# RPmaxstable: Simulation of Max-Stable Random Fields In RandomFields: Simulation and Analysis of Random Fields

## Description

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

## 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

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• Smith, R.L. (1990) Max-stable processes and spatial extremes Unpublished Manuscript.

RP, `RMmodel`, `RPgauss`, `RPbernoulli` `maxstableAdvanced`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38``` ```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 ```