# 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
- 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

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)
```

*Documentation reproduced from package spatstat, version 1.25-1, License: GPL (>= 2)*