pcfmulti(X, I, J, ..., r = NULL,
kernel = "epanechnikov", bw = NULL, stoyan = 0.15,
correction = c("translate", "Ripley"),
divisor = c("r", "d"),
Iname = "points satisfying condition I",
Jname = "points satisfying condition J")
X
from which distances are measured.X
to which
distances are measured.density.default
.density.default
."r"
(the default) or "d"
.I
and J
."fv"
.pcfcross
to arbitrary collections of points. The algorithm measures the distance from each data point
in subset I
to each data point in subset J
,
excluding identical pairs of points. The distances are
kernel-smoothed and renormalised to form a pair correlation
function.
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.divisor="d"
then a modified estimator is used:
the contribution from
an interpoint distance$d_{ij}$to the
estimate of$g(r)$is divided by$d_{ij}$instead of dividing by$r$. This usually improves the
bias of the estimator when$r$is close to zero. 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 arguments I
and J
specify two subsets of the
point pattern X
. They may be any type of subset indices, for example,
logical vectors of length equal to npoints(X)
,
or integer vectors with entries in the range 1 to
npoints(X)
, or negative integer vectors.
Alternatively, I
and J
may be functions
that will be applied to the point pattern X
to obtain
index vectors. If I
is a function, then evaluating
I(X)
should yield a valid subset index. This option
is useful when generating simulation envelopes using
envelope
.
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 $[-h,h]$,
the argument bw
is equivalent to $h/\sqrt{5}$.
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,
$h = c/\sqrt{\lambda}$,
where $\lambda$ is the (estimated) intensity of the
point process of type j
,
and $c$ is a constant in the range from 0.1 to 0.2.
The argument stoyan
determines the value of $c$.
pcfcross
,
pcfdot
,
pcf.ppp
.adult <- (marks(longleaf) >= 30)
juvenile <- !adult
p <- pcfmulti(longleaf, adult, juvenile)
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