R: Gneiting Covariance Model

RMgneiting {RandomFields} | R Documentation

## Gneiting Covariance Model

### Description

`RMgneiting` is a stationary isotropic covariance model which is only valid up to dimension 3, or 5 (see the argument `orig`). The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r) = (1 + 8 s r + 25 s^2 r^2 + 32 s^3 r^3)(1-s r)^8

if 0 <= r <= 1/s and

C(r)=0

otherwise. Here, s=0.301187465825. For a generalized model see also `RMgengneiting`.

### Usage

    RMgneiting(orig, var, scale, Aniso, proj)

### Arguments

`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.
`orig` | logical. if `TRUE` the above model is used. Otherwise the `RMgengneiting` model C(s r) with `kappa=3` as above, but but with `mu = 2.683509` and `s=0.2745640815` is used. The latter has the advantage of being closer to the Gaussian model and it is valid up to dimension 5. Default: `TRUE`

### Details

This isotropic covariance function is valid only for dimensions less than or equal to 3. It is 6 times differentiable and has compact support.

This model is an alternative to `RMgauss` as its graph is hardly distinguishable from the graph of the Gaussian model, but possesses neither the mathematical nor the numerical disadvantages of the Gaussian model.

It is a special case of `RMgengneiting` for the choice kappa=3, mu=1.5.

Note that, in the original work by Gneiting (1999), a numerical value slightly deviating from the optimal one was used for mu=1.5: s=10 sqrt(2)/47.

### Value

`RMgneiting` returns an object of class `RMmodel`.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

For the original version

- Gneiting, T. (1999) Correlation functions for atmospherical data analysis. Q. J. Roy. Meteor. Soc Part A 125, 2449-2464.

For the version (`orig=FALSE`)

- this package RandomFields

### See Also

`RMbigneiting`, `RMgengneiting`, `RMgauss`, `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

    plot(RMgneiting(), model2=RMgneiting(orig=FALSE), model3=RMgauss(),
         xlim=c(-3,3), maxchar=100)
    plot(RMgneiting(), model2=RMgneiting(orig=FALSE), model3=RMgauss(),
         xlim=c(1.5,2.5), maxchar=100)

    model <- RMgneiting(orig=FALSE, scale=0.4)
    x <- seq(0, 10, 0.2) ## nicer with 0.1 instead of 0.2
    z <- RFsimulate(model, x=x, y=x, z=x, T=c(1,1,4), maxGB=3)
    plot(z, MARGIN.slices=4, MARGIN.movie=3)

[Package RandomFields version 3.1.50 Index]