RandomFields (version 3.1.16)

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 $0 < \alpha \le 2$ 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, JASA 97, 590-600.
• Schlather, M. (2010) On some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.

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, 0.02)
plot(model)
plot(RFsimulate(model, x=x))