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, ..., from, correction)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).- correction,…
Arguments passed to
Kdot.- from
An alternative way to specify
i.
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", see fv.object,
which can be plotted directly using plot.fv.
Essentially a data frame containing columns
the vector of values of the argument \(r\) at which the function \(L_{i\bullet}\) has been estimated
the theoretical value \(L_{i\bullet}(r) = r\) for a stationary Poisson process
See Also
Examples
# NOT RUN {
data(amacrine)
L <- Ldot(amacrine, "off")
plot(L)
# }