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Calculates an estimate of the cross-type pair correlation function for a multitype point pattern.
pcfcross(X, i, j, ...,
r = NULL,
kernel = "epanechnikov", bw = NULL, stoyan = 0.15,
correction = c("isotropic", "Ripley", "translate"),
divisor = c("r", "d"))
The observed point pattern,
from which an estimate of the cross-type pair correlation function
The type (mark value)
of the points in X
from which distances are measured.
A character string (or something that will be converted to a
character string).
Defaults to the first level of marks(X)
.
The type (mark value)
of the points in X
to which distances are measured.
A character string (or something that will be
converted to a character string).
Defaults to the second level of marks(X)
.
Ignored.
Vector of values for the argument
Choice of smoothing kernel,
passed to density.default
.
Bandwidth for smoothing kernel,
passed to density.default
.
Coefficient for default bandwidth rule; see Details.
Choice of edge correction.
Choice of divisor in the estimation formula:
either "r"
(the default) or "d"
. See Details.
An object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
Essentially a data frame containing columns
the vector of values of the argument
the theoretical value
The cross-type pair correlation function
is a generalisation of the pair correlation function pcf
to multitype point patterns.
For two locations i
are independent of the points of type j
,
the theoretical value of the cross-type pair correlation is
For a stationary multitype point process, the cross-type pair correlation
function between marks Kest
for information
about
The command pcfcross
computes a kernel estimate of
the cross-type pair correlation function between marks
If divisor="r"
(the default), then the multitype
counterpart of the standard
kernel estimator (Stoyan and Stoyan, 1994, pages 284--285)
is used. By default, the recommendations of Stoyan and Stoyan (1994)
are followed exactly.
If divisor="d"
then a modified estimator is used:
the contribution from
an interpoint distance
There is also a choice of spatial edge corrections
(which are needed to avoid bias due to edge effects
associated with the boundary of the spatial window):
correction="translate"
is the Ohser-Stoyan translation
correction, and correction="isotropic"
or "Ripley"
is Ripley's isotropic correction.
The choice of smoothing kernel is controlled by the
argument kernel
which is passed to density
.
The default is the Epanechnikov kernel.
The bandwidth of the smoothing kernel can be controlled by the
argument bw
. Its precise interpretation
is explained in the documentation for density.default
.
For the Epanechnikov kernel with support bw
is equivalent to
If bw
is not specified, the default bandwidth
is determined by Stoyan's rule of thumb (Stoyan and Stoyan, 1994, page
285) applied to the points of type j
. That is,
j
,
and stoyan
determines the value of
The companion function pcfdot
computes the
corresponding analogue of Kdot
.
Mark connection function markconnect
.
# NOT RUN {
data(amacrine)
p <- pcfcross(amacrine, "off", "on")
p <- pcfcross(amacrine, "off", "on", stoyan=0.1)
plot(p)
# }
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