RMgneiting: 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 $r \ge 0$ 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

Value

RMgneiting returns an object of class RMmodel.

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 $mu=1.5$: $s=10 sqrt(2)/47$.

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

Examples

Run this code

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)

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