R: Power operator for Variograms and Covariance functions

RMpower {RandomFields} | R Documentation

## Power operator for Variograms and Covariance functions

### Description

`RMpower` yields a variogram or covariance model from a given variogram or covariance model. The variogram gamma of the model is given by

gamma=phi^alpha

if phi is a variogram model. The covariance C of the model is given by

C(h) = phi(0)-(phi(0)-phi(h))^alpha

if phi is a covariance model.

### Usage

    RMpower(phi, alpha, var, scale, Aniso, proj)

### Arguments

`phi` | a valid `RMmodel`; either a variogram model or a covariance model
`alpha` | a numerical value in the interval [0,1]
`var,scale,Aniso,proj` | optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

### Details

If γ is a variogram, then γ^α is a valid variogram for α in the interval [0,1].

### Value

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

### Author(s)

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

### References

Schlather, M. (2012) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J. M., Schlather, M. Advances and Challenges in Space-time Modelling of Natural Events, Springer, New York.

### 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 <- RMpower(RMgauss(), alpha=0.5)
    x <- seq(0, 10, 0.02)
    plot(model)
    plot(RFsimulate(model, x=x))

[Package RandomFields version 3.1.50 Index]