# 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, ..., from)
##### 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 X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).

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

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}Li. obtained by the edge corrections named.

Kdot, Lcross, Lest

• Ldot
##### Examples
# NOT RUN {
data(amacrine)
L <- Ldot(amacrine, "off")
plot(L)
# }

Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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