pcf.ppp(X, ..., kernel="epanechnikov", bw=NULL, stoyan=0.15,
correction=c("translate", "ripley"))
"ppp"
).density
.density
.density
."fv"
).
Essentially a data frame containing the variablesKest
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 $h/\sqrt{5}$.
Stoyan and Stoyan (1994, page 285) recommend using the Epanechnikov
kernel with support $[-h,h]$ chosen by the rule of thumn
$h = c/\sqrt{\lambda}$,
where bw
is missing, then this rule of thumb will be applied.
The argument stoyan
determines the value of $c$.Kest
,
pcf
,
density