RandomFields (version 3.0.10)

RMdewijsian: Generalized DeWijsian Variogram Model

Description

RMdewijsian 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; should be in the interval (0,2] to provide a valid variogram for a random field of any dimension.

var,scale,Aniso,proj

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

Value

• RMdewijsian returns an object of class RMmodel

Details

The parameter $\alpha$ must satisfy $\alpha \in (0,2]$. 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) whereas $\gamma(r) = \log(r^{\alpha}+1)$ is valid (cf. Wackernagel, H. (2003), p. 336).

References

• Chiles, J.-P. and Delfiner, P. (1999)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)
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))
RFoptions(seed=NA)