R: Locally Positive Definite Function Given by the Fractal...

RMlsfbm {RandomFields} | R Documentation

## Locally Positive Definite Function Given by the Fractal Brownian Motion

### Description

`RMlsfbm` is positive definite function on the unit ball in R^d centred at the origin,

C(r) = c - r^α

with 0 <= r = || x - y || <= 1

### Usage

    RMlsfbm(alpha, const, var, scale, Aniso, proj)

### Arguments

`alpha` | numeric in (0,2); refers to the fractal dimension of the process
`const` | the `const`ant c is given by the formula c = 2^{-α} Γ(d / 2 + α/2) Γ(1 - α/2) / Γ(d / 2) and should not be changed by the user in order to ensure positive definiteness.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Value

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

### Author(s)

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

### References

- Martini, J., Schlather, M., Simianer, H. (In preparation.)

### See Also

`RMbcw` generalizes `RMlsfbm` in case of c is given, `RMfbm`, `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 <- RMlsfbm(alpha=1, scale=10)
    x <- seq(0, 10, 0.02)
    plot(model, xlim=c(0,10))
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]