Model bridging stationary and intrinsically stationary processes
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.
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
|
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.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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))
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