RMmodelsAdvanced: Advanced features of the models
In RandomFields: Simulation and Analysis of Random Fields

Description Details Note Author(s) References See Also Examples

Here, further models and advanced comments for RMmodel are given. See also RFgetModelNames.

Further stationary and isotropic models

`RMaskey`	Askey model (generalized test or triangle model)
`RMbcw`	bridging model between `RMcauchy` and `RMgenfbm`
`RMbessel`	Bessel family
`RMcircular`	circular model
`RMconstant`	spatially constant model
`RMcubic`	cubic model (see Chiles and Delfiner)
`RMdagum`	Dagum model
`RMdampedcos`	exponentially damped cosine
`RMqexp`	variant of the exponential model
`RMfractdiff`	fractionally differenced process
`RMfractgauss`	fractional Gaussian noise
`RMgengneiting`	generalized Gneiting model
`RMgneitingdiff`	Gneiting model for tapering
`RMhyperbolic`	generalized hyperbolic model
`RMlgd`	Gneiting's local-global distinguisher
`RMlsfbm`	locally stationary fractal Brownian motion
`RMpenta`	penta model (see Chiles and Delfiner)
`RMpower`	Golubov's model
`RMwave`	cardinal sine

Variogram models (stationary increments/intrinsically stationary)

`RMbcw`	bridging model between `RMcauchy` and `RMgenfbm`
`RMdewijsian`	generalized version of the DeWijsian model
`RMgenfbm`	generalized fractal Brownian motion
`RMflatpower`	similar to fractal Brownian motion but always smooth at the origin

General composed models (operators)

Here, composed models are given that can be of any kind (stationary/non-stationary), depending on the submodel.

`RMbernoulli`	Correlation function of a binary field based on a Gaussian field
`RMexponential`	exponential of a covariance model
`RMintexp`	integrated exponential of a covariance model (INCLUDES `ma2`)
`RMpower`	powered variograms
`RMqam`	Porcu's quasi-arithmetic-mean model
`RMS`	details on the optional transformation arguments (`var`, `scale`, `Aniso`, `proj`)

Stationary and isotropic composed models (operators)

`RMcutoff`	Gneiting's modification towards finite range
`RMintrinsic`	Stein's modification towards finite range
`RMnatsc`	practical range
`RMstein`	Stein's modification towards finite range
`RMtbm`	Turning bands operator

Stationary space-time models
See RMmodelsSpaceTime.

Non-stationary models
See RMmodelsNonstationary.

Negative definite models that are not variograms

`RMsum`	a non-stationary variogram model

Models related to max-stable random fields (tail correlation functions)
See RMmodelsTailCorrelation.

Other covariance models

`RMcov`	covariance structure given by a variogram
`RMfixcov`	User defined covariance structure
`RMuser`	User defined model

Trend models

`Aniso`	for space transformation (not really trend, but similar)
`RMcovariate`	spatial covariates
`RMprod`	to model variability of the variance
`RMpolynome`	easy modelling of polynomial trends
`RMtrend`	for explicit trend modelling
`R.models`	for implicit trend modelling
`R.c`	for multivariate trend modelling

Auxiliary models
See Auxiliary RMmodels.

Note that, instead of the named arguments, a single argument k can be passed. This is possible if all the arguments are scalar. Then k must have a length equal to the number of arguments.
If an argument equals NULL the argument is not set (but must have a valid name).
Aniso can be given also by RMangle or any other RMmodel instead of a matrix
Note also that a completely different possibility exists to define a model, namely by a list. This format allows for easy flexible models and modifications (and some few more options, as well as some abbreviations to the model names, see PrintModelList()). Here, the argument var, scale, Aniso and proj must be passed by the model RMS. For instance,
- model <- RMexp(scale=2, var=5)
  is equivalent to
  model <- list("RMS", scale=2, var=5, list("RMexp"))
  The latter definition can be also obtained by
  
  print(RMexp(scale=2, var=5))
- model <- RMnsst(phi=RMgauss(var=7), psi=RMfbm(alpha=1.5), scale=2, var=5)
  is equivalent to
  model <- list("RMS", scale=2, var=5,
  list("RMnsst", phi=list("RMS", var=7, list("RMgauss")),
  psi=list("RMfbm", alpha=1.5)) ).
All models have secondary names that stem from RandomFields versions 2 and earlier and that can also be used as strings in the list notation. See RFgetModelNames(internal=FALSE) for the full list.

Alexander Malinowski; \martin

Chiles, J.-P. and Delfiner, P. (1999) Geostatistics. Modeling Spatial Uncertainty. New York: Wiley.
Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.
Schlather, M. (2011) Construction of covariance functions and unconditional simulation of random fields. In Porcu, E., Montero, J.M. and Schlather, M., Space-Time Processes and Challenges Related to Environmental Problems. New York: Springer.
Schlather, M., Malinowski, A., Menck, P.J., Oesting, M. and Strokorb, K. (2015) Analysis, simulation and prediction of multivariate random fields with package RandomFields. Journal of Statistical Software, 63 (8), 1-25, url = ‘http://www.jstatsoft.org/v63/i08/’

‘multivariate’, the corresponding vignette.
Yaglom, A.M. (1987) Correlation Theory of Stationary and Related Random Functions I, Basic Results. New York: Springer.
Wackernagel, H. (2003) Multivariate Geostatistics. Berlin: Springer, 3nd edition.

RFformula, RM, RMmodels, RMmodelsAuxiliary.

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

## a non-stationary field with a sharp boundary
## of the differentiabilities
x <- seq(-0.6, 0.6, len=50)
model <- RMwhittle(nu=0.8 + 1.5 * R.is(R.p(new="isotropic"), "<=", 0.5))
z <- RFsimulate(model=model, x, x, n=4)
plot(z)