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
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