RMgenfbm {RandomFields}

R Documentation

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.

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.

Value

RMgenfbm returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

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))

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