Variogram Model Similar to Fractal Brownian Motion
RMflatpower is an intrinsically stationary isotropic variogram
model. The corresponding centered semi-variogram only depends on the
distance r ≥ 0 between two points and is given by
γ(r) = r^2 / ( 1 + r^2)^α
where 0 < α ≤ 1.
For related models see RMgenfbm.
RMflatpower(alpha, var, scale, Aniso, proj)
alpha |
numeric in (0,1]; refers to the fractal dimension of the process |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
The model is always smooth at the origin.
The parameter α only gives the tail behaviour and satisfies 0 < α ≤ 1.
The variogram is unbounded and belongs to a non-stationary process with stationary increments.
RMflatpower returns an object of class RMmodel.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Oesting, M., Schlather, M., and Friederichs, P. (2014) Conditional Modelling of Extreme Wind Gusts by Bivariate Brown-Resnick Processes arxiv 1312.4584.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again model <- RMflatpower(alpha=0.5) x <- seq(0, 10, 0.1) plot(model) plot(RFsimulate(model, x=x))
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