RMfbm: Variogram Model of Fractal Brownian Motion

Description Usage Arguments Details Value References See Also Examples

View source: R/RMmodels.R

Description

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 RMgenfbm.

Usage

1
RMfbm(alpha, var, scale, Aniso, proj)

Arguments

alpha

numeric in (0,2]; refers to the fractal dimension of the process

var,scale,Aniso,proj

optional arguments; same meaning for any RMmodel. If not passed, the above variogram remains unmodified.

Details

The variogram is unbounded and belongs to a non-stationary process with stationary increments. For α=1 and scale=2 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).

Value

RMfbm returns an object of class RMmodel.

References

See Also

RMgenfbm, RMmodel, RFsimulate, RFfit.

Examples

1
2
3
4
5
6
7
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again

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

Example output

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)'.

RandomFields documentation built on Feb. 6, 2020, 5:13 p.m.