# RMpower: Power operator for Variograms and Covariance functions In RandomFields: Simulation and Analysis of Random Fields

## 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

 `1` ```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, [email protected]

## 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.

`RMmodel`, `RFsimulate`, `RFfit`.
 ```1 2 3 4 5 6 7``` ```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)) ```