Local-Global Distinguisher Family Covariance Model
RMlgd is a stationary isotropic covariance model, which is valid only for dimensions
d =1,2.
The corresponding covariance function only depends on the distance r ≥ 0 between
two points and is given by
C(r) =1 - β^(-1)(α + β)r^(α) 1_{[0,1]}(r) + α^(-1)(α + β)r^(-β) 1_{r>1}(r)
where β >0 and 0 < α ≤ (3-d)/2, with d denoting the dimension of the random field.
RMlgd(alpha, beta, var, scale, Aniso, proj)
alpha |
argument whose range depends on the dimension of the random field: 0< α ≤ (3-d)/2. |
beta |
positive number |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The model is only valid for dimension d=1,2.
This model admits simulating random fields where fractal dimension
D of the Gaussian sample and Hurst coefficient H
can be chosen independently (compare also RMgencauchy):
Here, the random field has fractal dimension
D = d+1 - α/2
and Hurst coefficient
H = 1-β/2
for 0< β ≤ 1.
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 <- RMlgd(alpha=0.7, beta=4, scale=0.5) x <- seq(0, 10, 0.02) plot(model) plot(RFsimulate(model, x=x))
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