RandomFields (version 3.0.32)

RMpower: 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.

Value

• RMpower returns an object of class RMmodel.

Details

If $\gamma$ is a variogram, then $\gamma^\alpha$ is a valid variogram for $\alpha$ in the interval [0,1].

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, if (interactive()) 0.02 else 1) 
plot(model, ylim=c(0,1))
plot(RFsimulate(model, x=x))
FinalizeExample()