# Linhom: L-function In spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

## Description

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

 `1` ``` 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(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, Moller and Waagepetersen (2000).

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.

## 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 has been estimated `theo` the theoretical value L(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(r) obtained by the edge corrections named.

and \rolf

## References

Baddeley, A., Moller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329–350.

`Kest`, `Lest`, `Kinhom`, `pcf`

## Examples

 ```1 2 3 4``` ``` data(japanesepines) X <- japanesepines L <- Linhom(X, sigma=0.1) plot(L, main="Inhomogeneous L function for Japanese Pines") ```

### Example output

```Loading required package: nlme