R: Modified DeWijsian Variogram Model

RMdewijsian {RandomFields} | R Documentation

## 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 ≥ 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 generalised 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).

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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))

[Package RandomFields version 3.1.50 Index]