Inhomogeneous Neighbourhood Density Function
Computes spatially-weighted versions of the the local K-function or L-function.
localKinhom(X, lambda, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL,
sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)
localLinhom(X, lambda, ..., rmax = NULL,
correction = "Ripley", verbose = TRUE, rvalue=NULL,
sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)X |
A point pattern (object of class |
lambda |
Optional.
Values of the estimated intensity function.
Either a vector giving the intensity values
at the points of the pattern |
... |
Extra arguments. Ignored if |
rmax |
Optional. Maximum desired value of the argument r. |
correction |
String specifying the edge correction to be applied.
Options are |
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 |
leaveoneout |
Logical value (passed to |
update |
Logical value indicating what to do when |
Given a spatial point pattern X, the
inhomogeneous neighbourhood density function
L[i](r) associated with the ith point
in X is computed by
L[i](r) = sqrt( (1/pi) * sum[j] e[i,j]/lambda[j])
where the sum is over all points j != i that lie
within a distance r of the ith point,
λ[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.
If rvalue is given, the result is a numeric vector
of length equal to the number of points in the point pattern.
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 the ith point.
The last two columns contain the r and theo values.
Mike Kuhn, Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
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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