# Lest

##### L-function

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

- Keywords
- spatial, nonparametric

##### Usage

`Lest(X, ...)`

##### Arguments

##### Details

This command computes an estimate of the \(L\)-function
for the spatial point pattern `X`

.
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 transformation to \(L\) was
proposed by Besag (1977).

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 \(L(r)\) is more appropriate for use in simulation envelopes and hypothesis tests.

See `Kest`

for the list of arguments.

##### 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

##### Variance approximations

If the argument `var.approx=TRUE`

is given, the return value
includes columns `rip`

and `ls`

containing approximations
to the variance of \(\hat L(r)\) under CSR.
These are obtained by the delta method from the variance
approximations described in `Kest`

.

##### References

Besag, J. (1977)
Discussion of Dr Ripley's paper.
*Journal of the Royal Statistical Society, Series B*,
**39**, 193--195.

##### See Also

##### Examples

```
# NOT RUN {
data(cells)
L <- Lest(cells)
plot(L, main="L function for cells")
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*