# 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, ...)`

##### 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
- Number or character string identifying the type (mark value)
of the points in
`X`

from which distances are measured. - j
- Number or character string identifying the type (mark value)
of the points in
`X`

to which distances are measured. - ...
- Arguments passed to
`Kcross`

.

##### 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

r the vector of values of the argument $r$ at which the function $L_{ij}$ has been estimated theo the theoretical value $L_{ij}(r) = r$ 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 $L_{ij}$ obtained by the edge corrections named.

##### See Also

##### Examples

```
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)
```

*Documentation reproduced from package spatstat, version 1.19-2, License: GPL (>= 2)*