pcfcross.inhom(X, i, j, lambdaI = NULL, lambdaJ = NULL, ..., r = NULL, breaks = NULL, kernel="epanechnikov", bw=NULL, stoyan=0.15, correction = c("isotropic", "Ripley", "translate"), sigma = NULL, varcov = NULL)
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)
.
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)
.
i
.
Either a vector giving the intensity values
at the points of type i
,
a pixel image (object of class "im"
) giving the
intensity values at all locations, or a function(x,y)
which
can be evaluated to give the intensity value at any location.
j
.
A numeric vector, pixel image or function(x,y)
.
density.default
.
density.default
.
density.default
.
density.ppp
to control the smoothing bandwidth, when lambdaI
or
lambdaJ
is estimated by kernel smoothing.
"fv"
).
Essentially a data frame containing the variablesas required.
The best intuitive interpretation is the following: the probability $p(r)$ of finding two points, of types $i$ and $j$ respectively, at locations $x$ and $y$ separated by a distance $r$ is equal to $$ p(r) = \lambda_i(x) lambda_j(y) g(r) \,{\rm d}x \, {\rm d}y $$ where $lambda[i]$ is the intensity function of the process of points of type $i$. For a multitype Poisson point process, this probability is $p(r) = lambda[i](x) * lambda[j](y)$ so $g[i,j](r) = 1$.
The command pcfcross.inhom
estimates the inhomogeneous
pair correlation using a modified version of
the algorithm in pcf.ppp
.
If the arguments lambdaI
and lambdaJ
are missing or
null, they are estimated from X
by kernel smoothing using a
leave-one-out estimator.
pcf.ppp
,
pcfinhom
,
pcfcross
,
pcfdot.inhom
data(amacrine)
plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
legendpos="bottom")
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