RMdewijsian: Modified De Wijsian Variogram Model

In RandomFields: Simulation and Analysis of Random Fields

Description

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.

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.

Details

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).

Value

RMdewijsian returns an object of class RMmodel.

Note

Note that the (non-modified) de Wijsian model equals γ(r) = \log(r).

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))

Example output

Loading required package: sp
Loading required package: RandomFieldsUtils

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

NULL
NOTE: simulation is performed with fixed random seed 0.
Set 'RFoptions(seed=NA)' to make the seed arbitrary.
New output format of RFsimulate: S4 object of class 'RFsp';
for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.