RandomFields (version 3.1.12)

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

$$C(r)=\varphi (r),0\le r\le d$$ $$C(r)=b_0((dR{)}^a-r^a{)}^{2a},d\le r\le dR$$ $$C(r)=0,dR\le r$$ 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, for instance,

RFgetModelNames(type="positive definite", domain="single variable", isotropy="isotropic", vdim=1).

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

• RMcutoff returns an object of class RMmodel

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

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
StartExample()

model <- RMexp()
plot(model, model.cutoff=RMcutoff(model, diameter=1), xlim=c(0, 4))

model <- RMstable(alpha = 0.8)
plot(model, model.cutoff=RMcutoff(model, diameter=2), xlim=c(0, 5))
x <- y <- seq(0, 4, 0.05)
plot(RFsimulate(RMcutoff(model), x=x, y = y))
FinalizeExample()