=3)
    }
    ## End(Not run)

    model <- RMgauss()
    x <- seq(0, 10, 0.05)
    z <- RFsimulate(RPschlather(model, xi=0), x, n=1000)
    plot(z)
    hist(unlist(z@data), 50, freq=FALSE)
    curve(exp(-x) * exp(-exp(-x)), from=-3, to=8, add=TRUE)

    ## for some more sophisticated models see maxstableAdvanced

[Package RandomFields version 3.1.50 Index]