CovarianceFct {RandomFields}R Documentation

Covariance And Variogram Models

Description

CovarianceFct returns the values of an isotropic covariance function

Variogram returns the values of an isotropic variogram model

PrintModelList prints the list of currently implemented models

GetModelNames returns a list of currently implemented models

Usage

CovarianceFct(x,model,param,dim=1)
Variogram(x,model,param,dim=1)
PrintModelList()
GetModelNames()

Arguments

x a vector of distances at which the covariance function or variogram should be evaluated
model character; name of the covariance function or variogram model; see below, or type PrintModelList() for all options
param vector of parameters; param=c(NA,variance,nugget,scale,...), in this order;
The dots ... stand for additional parameters of the model
dim dimension of the space in which the model is applied

Details

The first component of param is reserved for the mean of a random field and thus ignored in the evaluation of the covariance function or variogram. The parameters mean, variance, nugget, and scale must be given in this order; additional parameters have to be supplied in case of a parametrised class of models (e.g. hyperbolic, see below), in the order a, b, c.

The implemented models are in standard notation of a covariance function (variance 1, nugget 0, scale=1) and for positive real arguments x:

Let cov be a model given in standard notation. Then the covariance model applied with arbitrary variance, nugget, and scale equals

nugget + variance * cov( (.)/scale).

For a given covariance function cov the variogram gamma equals

gamma(x) = cov(0) - cov(x).

Note that the value of the covariance function or variogram depends also on RFparameters()$PracticalRange. If the latter is TRUE then the covariance function is internally rescaled such that cov(1)~=0.05 for standard parameters (scale==1).

Some models allow certain parameter combinations only for certain dimensions. As any model in d dimensions is also valid in 1 dimension, the default in CovarianceFct and Variogram is dim=1.

Value

CovarianceFct returns a vector of values of the covariance function.
Variogram returns a vector of values of the variogram model.
PrintModelList prints a table of the currently implemented covariance functions and the matching methods. PrintModelList returns NULL.
GetModelNames returns a list of implemented models

Author(s)

Martin Schlather, Martin.Schlather@uni-bayreuth.de http://www.geo.uni-bayreuth.de/~martin

References

Overviews:

Cauchy models, generalisations and extensions

Gneiting's models

Holeeffect model

Hyperbolic model

Power model

See Also

EmpiricalVariogram, RandomFields, RFparameters, ShowModels.

Examples

 PrintModelList()
 CovarianceFct(0:100, "bessel", c(NA,2,1,5,0.5))

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