R: Fractal Gaussian Model Family

RMfractgauss {RandomFields} | R Documentation

## Fractal Gaussian Model Family

### Description

`RMfractgauss` is a stationary isotropic covariance model. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r) = 0.5 ((r+1)^(α)-2r^(α)+|r-1|^(α))

with 0 < α ≤ 2. It can only be used for one-dimensional random fields.

### Usage

    RMfractgauss(alpha,var, scale, Aniso, proj)

### Arguments

`alpha` | 0 < α ≤ 2
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

The model is only valid for dimension d = 1 . It is the covariance function for the fractional Gaussian noise with self-affinity index (Hurst parameter) H=α /2 with 0 < α ≤ 2.

### Value

`RMfractgauss` returns an object of class `RMmodel`.

### Author(s)

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

### References

- Gneiting, T. and Schlather, M. (2004) Stochastic models which separate fractal dimension and Hurst effect. SIAM review 46, 269–282.

### 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 <- RMfractgauss(alpha=0.5, scale=0.2)
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]