Covariance and Variogram Models in RandomFields (RM commands)
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
Others
Alexander Malinowski; Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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)
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