Fractal Gaussian Model Family
RMfractgauss is a stationary isotropic covariance model.
The corresponding covariance function only depends on the distance r ≥ 0 between
two points and is given by
C(r) = 0.5 ((r+1)^(α)-2r^(α)+|r-1|^(α))
with 0 < α ≤ 2. It can only be used for one-dimensional random fields.
RMfractgauss(alpha,var, scale, Aniso, proj)
alpha |
0 < α ≤ 2 |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The model is only valid for dimension d = 1 . It is the covariance function for the fractional Gaussian noise with self-affinity index (Hurst parameter) H=α /2 with 0 < α ≤ 2.
RMfractgauss returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Gneiting, T. and Schlather, M. (2004) Stochastic models which separate fractal dimension and Hurst effect. SIAM review 46, 269–282.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMfractgauss(alpha=0.5, scale=0.2) x <- seq(0, 10, 0.02) plot(model) plot(RFsimulate(model, x=x))
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