RMfractgauss: Fractal Gaussian Model Family
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

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.

1	RMfractgauss(alpha,var, scale, Aniso, proj)

`alpha`	0 < α ≤ 2
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

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.

Gneiting, T. and Schlather, M. (2004) Stochastic models which separate fractal dimension and Hurst effect. SIAM review 46, 269–282.

RMmodel, RFsimulate, RFfit.

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))