RandomFields (version 3.0.32)

RMbrownresnick: Tail correlation function of the Brown-Resnick process

Description

RMbrownresnick defines the tail correlation function of the Brown-Resnick process. $$C(h) = 2 - 2\Phi(\sqrt{\gamma(h) / 2})$$ where $\phi$ is the standard normal distribution function and $\gamma$ is the semi-variogram.

Usage

RMbrownresnick(phi, var, scale, Aniso, proj);

Arguments

phi

variogram of class RMmodel.

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• object of class RMmodel

Details

For a given RMmodel the function RMbrownresnick(RMmodel()) 'returns' the tail correlation function of a Brown-Resnick process with variogram RMmodel.

References

Kabluchko, Z., Schlather, M. & de Haan, L (2009) Stationary max-stable random fields associated to negative definite functions Ann. Probab. 37, 2042-2065.

See Also

RFsimulate, RMm2r, RMm3b, RMmps, RMmodel.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
#plot covariance model of type RMbrownresnick
RMmodel <- RMfbm(alpha=1.5, scale=0.2)
plot(RMbrownresnick(RMmodel))

#simulate and plot corresponding Gaussian random field
x <- if (interactive()) seq(-5, 5, 0.05) else seq(-5, 5, 5)
z <- RFsimulate(RMbrownresnick(RMmodel), x=x, y=x, grid=TRUE)
plot(z)
FinalizeExample()