# Lcross

##### Multitype L-function (cross-type)

Calculates an estimate of the cross-type L-function for a multitype point pattern.

- Keywords
- spatial, nonparametric

##### Usage

`Lcross(X, i, j, ..., from, to)`

##### Arguments

- X
The observed point pattern, from which an estimate of the cross-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)`

.- j
The type (mark value) of the points in

`X`

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

.- …
Arguments passed to

`Kcross`

.- from,to
An alternative way to specify

`i`

and`j`

respectively.

##### Details

The cross-type L-function is a transformation of the cross-type K-function,
$$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$
where \(K_{ij}(r)\) is the cross-type K-function
from type `i`

to type `j`

.
See `Kcross`

for information
about the cross-type K-function.

The command `Lcross`

first calls
`Kcross`

to compute the estimate of the cross-type K-function,
and then applies the square root transformation.

For a marked point pattern in which the points of type `i`

are independent of the points of type `j`

,
the theoretical value of the L-function is
\(L_{ij}(r) = r\).
The square root also has the effect of stabilising
the variance of the estimator, so that \(L_{ij}\) 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 \(L_{ij}\) has been estimated

the theoretical value \(L_{ij}(r) = r\) for a stationary Poisson process

##### See Also

##### Examples

```
# NOT RUN {
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)
# }
```

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