RMdewijsian {RandomFields}

R Documentation

Modified De Wijsian 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.

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 generalized random field.

The modified RMdewijsian model \gamma(r) = \log(r^{\alpha}+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 \gamma(r) = \log(r).

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

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))

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