# clusterradius

##### Compute or Extract Effective Range of Cluster Kernel

Given a cluster point process model, this command returns a value beyond which the the probability density of the cluster offspring is neglible.

- Keywords
- spatial

##### Usage

`clusterradius(model, …)`# S3 method for kppm
clusterradius(model, …, thresh = NULL, precision = FALSE)

# S3 method for character
clusterradius(model, …, thresh = NULL, precision = FALSE)

##### Arguments

- model
Cluster model. Either a fitted cluster or Cox model (object of class

`"kppm"`

), or a character string specifying the type of cluster model.- …
Parameter values for the model, when

`model`

is a character string.- thresh
Numerical threshold relative to the cluster kernel value at the origin (parent location) determining when the cluster kernel will be considered neglible. A sensible default is provided.

- precision
Logical. If

`precision=TRUE`

the precision of the calculated range is returned as an attribute to the range. See details.

##### Details

Given a cluster model this function by default returns the effective
range of the model with the given parameters as used in spatstat. For
the Matern cluster model (see e.g. `rMatClust`

) this is
simply the finite radius of the offsring density given by the paramter
`scale`

irrespective of other options given to this function. The
remaining models in spatstat have infinite theoretical range, and an
effective finite value is given as follows: For the Thomas model (see
e.g. `rThomas`

the default is `4*scale`

where scale
is the scale or standard deviation parameter of the model. If
`thresh`

is given the value is instead found as described for the
other models below.

For the Cauchy model (see e.g. `rCauchy`

) and the Variance
Gamma (Bessel) model (see e.g. `rVarGamma`

) the value of
`thresh`

defaults to 0.001, and then this is used to compute the
range numerically as follows. If \(k(x,y)=k_0(r)\)
with \(r=\sqrt(x^2+y^2)\)
denotes the isotropic cluster kernel then \(f(r) = 2 \pi r
k_0(r)\) is the
density function of the offspring distance from the parent. The range
is determined as the value of \(r\) where \(f(r)\) falls below
`thresh`

times \(k_0(r)\).

If `precision=TRUE`

the precision related to the chosen range is
returned as an attribute. Here the precision is defined as the polar
integral of the kernel from distance 0 to the calculated
range. Ideally this should be close to the value 1 which would be
obtained for the true theretical infinite range.

##### Value

A positive numeric.

Additionally, the precision related to this range value is returned as
an attribute `"prec"`

, if `precision=TRUE`

.

##### See Also

`clusterkernel`

, `kppm`

,
`rMatClust`

, `rThomas`

, `rCauchy`

,
`rVarGamma`

, `rNeymanScott`

.

##### Examples

```
# NOT RUN {
fit <- kppm(redwood ~ x, "MatClust")
clusterradius(fit)
clusterradius("Thomas", scale = .1)
clusterradius("Thomas", scale = .1, thresh = 0.001)
clusterradius("VarGamma", scale = .1, nu = 2, precision = TRUE)
# }
```

*Documentation reproduced from package spatstat, version 1.49-0, License: GPL (>= 2)*