# linearK

##### Linear K Function

Computes an estimate of the linear \(K\) function for a point pattern on a linear network.

- Keywords
- spatial, nonparametric

##### Usage

`linearK(X, r=NULL, ..., correction="Ang", ratio=FALSE)`

##### Arguments

- X
Point pattern on linear network (object of class

`"lpp"`

).- r
Optional. Numeric vector of values of the function argument \(r\). There is a sensible default.

- …
Ignored.

- correction
Geometry correction. Either

`"none"`

or`"Ang"`

. See Details.- ratio
Logical. If

`TRUE`

, the numerator and denominator of the estimate will also be saved, for use in analysing replicated point patterns.

##### Details

This command computes the linear \(K\) function from point pattern data on a linear network.

If `correction="none"`

, the calculations do not include
any correction for the geometry of the linear network. The result is the
network \(K\) function as defined by Okabe and Yamada (2001).

If `correction="Ang"`

, the pair counts are weighted using
Ang's correction (Ang, 2010; Ang et al, 2012).

##### Value

Function value table (object of class `"fv"`

).

##### References

Ang, Q.W. (2010) Statistical methodology for spatial point patterns on a linear network. MSc thesis, University of Western Australia.

Ang, Q.W., Baddeley, A. and Nair, G. (2012)
Geometrically corrected second-order analysis of
events on a linear network, with applications to
ecology and criminology.
*Scandinavian Journal of Statistics* **39**, 591--617.

Okabe, A. and Yamada, I. (2001) The K-function method on a network and
its computational implementation. *Geographical Analysis*
**33**, 271-290.

##### See Also

##### Examples

```
# NOT RUN {
data(simplenet)
X <- rpoislpp(5, simplenet)
linearK(X)
linearK(X, correction="none")
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*