RandomFields (version 3.1.12)

RMfractgauss: Fractal Gaussian Model Family

Description

RMfractgauss is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance $r \ge 0$ between two points and is given by $$C(r) = 0.5 ((r+1)^{\alpha}-2r^{\alpha}+|r-1|^{\alpha})$$ with $0 < \alpha \le 2$. It can only be used for one-dimensional random fields.

Usage

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

Arguments

alpha

$0 < \alpha \le 2$

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

• RMfractgauss returns an object of class RMmodel.

Details

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) $H=\alpha /2$ with $0 < \alpha \le 2$.

References

• Gneiting, T. and Schlather, M. (2004) Stochastic models which separate fractal dimension and Hurst effect.SIAM review46, 269--282.

See Also

RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
StartExample()
model <- RMfractgauss(alpha=0.5, scale=0.2)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))
FinalizeExample()