RandomFields (version 3.0.5)

RMbr2bg: Transformation from Brown-Resnick to Bernoulli

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 $$C_{bg}(h) = \cos(\pi (2\Phi(\sqrt{\gamma(h) / 2}) -1) )$$ Here, $\Phi$ is the standard normal distribution function, and $\gamma$ is a semi-variogram with sill $$4(erf^{-1}(1/2))^2 = 2 * { \Phi^{-1}( 3 / 4 ) }^2 = 1.819746 / 2 = 0.9098728$$

Usage

RMbr2bg(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

• object of class RMmodel

Details

RMbr2bg binary random field RPbernoulli simulated with RMbr2bg(RMmodel()) has a uncentered covariance function that equals

1. the tail correlation function of the max-stable process constructed with this binary random field
2. the tail correlation function of Brown-Resnick process with variogramRMmodel.

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, RMbr2eg, RMmodel, RMm2r, RPbernoulli, RPbrownresnick, RPschlather,

Examples

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) 
step <- if (interactive()) 0.05 else 2
y <- seq(0, 10, step)
z <- RFsimulate(RPschlather(RMbr2eg(model)), y, y)
plot(z)

FinalizeExample()