RMbcw: Model bridging stationary and intrinsically stationary...
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

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.

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

`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.

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.

RMbcw returns an object of class RMmodel

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

RMlsfbm is equipped with Matheron's constant c for the fractional brownian motion, RMgenfbm, RMgencauchy, RMdewijsian, RMmodel, RFsimulate, RFfit.

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))