pcfcross(X, i, j, ...)X from which distances are measured.X to which distances are measured.pcf.ppp."fv", see fv.object,
which can be plotted directly using plot.fv.Essentially a data frame containing columns
"border", "bord.modif",
"iso" and/or "trans",
according to the selected edge corrections. These columns contain
estimates of the function $g_{i,j}$
obtained by the edge corrections named.pcf
to multitype point patterns. For two locations $x$ and $y$ separated by a distance $r$,
the probability $p(r)$ of finding a point of type $i$ at location
$x$ and a point of type $j$ at location $y$ is
$$p(r) = \lambda_i \lambda_j g_{i,j}(r) \,{\rm d}x \, {\rm d}y$$
where $\lambda_i$ is the intensity of the points
of type $i$.
For a completely random Poisson marked point process,
$p(r) = \lambda_i \lambda_j$
so $g_{i,j}(r) = 1$.
Indeed for any marked point pattern in which the points of type i
are independent of the points of type j,
the theoretical value of the cross-type pair correlation is
$g_{i,j}(r) = 1$.
For a stationary multitype point process, the cross-type pair correlation
function between marks $i$ and $j$ is formally defined as
$$g_{i,j}(r) = \frac{K_{i,j}^\prime(r)}{2\pi r}$$
where $K_{i,j}^\prime$ is the derivative of
the cross-type $K$ function $K_{i,j}(r)$.
of the point process. See Kest for information
about $K(r)$.
The command pcfcross computes a kernel estimate of
the cross-type pair correlation function between marks $i$ and
$j$. It uses pcf.ppp to compute kernel estimates
of the pair correlation functions for several unmarked point patterns,
and uses the bilinear properties of second moments to obtain the
cross-type pair correlation.
See pcf.ppp for a list of arguments that control
the kernel estimation.
markconnect.data(amacrine)
p <- pcfcross(amacrine, "off", "on")
plot(p)Run the code above in your browser using DataLab