Tail correlation function of the Brown-Resnick process
RMbrownresnick defines
the tail correlation function of the Brown-Resnick process.
C(h) = 2 - 2Φ(√{γ(h)} / 2)
where φ is the standard normal distribution function and γ is the semi-variogram.
RMbrownresnick(phi, var, scale, Aniso, proj)
For a given RMmodel the function
RMbrownresnick(RMmodel()) 'returns' the tail correlation
function of a Brown-Resnick process with variogram RMmodel.
object of class RMmodel
In the paper Kabluchko et al. (2009) the variogram instead of the semi-variogram is considered, so the formulae differ slightly.
In Version 3.0.33 a typo has been corrected.
Here, a definition is used that is consistent with the rest of the package.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Kabluchko, Z., Schlather, M. & de Haan, L (2009) Stationary max-stable random fields associated to negative definite functions Ann. Probab. 37, 2042-2065.
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.
RFsimulate,
RMm2r, RMm3b, RMmps,
RMmodel.
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 <- seq(-5, 5, 0.05) z <- RFsimulate(RMbrownresnick(RMmodel), x=x, y=x) plot(z)
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