pcfdot {spatstat} | R Documentation |
Calculates an estimate of the multitype pair correlation function
(from points of type i
to points of any type)
for a multitype point pattern.
pcfdot(X, i, ...)
X |
The observed point pattern, from which an estimate of the dot-type pair correlation function gdot[i](r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). |
i |
Number or character string identifying the type (mark value)
of the points in |
... |
Arguments passed to |
This is a generalisation of the pair correlation function 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 * gdot[i](r) dx dy
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 gdot[i](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(r) = Kdot[i]'(r)/ ( 2 * pi * r)
where Kdot[i]'(r) is the derivative of
the type-i
-to-any-type K function
Kdot[i](r).
of the point process. See Kdot
for information
about Kdot[i](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
.
An object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
Essentially a data frame containing columns
r |
the vector of values of the argument r at which the function gdot[i] has been estimated |
theo |
the theoretical value gdot[i](r) = r for independent marks. |
together with columns named
"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.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Mark connection function markconnect
.
Multitype pair correlation pcfcross
.
data(amacrine) p <- pcfdot(amacrine, "on") p <- pcfdot(amacrine, "on", stoyan=0.1) plot(p)