Inhomogeneous Multitype K Function
Computes spatially-weighted versions of the the local multitype K-function or L-function.
localKcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL,
..., rmax = NULL,
correction = "Ripley", sigma=NULL, varcov=NULL,
lambdaX=NULL, update=TRUE, leaveoneout=TRUE)
localLcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL, ..., rmax = NULL)X |
A point pattern (object of class |
from |
Type of points from which distances should be measured.
A single value;
one of the possible levels of |
to |
Type of points to which distances should be measured.
A single value;
one of the possible levels of |
lambdaFrom,lambdaTo |
Optional.
Values of the estimated intensity function
for the points of type |
... |
Extra arguments. Ignored if |
rmax |
Optional. Maximum desired value of the argument r. |
correction |
String specifying the edge correction to be applied.
Options are |
sigma, varcov |
Optional arguments passed to |
lambdaX |
Optional.
Values of the estimated intensity function
for all points of |
update |
Logical value indicating what to do when |
leaveoneout |
Logical value (passed to |
The functions localKcross.inhom and localLcross.inhom
are inhomogeneous or weighted versions of the
local multitype K and L functions implemented in
localKcross and localLcross.
Given a multitype spatial point pattern X,
and two designated types from and to,
the local multitype K function is
defined for each point X[i] that belongs to type from,
and is computed by
K[i](r) = sqrt( (1/pi) * sum[j] e[i,j]/lambda[j])
where the sum is over all points j != i
of type to 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 function
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 of type from.
The corresponding L function L[i](r) is computed by applying the transformation L(r) = sqrt(K(r)/(2*pi)).
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
of type from.
The last two columns contain the r and theo values.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.
X <- amacrine # compute all the local L functions L <- localLcross.inhom(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)
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