RandomFields (version 3.0.32)

RMdewijsian: Modified DeWijsian Variogram Model

Description

The modified RMdewijsian model is an intrinsically stationary isotropic variogram model. The corresponding centered semi-variogram only depends on the distance $r \ge 0$ between two points and is given by $$\gamma(r) = \log(r^{\alpha}+1)$$ where $\alpha \in (0,2]$.

Usage

RMdewijsian(alpha, var, scale, Aniso, proj)

Arguments

alpha

a numerical value; in the interval (0,2].

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above variogram remains unmodified.

Value

• RMdewijsian returns an object of class RMmodel

Details

Originally, the logarithmic model $\gamma(r) = \log(r)$ was named after de Wijs and reflects a principle of similarity (cf. Chiles, J.-P. and Delfiner, P. (1999), p. 90). But note that $\gamma(r) = \log(r)$ is not a valid variogram ($\gamma(0)$ does not vanish) and can only be understood as a characteristic of a generalised random field.

The modified RMdewijsian model $\gamma(r) = \log(r^{\alpha}+1)$ is a valid variogram model (cf. Wackernagel, H. (2003), p. 336).

References

% \item Chiles, J.-P. and Delfiner, P. (1999) % \emph{Geostatistics. Modeling Spatial Uncertainty.} % New York: Wiley.
• Wackernagel, H. (2003)Multivariate Geostatistics.Berlin: Springer, 3nd edition. % \item Martin's Toledo-Chapter: Construction of covariance functions % and unconditional simulation of random fields, Example 7

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
model <- RMdewijsian(alpha=1)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
FinalizeExample()