R: Generalized Fractal Brownian Motion Variogram Model

RMgenfbm {RandomFields} | R Documentation

## Generalized Fractal Brownian Motion Variogram Model

### Description

`RMgenfbm` 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)=(r^{α}+1)^{β/α}-1

where 0 < α ≤ 2 and β \in (0,2].
See also `RMfbm`.

### Usage

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

### Arguments

`alpha` | a numerical value; should be in the interval (0,2].
`beta` | a numerical value; should be 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

Here the variogram of `RMfbm` is modified by the transformation (γ+1)^{δ/-1} on variograms γ for delta \in (0,1]. This original modification allows for further generalization, cf. `RMbcw`.

### Value

`RMgenfbm` returns an object of class `RMmodel`

### Author(s)

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

### References

- Gneiting, T. (2002) Nonseparable, stationary covariance functions for space-time data, JASA 97, 590-600.

- Schlather, M. (2010) On some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.

### See Also

`RMbcw` `RMfbm`, `RMmodel`, `RMflatpower`, `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 <- RMgenfbm(alpha=1, beta=0.5)
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]