# 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.

##### 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`

`"fv"`

, see `fv.object`

,
which can be plotted directly using `plot.fv`

.

Essentially a data frame containing columns
`"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`

*Documentation reproduced from package spatstat, version 1.14-7, License: GPL (>= 2)*