RandomFields (version 3.0.5)

Max-stable random fields: 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 ll{ 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 ll{ 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 functionsAnn. Probab.37, 2042-2065.
• Schlather, M. (2002) Models for stationary max-stable random fields.Extremes5, 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• Smith, R.L. (1990) Max-stable processes and spatial extremes Unpublished Manuscript.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

model <- RMfbm(alpha=1.5)
x <-  seq(0, 8, if (interactive()) 0.02 else 4) 
z <- RFsimulate(RPbrownresnick(model), x=x, n=if (interactive()) 4 else 1)
plot(z)
\dontshow{
## to do : seq(0, 10, 0.02) oben ist furchtbar langsam. Warum?
}

\dontshow{
model <- RMball()
x <- seq(0, 10, 5) # nice for   x <- seq(0, 10, 0.02)
n <- if (interactive()) 1000 else 1
z <- RFsimulate(RPsmith(model, xi=0), x, n=n, 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)
}

model <- RMgauss()
n <- if (interactive()) 100 else 1
x <- seq(0, 10, if (interactive()) 0.05 else 5)
z <- RFsimulate(RPschlather(model, xi=0), x, n=n)
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
FinalizeExample()