RMflatpower {RandomFields}

R Documentation

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.

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.

Value

RMflatpower returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

• Oesting, M., Schlather, M., and Friederichs, P. (2014) Conditional Modelling of Extreme Wind Gusts by Bivariate Brown-Resnick Processes arxiv 1312.4584.

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, 0.1)
plot(model)
plot(RFsimulate(model, x=x))

---