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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