# 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.

- Keywords
- spatial, nonparametric

##### 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, 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

the vector of values of the argument \(r\) at which the function \(L\) has been estimated

the theoretical value \(L(r) = r\) for a stationary Poisson process

##### References

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

##### See Also

##### Examples

```
# NOT RUN {
data(japanesepines)
X <- japanesepines
L <- Linhom(X, sigma=0.1)
plot(L, main="Inhomogeneous L function for Japanese Pines")
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*