RandomFields (version 3.0.10)

RMgenfbm: Generalized Fractal Brownian Motion Variogram Model

Description

RMgenfbm is an intrinsically stationary isotropic variogram model. The corresponding centered semi-variogram only depends on the distance $r \ge 0$ between two points and is given by $$\gamma(r) = (r^{\alpha}+1)^{\delta}-1$$ where $\alpha \in (0,2]$ and $\delta < 1$. See also RMfbm.

Usage

RMgenfbm(alpha, delta, var, scale, Aniso, proj)

Arguments

alpha

a numerical value; should be in the interval (0,2].

delta

a numerical value; should be in the interval (0,1).

var,scale,Aniso,proj

optional parameters; same meaning for any RMmodel. If not passed, the above variogram remains unmodified.

Value

• RMgenfbm returns an object of class RMmodel

Details

Here the variogram of RMfbm is slightly modified by the transformation $(\gamma+1)^\delta-1$ on variograms $\gamma$.

References

• Stein, M.L. (2002) Fast and exact simulation of fractional Brownian surfaces.J. Comput. Graph. Statist.11, 587--599 % \item Martin's Toledo-Chapter: Construction of covariance functions % and unconditional simulation of random fields, Application to variograms

See Also

RMfbm, RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0)
model <- RMgenfbm(alpha=1, delta=0.5)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
RFoptions(seed=NA)