| RMbr2eg {RandomFields} | R Documentation |
This function can be used to model a max-stable process based on 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
RMbr2eg(phi, var, scale, Aniso, proj)
phi |
covariance function of class |
var, scale, Aniso, proj |
optional arguments; same meaning for any
|
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.
object of class RMmodel
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
maxstableAdvanced,
RMbr2bg,
RMmodel,
RMm2r,
RPbernoulli,
RPbrownresnick,
RPschlather.
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))
x <- seq(0, 10, 0.05)
z <- RFsimulate(RPschlather(binary.model), x, x)
plot(z)