# RMcutoff: Gneiting's modification towards finite range In RandomFields: Simulation and Analysis of Random Fields

## 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)=φ(r), 0≤ r ≤ d

C(r) = b_0 ((dR)^a - r^a)^{2 a}, d ≤ r ≤ dR

C(r) = 0, dR ≤ r

The parameters R and b_0 are chosen internally such that C is a smooth function.

## Usage

 `1` ```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.

## 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 φ and the parameters.

For certain models phi, e.g. `RMstable`, `RMwhittle` and `RMgencauchy`, some sufficient conditions are known (cf. Gneiting et al. (2006)).

## Value

`RMcutoff` returns an object of class `RMmodel`

## Author(s)

Martin Schlather, [email protected]

## References

• Gneiting, T., Sevecikova, H, Percival, D.B., Schlather M., Jiang Y. (2006) Fast and Exact Simulation of Large Gaussian 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

`RMmodel`, `RFsimulate`, `RFfit`.
 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again 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)) ```