localKinhom(X, lambda, ..., correction = "Ripley", verbose = TRUE, rvalue=NULL, sigma = NULL, varcov = NULL) localLinhom(X, lambda, ..., correction = "Ripley", verbose = TRUE, rvalue=NULL, sigma = NULL, varcov = NULL)"ppp").X,
a pixel image (object of class "im") giving the
intensity values at all locations, a fitted point process model
(object of class "ppm") or a function(x,y) which
can be evaluated to give the intensity value at any location.
lambda is present.
Passed to density.ppp if lambda is omitted.
"none", "translate", "Ripley",
"translation", "isotropic" or "best".
Only one correction may be specified.
density.ppp to control
the kernel smoothing procedure for estimating lambda,
if lambda is missing.
rvalue is given, the result is a numeric vector
of length equal to the number of points in the point pattern.If rvalue is absent, the result is
an object of class "fv", see fv.object,
which can be plotted directly using plot.fv.
Essentially a data frame containing columnstogether with columns containing the values of the
neighbourhood density function for each point in the pattern.
Column i corresponds to the ith point.
The last two columns contain the r and theo values.
localKinhom and localLinhom
are inhomogeneous or weighted versions of the
neighbourhood density function implemented in
localK and localL. Given a spatial point pattern X, the
inhomogeneous neighbourhood density function
$L[i](r)$ associated with the $i$th point
in X is computed by
$$
L_i(r) = \sqrt{\frac 1 \pi \sum_j \frac{e_{ij}}{\lambda_j}}
$$
where the sum is over all points $j != i$ that lie
within a distance $r$ of the $i$th point,
$\lambda[j]$ is the estimated intensity of the
point pattern at the point $j$,
and $e[i,j]$ is an edge correction
term (as described in Kest).
The value of $L[i](r)$ can also be interpreted as one
of the summands that contributes to the global estimate of the
inhomogeneous L function (see Linhom).
By default, the function $L[i](r)$ or
$K[i](r)$ is computed for a range of $r$ values
for each point $i$. The results are stored as a function value
table (object of class "fv") with a column of the table
containing the function estimates for each point of the pattern
X.
Alternatively, if the argument rvalue is given, and it is a
single number, then the function will only be computed for this value
of $r$, and the results will be returned as a numeric vector,
with one entry of the vector for each point of the pattern X.
Kinhom,
Linhom,
localK,
localL.
data(ponderosa)
X <- ponderosa
# compute all the local L functions
L <- localLinhom(X)
# plot all the local L functions against r
plot(L, main="local L functions for ponderosa", legend=FALSE)
# plot only the local L function for point number 7
plot(L, iso007 ~ r)
# compute the values of L(r) for r = 12 metres
L12 <- localL(X, rvalue=12)
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