R: Local-Global Distinguisher Family Covariance Model

RMlgd {RandomFields} | R Documentation

## Local-Global Distinguisher Family Covariance Model

### Description

`RMlgd` is a stationary isotropic covariance model, which is valid only for dimensions d =1,2. The corresponding covariance function only depends on the distance r ≥ 0 between two points and is given by

C(r) =1 - β^(-1)(α + β)r^(α) 1_{[0,1]}(r) + α^(-1)(α + β)r^(-β) 1_{r>1}(r)

where β >0 and 0 < α ≤ (3-d)/2, with d denoting the dimension of the random field.

### Usage

    RMlgd(alpha, beta, var, scale, Aniso, proj)

### Arguments

`alpha` | argument whose range depends on the dimension of the random field: 0< α ≤ (3-d)/2.
`beta` | beta > 0.
`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=1,2.

This model admits simulating random fields where fractal dimension D of the Gaussian sample and Hurst coefficient H can be chosen independently (compare also `RMgencauchy`.):

Here, the random field has fractal dimension

D = d+1 - α/2

and Hurst coefficient

H = 1-β/2

for 0< β ≤ 1.

### Value

`RMlgd` 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 <- RMlgd(alpha=0.7, beta=4, scale=0.5)
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]