R: Variogram Model Similar to Fractal Brownian Motion

RMflatpower {RandomFields} | R Documentation

## Variogram Model Similar to Fractal Brownian Motion

### Description

`RMflatpower` 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^2 / ( 1 + r^2)^α

where 0 < α ≤ 1.

For related models see `RMgenfbm`.

### Usage

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

### Arguments

`alpha` | numeric in (0,1]; refers to the fractal dimension of the process
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above variogram remains unmodified.

### Details

The model is always smooth at the origin.

The parameter α only gives the tail behaviour and satisfies 0 < α ≤ 1.

The variogram is unbounded and belongs to a non-stationary process with stationary increments.

### Value

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

### Author(s)

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

### References

- Oesting, M., Schlather, M., and Friederichs, P. (2014) Conditional Modelling of Extreme Wind Gusts by Bivariate Brown-Resnick Processes arxiv 1312.4584.

### See Also

`RMgenfbm`, `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 <- RMflatpower(alpha=0.5)
    x <- seq(0, 10, 0.1)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]