Ldot
Multitype L-function (i-to-any)
Calculates an estimate of the multitype L-function
(from type i to any type)
for a multitype point pattern.
- Keywords
- spatial, nonparametric
Usage
Ldot(X, i, ...)Arguments
- X
- The observed point pattern, from which an estimate of the dot-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
- The type (mark value)
of the points in
Xfrom which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level ofmarks(X). - ...
- Arguments passed to
Kdot.
Details
This command computes
$$L_{i\bullet}(r) = \sqrt{\frac{K_{i\bullet}(r)}{\pi}}$$
where $K_{i\bullet}(r)$ is the multitype $K$-function
from points of type i to points of any type.
See Kdot for information
about $K_{i\bullet}(r)$.
The command Ldot first calls
Kdot to compute the estimate of the i-to-any
$K$-function, and then applies the square root transformation.
For a marked Poisson point process, the theoretical value of the L-function is $L_{i\bullet}(r) = r$. The square root also has the effect of stabilising the variance of the estimator, so that $L_{i\bullet}$ 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 $L_{i\bullet}$ has been estimated theo the theoretical value $L_{i\bullet}(r) = r$ 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 $L_{i\bullet}$ obtained by the edge corrections named.
See Also
Examples
data(amacrine)
L <- Ldot(amacrine, "off")
plot(L)