Variogram Model Similar to Fractal Brownian Motion

Description

RMflatpower 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^2 / ( 1 + r^2)^α

where 0 < α ≤ 1.

For related models see RMgenfbm.

Usage

RMflatpower(alpha, var, scale, Aniso, proj)

Arguments

Details

The model is always smooth at the origin.

The parameter α only gives the tail behaviour and satisfies 0 < α ≤ 1.

The variogram is unbounded and belongs to a non-stationary process with stationary increments.

Value

RMflatpower returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

References

• Oesting, M., Schlather, M., and Friederichs, P. (2014) Conditional Modelling of Extreme Wind Gusts by Bivariate Brown-Resnick Processes arxiv 1312.4584.

See Also

RMgenfbm, RMmodel, RFsimulate, RFfit.

Examples

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

model <- RMflatpower(alpha=0.5)
x <- seq(0, 10, 0.1)
plot(model)
plot(RFsimulate(model, x=x))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RandomFields)
Loading required package: sp
Loading required package: RandomFieldsUtils
This is RandomFieldsUtils Version: 0.2.1
This is RandomFields Version: 3.1.16

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

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/RandomFields/RMoesting.Rd_%03d_medium.png", width=480, height=480)
> ### Name: RMflatpower
> ### Title: Variogram Model Similar to Fractal Brownian Motion
> ### Aliases: RMflatpower
> ### Keywords: spatial models
> 
> ### ** Examples
> 
> RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
> ##                   RFoptions(seed=NA) to make them all random again
> 
> model <- RMflatpower(alpha=0.5)
> x <- seq(0, 10, 0.1)
> plot(model)
NULL
> plot(RFsimulate(model, x=x))
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)'.
> ## Don't show: 
> FinalizeExample()
> ## End(Don't show)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>