RMgenfbm: Generalized Fractal Brownian Motion Variogram Model
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value References See Also Examples

RMgenfbm 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}+1)^{β/α}-1

where 0 < α ≤ 2 and β \in (0,2].
See also RMfbm.

1	RMgenfbm(alpha, beta, var, scale, Aniso, proj)

`alpha`	a numerical value; should be in the interval (0,2].
`beta`	a numerical value; should be in the interval (0,2].
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above variogram remains unmodified.

Here, the variogram of RMfbm is modified by the transformation (γ+1)^{δ/-1} on variograms γ for δ \in (0,1]. This original modification allows for further generalization, cf. RMbcw.

RMgenfbm returns an object of class RMmodel.

Gneiting, T. (2002) Nonseparable, stationary covariance functions for space-time data, JASA 97, 590-600.
Schlather, M. (2010) On some covariance models based on normal scale mixtures. Bernoulli, 16, 780-797.

RMbcw, RMfbm, RMmodel, RMflatpower, RFsimulate, RFfit.

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

model <- RMgenfbm(alpha=1, beta=0.5)
x <- seq(0, 10, 0.02)
plot(model)
plot(RFsimulate(model, x=x))

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)'.