RandomFields: RMgenfbm – R documentation

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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 ≥ 0 between two points and is given by

γ(r)=(r^{α}+1)^{β/α}-1

where 0 < α ≤ 2 and β \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 (γ+1)^{δ/-1} on variograms γ for δ \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.

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))

RandomFields

Simulation and Analysis of Random Fields

v3.3.10

GPL (>= 3)

Authors

Martin Schlather [aut, cre], Alexander Malinowski [aut], Marco Oesting [aut], Daphne Boecker [aut], Kirstin Strokorb [aut], Sebastian Engelke [aut], Johannes Martini [aut], Felix Ballani [aut], Olga Moreva [aut], Jonas Auel[ctr], Peter Menck [ctr], Sebastian Gross [ctr], Ulrike Ober [ctb], Paulo Ribeiro [ctb], Brian D. Ripley [ctb], Richard Singleton [ctb], Ben Pfaff [ctb], R Core Team [ctb]

Initial release