localKinhom
Inhomogeneous Neighbourhood Density Function
Computes spatially-weighted versions of the the local $K$-function or $L$-function.
- Keywords
- spatial, nonparametric
Usage
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)
Arguments
- X
- A point pattern (object of class
"ppp"
). - lambda
- Optional.
Values of the estimated intensity function.
Either a vector giving the intensity values
at the points of the pattern
X
, a pixel image (object of class"im"
) giving the intensity values at all locatio - ...
- Extra arguments. Ignored if
lambda
is present. Passed todensity.ppp
iflambda
is omitted. - correction
- String specifying the edge correction to be applied.
Options are
"none"
,"translate"
,"Ripley"
,"translation"
,"isotropic"
or"best"
. Only one correction may be spec - verbose
- Logical flag indicating whether to print progress reports during the calculation.
- rvalue
- Optional. A single value of the distance argument $r$ at which the function L or K should be computed.
- sigma, varcov
- Optional arguments passed to
density.ppp
to control the kernel smoothing procedure for estimatinglambda
, iflambda
is missing.
Details
The functions 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 $j \neq i$ 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 $e_{ij}$ 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
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
.
Value
- If
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"
, seefv.object
, which can be plotted directly usingplot.fv
. Essentially a data frame containing columns r the vector of values of the argument $r$ at which the function $K$ has been estimated theo the theoretical value $K(r) = \pi r^2$ or $L(r)=r$ for a stationary Poisson process - together with columns containing the values of the
neighbourhood density function for each point in the pattern.
Column
i
corresponds to thei
th point. The last two columns contain ther
andtheo
values.
See Also
Examples
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)