Lcross
Multitype L-function (cross-type)
Calculates an estimate of the cross-type L-function for a multitype point pattern.
- Keywords
- spatial, nonparametric
Usage
Lcross(X, i, j, ...)Arguments
- X
- The observed point pattern, from which an estimate of the cross-type $L$ function $L_{ij}(r)$ will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
- i
- Number or character string identifying the type (mark value)
of the points in
Xfrom which distances are measured. - j
- Number or character string identifying the type (mark value)
of the points in
Xto which distances are measured. - ...
- Arguments passed to
Kcross.
Details
The cross-type L-function is a transformation of the cross-type K-function,
$$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$
where $K_{ij}(r)$ is the cross-type K-function
from type i to type j.
See Kcross for information
about the cross-type K-function.
The command Lcross first calls
Kcross to compute the estimate of the cross-type K-function,
and then applies the square root transformation.
For a marked point pattern in which the points of type i
are independent of the points of type j,
the theoretical value of the L-function is
$L_{ij}(r) = r$.
The square root also has the effect of stabilising
the variance of the estimator, so that $L_{ij}$ is more appropriate
for use in simulation envelopes and hypothesis tests.
Value
- 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 $L_{ij}$ has been estimated theo the theoretical value $L_{ij}(r) = r$ for a stationary Poisson process - together with columns named
"border","bord.modif","iso"and/or"trans", according to the selected edge corrections. These columns contain estimates of the function $L_{ij}$ obtained by the edge corrections named.
See Also
Examples
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)