RMfbm is an intrinsically stationary isotropic variogram
model. The corresponding centered semi-variogram only depends on the
distance r ≥ 0 between two points and is given by
γ(r) = r^α
where 0 < α ≤ 2.
By now, the model is implemented for dimensions up to 3.
For a generalized model see also
numeric in (0,2]; refers to the fractal dimension of the process
optional arguments; same meaning for any
The variogram is unbounded and belongs to a non-stationary process with
stationary increments. For α=1 and
we get a variogram corresponding to a standard Brownian Motion.
For 0 < α < 2 the quantity H=α/2 is called Hurst index and determines the fractal dimension D of the corresponding Gaussian sample paths
D = d + 1 - H
where d is the dimension of the random field (see Chiles and Delfiner, 1999, p. 89).
RMfbm returns an object of class
Chiles, J.-P. and P. Delfiner (1999) Geostatistics. Modeling Spatial Uncertainty. New York, Chichester: John Wiley & Sons.
Stein, M.L. (2002) Fast and exact simulation of fractional Brownian surfaces. J. Comput. Graph. Statist. 11, 587–599.
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Loading required package: sp Loading required package: RandomFieldsUtils Attaching package: 'RandomFields' The following object is masked from 'package:RandomFieldsUtils': RFoptions The following objects are masked from 'package:base': abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1, floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin, sinh, sqrt, tan, tanh, trunc NULL NOTE: simulation is performed with fixed random seed 0. Set 'RFoptions(seed=NA)' to make the seed arbitrary. New output format of RFsimulate: S4 object of class 'RFsp'; for a bare, but faster array format use 'RFoptions(spConform=FALSE)'.
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