# 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", 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.

- …
Arguments passed to

`density.default`

to control the smoothing.- correction
Geometry correction. Either

`"none"`

or`"Ang"`

. See Details.- ratio
Logical. If

`TRUE`

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

##### 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`

.

The bandwidth for smoothing the pairwise distances
is determined by arguments `…`

passed to `density.default`

, mainly the arguments
`bw`

and `adjust`

. The default is
to choose the bandwidth by Silverman's rule of thumb
`bw="nrd0"`

explained in `density.default`

.

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"`

).

If `ratio=TRUE`

then the return value also has two
attributes called `"numerator"`

and `"denominator"`

which are `"fv"`

objects
containing the numerators and denominators of each
estimate of \(g(r)\).

##### 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)
linearpcf(X)
linearpcf(X, correction="none")
# }
```

*Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)*