# Ldot

0th

Percentile

##### 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
Number or character string identifying the type (mark value) of the points in X from which distances are measured.
...
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", see fv.object, which can be plotted directly using plot.fv.

Essentially a data frame containing columns

• rthe vector of values of the argument $r$ at which the function $L_{i\bullet}$ has been estimated
• theothe 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.

Kdot, Lcross, Lest

• Ldot
##### Examples
data(amacrine)
L <- Ldot(amacrine, "off")
plot(L)
Documentation reproduced from package spatstat, version 1.16-3, License: GPL (>= 2)

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