Jmulti(X, I, J, eps=NULL, r=NULL, breaks=NULL, ..., disjoint=NULL, correction=NULL)X from which distances are
measured. See Details.
X to which distances are measured.
See Details.
Jest). There is a sensible default.
I and J are disjoint.
If missing, this value will be computed by inspecting the
vectors I and J.
"none", "rs", "km",
"Hanisch" and "best".
Alternatively correction="all" selects all options.
"fv" (see fv.object).Essentially a data frame containing six numeric columnsJmulti
generalises Jest (for unmarked point
patterns) and Jdot and Jcross (for
multitype point patterns) to arbitrary marked point patterns.Suppose $X[I]$, $X[J]$ are subsets, possibly overlapping, of a marked point process. Define $$J_{IJ}(r) = \frac{1 - G_{IJ}(r)}{1 - F_J(r)}$$ where $F[J](r)$ is the cumulative distribution function of the distance from a fixed location to the nearest point of $X[J]$, and $GJ(r)$ is the distribution function of the distance from a typical point of $X[I]$ to the nearest distinct point of $X[J]$.
The argument X must be a point pattern (object of class
"ppp") or any data that are acceptable to as.ppp.
The arguments I and J specify two subsets of the
point pattern. 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.
It is assumed that X can be treated
as a realisation of a stationary (spatially homogeneous)
random spatial point process in the plane, observed through
a bounded window.
The window (which is specified in X as Window(X))
may have arbitrary shape.
Biases due to edge effects are
treated in the same manner as in Jest.
The argument r is the vector of values for the
distance $r$ at which $J[IJ](r)$ should be evaluated.
It is also used to determine the breakpoints
(in the sense of hist)
for the computation of histograms of distances. The reduced-sample and
Kaplan-Meier estimators are computed from histogram counts.
In the case of the Kaplan-Meier estimator this introduces a discretisation
error which is controlled by the fineness of the breakpoints.
First-time users would be strongly advised not to specify r.
However, if it is specified, r must satisfy r[1] = 0,
and max(r) must be larger than the radius of the largest disc
contained in the window. Furthermore, the successive entries of r
must be finely spaced.
Jcross,
Jdot,
Jest
trees <- longleaf
# Longleaf Pine data: marks represent diameter
Jm <- Jmulti(trees, marks(trees) <= 15, marks(trees) >= 25)
plot(Jm)
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