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

γ (r) = r^{2} / (1 + r^{2})^{α}

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.

Examples

Run this code

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))
FinalizeExample()

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