RandomFields (version 3.0.5)

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 $$\gamma(r) = (r^{\alpha}+1)^{\beta/\alpha}-1$$ where $\alpha \in (0,2]$ and $\beta \in (0,2]$. See also RMfbm.

Usage

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

Arguments

alpha

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

beta

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

var,scale,Aniso,proj

optional arguments; 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 modified by the transformation $(\gamma+1)^{\delta/-1}$ on variograms $\gamma$ for $delta \in (0,1]$. This original modification allows for further generalization, cf. RMbcw.

References

• Gneiting, T. (2002) Nonseparable, stationary covariance functions for space-time data,JASA97, 590-600.
• Schlather, M. (2010) On some covariance models based on normal scale mixtures.Bernoulli,16, 780-797.

  % \item Martin's Toledo-Chapter: Construction of covariance functions % and unconditional simulation of random fields, Application to variograms

See Also

RMbcw RMfbm, RMmodel, RMflatpower, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
model <- RMgenfbm(alpha=1, beta=0.5)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model)
plot(RFsimulate(model, x=x))
FinalizeExample()