Covariance and Variogram Models in RandomFields

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 parameters. %Parameter %corresponding to specific covariance model
  • varis the optional variance parameter$v$,
  • scalethe optional scale parameter$s$,
  • Anisothe optional anisotropy matrix$A$, and
  • projis the optional projection vector which defines a diagonal matrix of zeros and ones andprojgives the positions of the ones (integer values).
With $\phi$ denoting the original model, the transformed model is $C(h) = v * \phi(A*h/s)$.

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 ll{ 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)

ll{ RMfbm fractal Brownian motion }

Basic Operations

ll{ RMmult product of covariance models RMplus sum of covariance models }

Basic models for mixed effect modelling

ll{ RMconstant constant pre-defined covariance RMfixed fixed or trend effects; Caution: RMfixed is not a function and can be used only in formula notation }

Trend ll{ RMtrend trend }

See RMmodelsAdvanced for many more, advanced models.


  • Chiles, J.-P. and Delfiner, P. (1999)Geostatistics. Modeling Spatial Uncertainty.New York: Wiley. % \item Gneiting, T. and Schlather, M. (2004) % Statistical modeling with covariance functions. % \emph{In preparation.}
  • 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.

See Also

RFformula, RMmodelsAdvanced, RMmodelsAuxiliary

  • RM
  • RMmodel
  • RMmodels
  • [,RMmodel,ANY,ANY-method
  • [<-,RMmodel,ANY,ANY-method
RFgetModelNames(type="positive definite", domain="single variable",
                isotropy="isotropic", operator=FALSE)
Documentation reproduced from package RandomFields, version 3.0.5, License: GPL (>= 3)

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