R: Class 'RMmodelgenerator'

RMmodelgenerator-class {RandomFields} | R Documentation

## Class `RMmodelgenerator`

### Description

Class for all functions of this package with prefix `RM`, i.e. all functions that generate objects of class `RMmodel`; direct extension of class `function`

### Creating Objects

Objects should not be created by the user!

### Slots

`.Data`:

  function; the genuine funtion that generates an objects of class `RMmodel`

`type`:

  character string; specifies the cathegory of RMmodel-function, see Details

`domain`:

  character string; specifies whether the corresponding function(s) depend on 1 or 2 variables, see Details

`isotropy`:

  character string; specifies the type of isotropy of the corresponding covariance model, see Details

`operator`:

  logical; specifies whether the underlying covariance model is an operator, see Details

`monotone`:

  character string; specifies the kind of monotonicity of the model

`finiterange`:

  logical; specifies whether the underlying covariance model has finite range, see Details

`simpleArguments`:

  logical. If `TRUE` than all the parameters are real valued (or integer valued).

`maxdim`:

  numeric; the maximal dimension, in which the corresponding model is a valid covariance model, see Details

`vdim`:

  numeric; dimension of the value of the random fiels at a single fixed location, equals 1 in most cases, see Details

### Extends

Class `function`, directly.

### Methods

show

  `signature(x = "RMmodel")`: returns the structure of `x`

print

  `signature(x = "RMmodel")`: identical with `show`-method

[

  `signature(x = "RMmodelgenerator")`: enables accessing the slots via the "["-operator, e.g. x["maxdim"]

[<-

  `signature(x = "RMmodelgenerator")`: enables replacing the slots via the "["-operator

### Details

`type`:

  can be one of the following strings:

  `'tail correlation function'`:

    indicates that the function returns a tail correlation function (a subclass of the set of positive definite functions)

  `'positive definite'`:

    indicates that the function returns a covariance function (positive definite function)

  `'negative definite'`:

    indicates that the function returns a variogram model (negative definite function)

  `'process'`:

    functions of that type determine the class of processes to be simulated

  `'method for Gauss processes'`:

    methods to simulate Gaussian random fields

  `'method for Brown-Resnick processes'`:

    methods to simulate Brown-Resnick fields

  `'point-shape function'`:

    functions of that type determine the distribution of points in space

  `'distribution family'`:

    e.g. (multivariate) uniform distribtion, normal distribution, etc., defined in RandomFields. See RR for a complete list.

  `'shape function'`:

    functions used in, e.g., M3 processes (RPsmith)

  `'trend'`:

    RMtrend or a mixed model

  `'interface'`:

    indicates internal models which are usually not visible for the users. These functions are the internal representations of `RFsimulate`, `RFcov`, etc.. See RF for a complete list.

  `'undefined'`:

    some models can take different types, depending on the parameter values and/or the submodels

  `'other type'`:

    very very special internal functions, not belonging to any of the above types.

`domain`:

  can be one of the following strings:

  `'single variable'`:

    Function depending on a single variable

  `'kernel'`:

    model refers to a kernel, e.g., an non-stationary convariance function

  `'framework dependent'`:

    domain depends on the calling model

  `'mismatch'`:

    this option is used only internaly and should never appear

`isotropy`:

  can be one of the following strings:

  `'isotropic'`:

    indicates that the model is isotropic

  `'space-isotropic'`:

    indicates that the spatial part of a spatio-temporal model is isotropic

  `'zero-space-isotropic'`:

    this property refers to space-time models; the model is called zerospaceisotropic if it is isotropic as soon as the time-component is zero

  `'vector-isotropic'`:

    multivariate vector model (flow fields) have a different notion of isotropy

  `'symmetric'`:

    the most basic property of any covariance function or variogram model

  `'cartesian system'`, `'earth system'`, `'spherical system'`, `'cylinder system'`:

    different coordinate systems

  `'non-dimension-reducing'`:

    the property f(x) = f(-x)^\top does not hold

  `'parameter dependent'`:

    indicates that the type of isotropy of the model depends on the parameters passed to the model; in particular parameters may be submodels if an operator model is considered

  `'<mismatch>'`:

    this option is used only internaly and should never appear

`operator`:

  if `TRUE`, the model requires at least one submodel

`monotone`:
  `'mismatch in monotonicity'`:

    used if a statement on the monotonocity does not make sense, e.g. for `RRmodels`

  `'submodel dependent monotonicity'`:

    only for operators, e.g. `RMS`

  `'previous model dependent monotonicity'`:

    internal; should not be used

  `'parameter dependent monotonicity'`:

    some models change their properties according to the parameters

  `'not monotone'`:

    none of the above cathegories; either the function is not monotone or properties are not known

  `'monotone'`:

    isotone or antitone

  `'Gneiting-Schaback class'`:

    function belonging to Euclid's hat in Gneiting's 1999 paper

  `'normal mixture'`:

    scale mixture of the Gaussian model

  `'completely monotone'`:

    completely monotone function

  `'Bernstein'`:

    Bernstein function

  Note that

  - `'not monotone'` includes `'monotone'` and `'Bernstein'`

  - `'monotone'` includes `'Gneiting-Schaback class'`

  - `'Gneiting-Schaback class'` includes `'normal mixture'`

  - `'normal mixture'` includes `'completely monotone'`

`finiterange`:

  if `TRUE`, the covariance of the model has finite range

`maxdim`:

  if a positive integer, `maxdim` gives the maximum dimension in which the model is a valid covariance model, can be `Inf`; `vdim=-1` means that the actual maxdim depends on the parameters; `vdim=-2` means that the actual maxdim depends on the submodel(s)

`vdim`:

  if a positive integer, `vdim` gives the dimension of the random field, i.e. univariate, bi-variate, ...; `vdim=-1` means that the actual vdim depends on the parameters; `vdim=-2` means that the actual vdim depends on the submodel(s)

### Author(s)

Alexander Malinowski Alexander.Malinowski@web.de; Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### References

- Gneiting, T. (1999) Radial positive definite functions generated by Euclid's hat, J. Multivariate Anal., 69, 88-119.

### See Also

`RMmodel`, `RFgetModelNames`

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again
    RFgetModelNames()

[Package RandomFields version 3.1.50 Index]