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RandomFields (version 3.0.35)

RMcutoff: Gneiting's modification towards finite range

Description

RMcutoff is a functional on univariate stationary isotropic covariance functions $\phi$.

The corresponding function $C$ (which is not necessarily a covariance function, see details) only depends on the distance $r$ between two points in $d$-dimensional space and is given by

$$C(r)=\phi(r), 0\le r \le d$$ $$C(r) = b_0 ((dR)^a - r^a)^{2 a}, d \le r \le dR$$ $$C(r) = 0, dR \le r$$ The parameters $R$ and $b_0$ are chosen internally such that $C$ is a smooth function.

Usage

RMcutoff(phi, diameter, a, var, scale, Aniso, proj)

Arguments

phi
a univariate stationary isotropic covariance model (see RFgetModelNames(type="positive definite", domain="single variable", isotropy="isotropy", vdim=1)) which is valid in dimension fulldim.
diameter
a numerical value; should be greater than 0; the diameter of the domain on which the simulation is done
a
a numerical value; should be greater than 0; has been shown to be optimal for $a = 1/2$ or $a =1$.
var,scale,Aniso,proj
optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

Details

The algorithm that checks the given parameters knows only about some few necessary conditions. Hence it is not ensured that the cutoff-model is a valid covariance function for any choice of $\phi$ and the parameters. For certain models $\phi$, e.g. RMstable, RMwhittle and RMgencauchy, some sufficient conditions are known (cf. Gneiting et al. (2006)).

References

  • Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M., Jiang Y. (2006) Fast and Exact Simulation of Large {G}aussian Lattice Systems in {$R^2$}: Exploring the Limits.J. Comput. Graph. Stat.15, 483--501.
  • Stein, M.L. (2002) Fast and exact simulation of fractional Brownian surfaces.J. Comput. Graph. Statist.11, 587--599

See Also

RMmodel, RFsimulate, RFfit.

Examples

Run this code
## For examples see the help page of 'RFsimulateAdvanced' ##
model <- RMexp()
plot(model, model.cutoff=RMcutoff(model, diameter=1), xlim=c(0, 4))

FinalizeExample()

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