RMgneiting: Gneiting Covariance Model

Description

RMgneiting is a stationary isotropic covariance model which is only valid up to dimension 3. 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 $0 \ge r \ge \frac{1}{s}$ and $$C(r)=0$$ otherwise, with $s=0.301187465825$. For a generalized model see also RMgengneiting.

Usage

RMgneiting(var, scale, Aniso, proj)

Arguments

var,scale,Aniso,proj

optional parameters; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

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: $s=\frac{10 \sqrt(2)}{47}$.

References

Gneiting, T. (1999) Correlation functions for atmospherical data analysis.Q. J. Roy. Meteor. SocPart A125, 2449-2464.

Examples

Run this code

set.seed(0)
scale <- 0.4
model <- RMgneiting(scale = scale)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
points(x, RFcov(RMgauss(scale = scale), x), col="red")
plot(RFsimulate(model, x=x))

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