Model bridging stationary and intrinsically stationary processes

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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 ≥ 0 between two points and is given by

γ(r)=[(r^{α}+1)^{β/alpha}-1] / (2^{β/alpha}-1)

where 0 < α ≤ 2 and β <= 2.

Usage

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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.

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.

Value

RMbcw returns an object of class RMmodel

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

References

  • Schlather, M (2014) A parameteric variogram model bridging between stationary and intrinsically stationary processes. arxiv 1412.1914.

See Also

RMgenfbm, RMgencauchy, RMdewijsian, RMmodel, RFsimulate, RFfit.

Examples

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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, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

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