Modified De Wijsian Variogram Model
The modified RMdewijsian model
is an intrinsically stationary isotropic variogram model.
The corresponding centered semi-variogram only depends on the distance
r ≥ 0 between two points and is given by
γ(r)=log(r^{α}+1)
where 0 < α ≤ 2.
RMdewijsian(alpha, var, scale, Aniso, proj)
alpha |
a numerical value; in the interval (0,2]. |
var,scale,Aniso,proj |
optional arguments; same meaning for any
|
Originally, the logarithmic model γ(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 γ(r) = \log(r) is not a valid variogram (γ(0) does not vanish) and can only be understood as a characteristic of a generalized random field.
The modified RMdewijsian model
γ(r) = \log(r^{α}+1) is a valid variogram model
(cf. Wackernagel, H. (2003), p. 336).
RMdewijsian returns an object of class RMmodel.
Note that the (non-modified) de Wijsian model equals γ(r) = \log(r).
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Wackernagel, H. (2003) Multivariate Geostatistics. Berlin: Springer, 3nd edition.
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))
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