RMmodel: Covariance and Variogram Models in 'RandomFields' (RM...
In RandomFields: Simulation and Analysis of Random Fields

Description Details Author(s) References See Also Examples

Summary of implemented covariance and variogram models

To generate a covariance or variogram model for use within RandomFields, calls of the form

RM_name_(..., var, scale, Aniso, proj)

can be used, where _name_ has to be replaced by a valid model name.

... can take model specific arguments.
var is the optional variance argument v,
scale the optional scale argument s,
Aniso an optional anisotropy matrix A or given by RMangle, and
proj is the optional projection.

With φ denoting the original model, the transformed model is C(h) = v * φ(A*h/s). See RMS for more details.

RM_name_ must be a function of class RMmodelgenerator. The return value of all functions RM_name_ is of class RMmodel.

The following models are available (cf. RFgetModelNames):

Basic stationary and isotropic models

`RMcauchy`	Cauchy family
`RMexp`	exponential model
`RMgencauchy`	generalized Cauchy family
`RMgauss`	Gaussian model
`RMgneiting`	differentiable model with compact support
`RMmatern`	Whittle-Matern model
`RMnugget`	nugget effect model
`RMspheric`	spherical model
`RMstable`	symmetric stable family or powered exponential model
`RMwhittle`	Whittle-Matern model, alternative parametrization

Variogram models (stationary increments/intrinsically stationary)

`RMfbm`	fractal Brownian motion

Basic Operations

`RMmult`, `*`	product of covariance models
`RMplus`, `+`	sum of covariance models or variograms

Others

`RMtrend`	trend
`RMangle`	defines a 2x2 anisotropy matrix by rotation and stretch arguments.

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.
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.

RM for an overview over more advanced classes of models
RC, RF, RP, RR, R., RFcov, RFformula, RMmodelsAdvanced, RMmodelsAuxiliary, trend modelling

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

## an example of a simple model
model <- RMexp(var=1.6, scale=0.5) + RMnugget(var=0) #exponential + nugget
plot(model)