# Linhom

##### L-function

Calculates an estimate of the inhomogeneous version of the $L$-function (Besag's transformation of Ripley's $K$-function) for a spatial point pattern.

##### Usage

`Linhom(...)`

##### Arguments

- ...
- Arguments passed to
`Kinhom`

to estimate the inhomogeneous K-function.

##### Details

This command computes an estimate of the inhomogeneous version of the $L$-function for a spatial point pattern

The original $L$-function is a transformation
(proposed by Besag) of Ripley's $K$-function,
$$L(r) = \sqrt{\frac{K(r)}{\pi}}$$
where $K(r)$ is the Ripley $K$-function of a spatially homogeneous
point pattern, estimated by `Kest`

.

The inhomogeneous $L$-function is the corresponding transformation
of the inhomogeneous $K$-function, estimated by `Kinhom`

.
It is appropriate when the point pattern clearly does not have a
homogeneous intensity of points. It was proposed by
Baddeley,

The command `Linhom`

first calls
`Kinhom`

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

For a Poisson point pattern (homogeneous or inhomogeneous), the theoretical value of the inhomogeneous $L$-function is $L(r) = r$. The square root also has the effect of stabilising the variance of the estimator, so that $L$ is more appropriate for use in simulation envelopes and hypothesis tests. }

`"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 $L(r)$ obtained by the edge corrections
named.
*Statistica Neerlandica* **54**, 329--350.
}
`Kest`

,
`Lest`

,
`Kinhom`

,
`pcf`

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*