| RMmodel {RandomFields} | R Documentation |
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 vector which defines a
diagonal matrix of zeros and ones and proj gives the
positions of the ones (integer values). In a space-time framework, also
"space" and "time" are valid values.
With φ denoting the original model, the transformed model is C(h) = v * φ(A*h/s).
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 |
Basic models for mixed effect modelling
RMfixcov | constant pre-defined covariance |
RMfixed | fixed or trend effects; Caution: RMfixed is not a function and can be used only in formula notation |
Others
RMtrend | trend |
RMangle | defines a 2x2 anisotropy matrix by rotation and stretch arguments. |
Alexander Malinowski, malinowski@math.uni-mannheim.de
Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software
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)