R: Model bridging stationary and intrinsically stationary...

RMbcw {RandomFields} | R Documentation

## Model bridging stationary and intrinsically stationary processes

### Description

`RMbcw` is a variogram model that bridges between some intrinsically stationary isotropic processes and some stationary ones. It reunifies the `RMgenfbm` ‘b’, `RMgencauchy` ‘c’ and `RMdewijsian` ‘w’.

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/alpha}-1] / (2^{β/alpha}-1)

where 0 < α ≤ 2 and β <= 2.

### Usage

    RMbcw(alpha, beta, c, 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 (-infty,2].
`c` | only for experts. If given, a not necessariy positive definite function c-γ(r) is built.
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above variogram remains unmodified.

### Details

For betaa >0, beta<0, beta=0 we have the generalised fractal Brownian motion `RMgenfbm`, the generalised Cauchy model `RMgencauchy`, and the de Wisjian model `RMdewijsian`, respectively.

Hence its two arguments `alpha` and `beta` allow for modelling the smoothness and a wide range of tail behaviour, respectively.

### Value

`RMbcw` returns an object of class `RMmodel`

### Author(s)

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

### References

- Schlather, M (2014) A parameteric variogram model bridging between stationary and intrinsically stationary processes. arxiv 1412.1914.

### See Also

`RMlsfbm` is equipped with Matheron's constant c for the fractional brownian motion, `RMgenfbm`, `RMgencauchy`, `RMdewijsian`, `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 <- RMbcw(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]