RandomFields (version 3.1.16)

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 $0 < \alpha \le 2$.

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

• Wackernagel, H. (2003) Multivariate Geostatistics. Berlin: Springer, 3nd edition.

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, 0.02)
plot(model)
plot(RFsimulate(model, x=x))