# pcf.ppp

0th

Percentile

##### Pair Correlation Function of Point Pattern

Estimates the pair correlation function of a point pattern using kernel methods.

##### Usage
pcf.ppp(X, ..., kernel="epanechnikov", bw=NULL, stoyan=0.15,
correction=c("translate", "ripley"))
##### Arguments
X
A point pattern (object of class "ppp").
kernel
Choice of smoothing kernel, passed to density.
bw
Bandwidth for smoothing kernel, passed to density.
...
Other arguments passed to the kernel density estimation function density.
stoyan
Bandwidth coefficient; see Details.
correction
Choice of edge correction.
##### Details

The pair correlation function of a stationary point process is $$g(r) = \frac{K'(r)}{2\pi r}$$ where $K'(r)$ is the derivative of $K(r)$, the reduced second moment function (aka Ripley's $K$ function'') of the point process. See Kest for information about $K(r)$. For a stationary Poisson process, the pair correlation function is identically equal to 1. Values $g(r) < 1$ suggest inhibition between points; values greater than 1 suggest clustering.

This routine computes an estimate of $g(r)$ by the kernel smoothing method (Stoyan and Stoyan (1994), pages 284--285). By default, their recommendations are followed exactly.

If correction="translate" then the translation correction is used. The estimate is given in equation (15.15), page 284 of Stoyan and Stoyan (1994).

If correction="ripley" then Ripley's isotropic edge correction is used; the estimate is given in equation (15.18), page 285 of Stoyan and Stoyan (1994).

If correction=c("translate", "ripley") then both estimates will be computed.

The choice of smoothing kernel is controlled by the argument kernel which is passed to density. The default is the Epanechnikov kernel, recommended by Stoyan and Stoyan (1994, page 285).

The bandwidth of the smoothing kernel can be controlled by the argument bw. Its precise interpretation is explained in the documentation for density. For the Epanechnikov kernel, the argument bw is equivalent to $h/\sqrt{5}$.

• as required.

##### Aliases
• pcf.ppp
Documentation reproduced from package spatstat, version 1.6-5, License: GPL version 2 or newer

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