# 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)`

##### 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

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)
# }
```

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