RandomFields (version 3.0.35)

RMbcw: Model bridging stationary and intrinsically stationary processes

Description

RMbcw is a variogram model that bridges between some intrinsically stationary isotropic processes and some stationary ones. It reunifies the RMgenfbm, RMdewijsian and RMgencauchy.

The corresponding centered semi-variogram only depends on the distance $r \ge 0$ between two points and is given by $$\gamma(r) = \frac{(r^{\alpha}+1)^{\beta/alpha}-1}{2^{\beta/alpha} -1}$$ where $\alpha \in (0,2]$ and $beta \le 2$.

Usage

RMbcw(alpha, beta, var, scale, Aniso, proj)

Arguments

alpha

a numerical value; should be in the interval (0,2].

beta

a numerical value; should be in the interval (-infty,2].

var,scale,Aniso,proj

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

Value

• RMbcw returns an object of class RMmodel

Details

For $betaa >0$, $beta<0$, $beta="0$" we="" have="" the="" generalised="" fractal="" brownian="" motion="" RMgenfbm, the generalised Cauchy model RMgencauchy, and the de Wisjian model RMdewijsian, respectively.

Hence its two arguments alpha and beta allow for modelling the smoothness and a wide range of tail behaviour, respectively.

References

• Schilling, R.L., Song, R., Vondracek, Z. (2010) Berstein functions. Theory and Applications. De Gruyter
• Schlather, M (2014) A parameteric variogram model bridging between stationary and intrinsically stationary processes.Submitted, -- % \item Martin's Toledo-Chapter: Construction of covariance functions % and unconditional simulation of random fields, Application to variograms

See Also

RMgenfbm, RMgencauchy, RMdewijsian, 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 <- RMbcw(alpha=1, beta=0.5)
x <- seq(0, 10, if (interactive()) 0.02 else 1) 
plot(model)
plot(RFsimulate(model, x=x))
FinalizeExample()