# Lest

##### L-function

Calculates an estimate of Ripley's L-function for a spatial point pattern.

- Keywords
- spatial, nonparametric

##### Usage

`Lest(...)`

##### Arguments

- ...
- Arguments passed to
`Kest`

to estimate the K-function.

##### Details

This command computes an estimate of the L-function for a spatial point pattern. The L-function is a transformation of Ripley's K-function, $$L(r) = \sqrt{\frac{K(r)}{\pi}}$$ where $K(r)$ is the K-function.

See `Kest`

for information
about Ripley's K-function.

The command `Lest`

first calls
`Kest`

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

For a completely random (uniform Poisson) point pattern, the theoretical value of the 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.

##### See Also

##### Examples

```
data(cells)
L <- Lest(cells)
plot(L, main="L function for cells")
```

*Documentation reproduced from package spatstat, version 1.17-0, License: GPL (>= 2)*