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. We also apply the same definition to
other variants of the classical $K$ function,
such as the multitype $K$ functions
(see Kcross, Kdot) and the
inhomogeneous $K$ function (see Kinhom).
For all these variants, the benchmark value of
$K(r) = \pi r^2$ corresponds to
$g(r) = 1$.
This routine computes an estimate of $g(r)$
either directly from a point pattern,
or indirectly from an estimate of $K(r)$ or one of its variants.
This function is generic, with methods for
the classes "ppp", "fv" and "fasp".
If X is a point pattern (object of class "ppp")
then the pair correlation function is estimated using
a traditional kernel smoothing method (Stoyan and Stoyan, 1994).
See pcf.ppp for details.
If X is a function value table (object of class "fv"),
then it is assumed to contain estimates of the $K$ function
or one of its variants (typically obtained from Kest or
Kinhom).
This routine computes an estimate of $g(r)$
using smoothing splines to approximate the derivative.
See pcf.fv for details.
If X is a function value array (object of class "fasp"),
then it is assumed to contain estimates of several $K$ functions
(typically obtained from Kmulti or
alltypes). This routine computes
an estimate of $g(r)$ for each cell in the array,
using smoothing splines to approximate the derivatives.
See pcf.fasp for details.