# VariogramModel

VariogramModel["model",{params}]

represents the function for the variogram model specified by "model".

# Details    • VariogramModel is also known as variogram and semivariogram.
• represents a function generated by EstimatedVariogramModel.
• VariogramModel is typically used as a local model of spatial dependence when predicting values of a spatial field, as in SpatialEstimate.
• The following tables enumerate valid variogram model families grouped into tables with similar features.
• Variogram models that reach the sill within a finite range:
• {"Askey",a,b,c}  {"BoundedLinear",a,b}  {"Circular",a,b}  {"Cubic",a,b}  {"EuclidsHat",a,b,c}  {"Pentaspherical",a,b}  {"Spherical",a,b}  {"WhiteNoise",a} • Variogram models that reach the sill asymptotically where the effective range is defined at 95% of the sill:
• {"Dagum",a,b,c,d}  {"Exponential",a,b}  {"Gaussian",a,b}  {"GeneralizedCauchy",a,b,c,d}  {"Matern",a,b,c}  {"PoweredExponential",a,b,c} • Variogram models oscillating around the sill and reaching the sill asymptotically. The range is defined at the first crossing of the sill:
• {"GaussianLaguerre",a,b,c,d}  {"Poisson",a,b,c}  {"SineHoleEffect",a,b} • Variogram models that are unbounded. These occur when data has a global trend:
• {"Linear",a}  {"Power",a,b} • VariogramModel works like Function.
• VariogramModel[]["prop"] can be used to access different properties for the variogram model.
• The following properties "prop" can be used:
•  "ModelFormula" model function without variance noise "Name" name of the variogram model "SpatialNoiseLevel" value of the spatial noise variance "Parameters" parameters of the variogram model function "Properties" list of available properties "Range" range of the function model "Sill" sill of the function model "Visualization" plot of the function model
• Additional properties "prop" can be used when VariogramModel is obtained from EstimatedVariogramModel:
•  "BinnedVariogram" binned variogram used for model fitting "WeightedSumOfResiduals" weighted sum of residuals from the fitting procedure
• The following option can be given:
•  SpatialNoiseLevel Automatic specify the noise level in the model

# Examples

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## Basic Examples(1)

Gaussian model:

Value at a distance:

Variogram range:

Plot as a function of distance:

## Scope(3)

### Basic Uses(2)

Explicit spherical model:

With noise variance:

Estimate a variogram model for random data:

White noise model:

### Variogram Models(1)

Spherical model:

With noise variance:

## Possible Issues(1)

For symbolic variogram representation, not all properties are defined:

List all the properties:

Some properties are available only after fitting the model to data: