covmodel {constrainedKriging} | R Documentation |
Create isotropic covariance model
Description
Function to generate isotropic covariance models, or add an isotropic covariance model to an existing isotropic model.
Usage
covmodel(modelname, mev, nugget,variance, scale, parameter, add.covmodel)
## S3 method for class 'covmodel'
print(x, ...)
Arguments
modelname |
a character scalar with the name of an isotropic
covariance model, see Details for a list of implemented models. A
call of |
mev |
a numeric scalar, variance of the measurement error. |
nugget |
a numeric scalar, variance of microstructure white noise process with range smaller than the minimal distance between any pair of support data. |
variance |
a numeric scalar, partial sill of the covariance model. |
scale |
a numeric scalar, scale ("range") parameter of the covariance model. |
parameter |
a numeric vector of further covariance parameters, missing
for some model like |
add.covmodel |
an object of the class |
x |
a covariance model generated by |
... |
further printing arguments |
Details
The name and parametrisation of the covariance models originate from the
function CovarianceFct
of the archived package RandomFields,
version 2.0.71.
The following isotropic covariance functions are implemented (equations
taken from help page of function CovarianceFct
of archived package
RandomFields, version 2.0.71, note that the variance and range
parameters are equal to 1 in the following formulae and is the
lag distance.):
-
bessel
For a 2-dimensional region, the parameter
must be greater than or equal to 0.
-
cauchy
The parameter
must be positive.
-
cauchytbm
The parameter
must be in (0,2] and
positive. The model is valid for 3 dimensions. It allows for simulating random fields where fractal dimension and Hurst coefficient can be chosen independently.
-
circular
This isotropic covariance function is valid only for dimensions less than or equal to 2.
-
constant
-
cubic
This model is valid only for dimensions less than or equal to 3. It is a 2 times differentiable covariance functions with compact support.
-
dampedcosine
(hole effect model)This model is valid for 2 dimensions iff
.
-
exponential
This model is a special case of the
whittle
model (for) and the
stable
model (for).
-
gauss
This model is a special case of the
stable
model (for). See
gneiting
for an alternative model that does not have the disadvantages of the Gaussian model. -
gencauchy
(generalisedcauchy
)The parameter
must be in (0,2] and
positive. This model allows for random fields where fractal dimension and Hurst coefficient can be chosen independently.
-
gengneiting
(generalisedgneiting
) Ifand let
then
If
and let
then
If
and let
then
The parameter
is a positive integer; here only the cases
are implemented. For two dimensional regions the parameter
must greater than or equal to
.
-
gneiting
where
. This covariance function is valid only for dimensions less than or equal to 3. It is a 6 times differentiable covariance functions with compact support. It is an alternative to the
gaussian
model since its graph is visually hardly distinguishable from the graph of the Gaussian model, but possesses neither the mathematical and nor the numerical disadvantages of the Gaussian model. -
hyperbolic
The parameters are such that
,
and
or
,
and
or
,
, and
.
Note that this class is over-parametrised; always one of the three parameters,
, and scale can be eliminated in the formula.
-
lgd1
(local-global distinguisher)Here
and
msut be in
. The random field has for 2-dimensional regions fractal dimension
and Hurst coefficient
for
-
matern
The parameter
must be positive. This is the model of choice if the smoothness of a random field is to be parametrised: if
then the graph is
times differentiable.
-
nugget
-
penta
valid only for dimensions less than or equal to 3. This is a 4 times differentiable covariance functions with compact support.
-
power
This covariance function is valid for 2 dimensions iff
. For
we get the well-known triangle (or tent) model, which is valid on the real line, only.
-
qexponential
The parameter
must be in
.
-
spherical
This covariance function is valid only for dimensions less than or equal to 3.
-
stable
The parameter
must be in
. See
exponential
andgaussian
for special cases. -
wave
This isotropic covariance function is valid only for dimensions less than or equal to 3. It is a special case of the
bessel
model (for).
-
whittle
The parameter
must be positive. This is the model of choice if the smoothness of a random field is to be parametrised: if
then the graph is
times differentiable.
The default values of the arguments
mev
,
nugget
,
variance
and scale
are eq 0.
Value
an object of the class covmodel
that defines a covariance model.
Author(s)
Christoph Hofer, christoph.hofer@alumni.ethz.ch
Examples
# table with all available covariance models and their
# parameters
covmodel()
# exponential model without a measurement error and without a nugget,
# partial sill = 10, scale parameter = 15
covmodel(modelname = "exponential", variance = 10, scale = 15)
# exponential model with a measurement error ( mev = 0.5) and a
# nugget (nugget = 2.1), exponential partial sill (variance = 10)
# and scale parameter = 15
covmodel(modelname = "exponential", mev = 0.5, nugget = 2.1,
variance = 10, scale = 15)