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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 ‘b’, RMgencauchy ‘c’ and RMdewijsian ‘w’.

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/α}-1] / (2^{β/α}-1)

where 0 < α ≤ 2 and β <= 2.

Usage

RMbcw(alpha, beta, c, 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].

c

only for experts. If given, a not necessarily positive definite function c-γ(r) is built.

var,scale,Aniso,proj

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

Details

For β >0, β<0, β=0 we have the generalized fractal Brownian motion RMgenfbm, the generalized 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)

References

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

See Also

RMlsfbm is equipped with Matheron's constant c for the fractional brownian motion, 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, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

RandomFields

Simulation and Analysis of Random Fields

v3.3.10
GPL (>= 3)
Authors
Martin Schlather [aut, cre], Alexander Malinowski [aut], Marco Oesting [aut], Daphne Boecker [aut], Kirstin Strokorb [aut], Sebastian Engelke [aut], Johannes Martini [aut], Felix Ballani [aut], Olga Moreva [aut], Jonas Auel[ctr], Peter Menck [ctr], Sebastian Gross [ctr], Ulrike Ober [ctb], Paulo Ribeiro [ctb], Brian D. Ripley [ctb], Richard Singleton [ctb], Ben Pfaff [ctb], R Core Team [ctb]
Initial release

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