# linearpcf

0th

Percentile

##### 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.

linearK, linearpcfinhom, lpp

• linearpcf
##### Examples
data(simplenet)
X <- rpoislpp(5, simplenet)
linearpcf(X)
linearpcf(X, correction="none")
Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)

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