i to points of any type)
for a multitype point pattern.pcfdot(X, i, ...)X from 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 nonzero
distance $r$,
the probability $p(r)$ of finding a point of type $i$ at location
$x$ and a point of any type at location $y$ is
$$p(r) = \lambda_i \lambda g_{i\bullet}(r) \,{\rm d}x \, {\rm d}y$$
where $\lambda$ is the intensity of all points,
and $\lambda_i$ is the intensity of the points
of type $i$.
For a completely random Poisson marked point process,
$p(r) = \lambda_i \lambda$
so $g_{i\bullet}(r) = 1$.
For a stationary multitype point process, the
type-i-to-any-type pair correlation
function between marks $i$ and $j$ is formally defined as
$$g_{i\bullet}(r) = \frac{K_{i\bullet}^\prime(r)}{2\pi r}$$
where $K_{i\bullet}^\prime$ is the derivative of
the type-i-to-any-type $K$ function
$K_{i\bullet}(r)$.
of the point process. See Kdot for information
about $K_{i\bullet}(r)$.
The command pcfdot computes a kernel estimate of
the multitype pair correlation function from points of type $i$
to points of any type.
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
multitype pair correlation.
See pcf.ppp for a list of arguments that control
the kernel estimation.
The companion function pcfcross computes the
corresponding analogue of Kcross.
markconnect. Multitype pair correlation pcfcross.
Pair correlation pcf,pcf.ppp.
Kdot
data(amacrine)
p <- pcfdot(amacrine, "on")
p <- pcfdot(amacrine, "on", stoyan=0.1)
plot(p)Run the code above in your browser using DataLab