RandomFields (version 3.0.32)

RMflatpower: Variogram Model Similar to Fractal Brownian Motion

Description

RMflatpower is an intrinsically stationary isotropic variogram model. The corresponding centered semi-variogram only depends on the distance $r \ge 0$ between two points and is given by $$\gamma(r) = r^2 / ( 1 + r^2)^\alpha$$ where $\alpha \in (0,1]$. For related models see RMgenfbm.

Usage

RMflatpower(alpha, var, scale, Aniso, proj)

Arguments

alpha

numeric in $(0,1]$; refers to the fractal dimension of the process

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above variogram remains unmodified.

Value

• RMflatpower returns an object of class RMmodel.

Details

The model is always smooth at the origin. The parameter $\alpha$ only gives the tail behaviour and satisfies $\alpha \in (0,1]$.

The variogram is unbounded and belongs to a non-stationary process with stationary increments.

References

• Oesting, M., Schlather, M., and Friederichs, P. (2014) Conditional Modelling of Extreme Wind Gusts by Bivariate {Brown-Resnick} Processesarxiv1312.4584.

See Also

RMgenfbm, 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 <- RMflatpower(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()