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RandomFields (version 3.0.62)

RMbr2eg: Transformation from Brown-Resnick to Gauss

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 $$C_{eg}(h) = 1 - 2 (1 - 2 \Phi(\sqrt{\gamma(h) / 2}) )^2$$ Here, $\Phi$ is the standard normal distribution function, and $\gamma$ is a semi-variogram with sill $$4(erf^{-1}(1/\sqrt 2))^2 = 2 * [\Phi^{-1}( [1 + 1/\sqrt 2] / 2)]^2 = 4.425098 / 2 = 2.212549$$

Usage

RMbr2eg(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.

Value

Details

RMbr2eg The extremal Gaussian model RPschlather simulated with RMbr2eg(RMmodel()) has tail correlation function that equals 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.

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, RMbr2bg, RMmodel, RMm2r, RPbernoulli, RPbrownresnick, RPschlather,

Examples

Run this code
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) 
binary.model <- RPbernoulli(RMbr2bg(model))
step <- if (interactive()) 0.05 else 2
y <- seq(0, 10, step)
z <- RFsimulate(RPschlather(binary.model), y, y)
plot(z)

FinalizeExample()

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