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localK(X, ..., correction = "Ripley", verbose = TRUE, rvalue=NULL)
localL(X, ..., correction = "Ripley", verbose = TRUE, rvalue=NULL)
"ppp"
)."none"
, "translate"
, "Ripley"
,
"isotropic"
or "best"
.
Only one correction may be specified.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 columns
i
corresponds to the i
th point.
The last two columns contain the r
and theo
values.localL
computes the neighbourhood density function,
a local version of the $L$-function (Besag's transformation of Ripley's
$K$-function) that was proposed by Getis and Franklin (1987).
The command localK
computes the corresponding
local analogue of the K-function. Given a spatial point pattern X
, the neighbourhood density function
$L_i(r)$ associated with the $i$th point
in X
is computed by
X
, and $e_{ij}$ 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 L
function.
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
.
Inhomogeneous counterparts of localK
and localL
are computed by localKinhom
and localLinhom
.
Kest
,
Lest
,
localKinhom
,
localLinhom
.data(ponderosa)
X <- ponderosa
# compute all the local L functions
L <- localL(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)
# Spatially interpolate the values of L12
# Compare Figure 5(b) of Getis and Franklin (1987)
X12 <- X %mark% L12
Z <- smooth.ppp(X12, sigma=5, dimyx=128)
plot(Z, col=topo.colors(128), main="smoothed neighbourhood density")
contour(Z, add=TRUE)
points(X, pch=16, cex=0.5)
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