# linearpcf

##### Linear Pair Correlation Function

Computes an estimate of the linear pair correlation function for a point pattern on a linear network.

- Keywords
- spatial, nonparametric

##### Usage

`linearpcf(X, r=NULL, ..., correction="Ang")`

##### 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.
- ...
- Arguments passed to
`density.default`

to control the smoothing. - correction
- Geometry correction.
Either
`"none"`

or`"Ang"`

. See Details.

##### Details

This command computes the linear pair correlation function from point pattern data on a linear network.

The pair correlation function is estimated from the
shortest-path distances between each pair of data points,
using the fixed-bandwidth kernel smoother
`density.default`

,
with a bias correction at each end of the interval of $r$ values.
To switch off the bias correction, set `endcorrect=FALSE`

.
If `correction="none"`

, the calculations do not include
any correction for the geometry of the linear network. The result is
an estimate of the first derivative of the
network $K$ function defined by Okabe and Yamada (2001).

If `correction="Ang"`

, the pair counts are weighted using
Ang's correction (Ang, 2010). The result is an estimate of the
pair correlation function in the linear network.

##### 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

```
data(simplenet)
X <- rpoislpp(5, simplenet)
linearpcf(X)
linearpcf(X, correction="none")
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*