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
X
from which distances are measured. - j
- Number or character string identifying the type (mark value)
of the points in
X
to 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)