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

## Description

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

## Usage

 `1` ``` Lest(X, ...) ```

## Arguments

 `X` The observed point pattern, from which an estimate of L(r) will be computed. An object of class `"ppp"`, or data in any format acceptable to `as.ppp()`. `...` Other arguments passed to `Kest` to control the estimation procedure.

## 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(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

 `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.

## Variance approximations

If the argument `var.approx=TRUE` is given, the return value includes columns `rip` and `ls` containing approximations to the variance of Lest(r) under CSR. These are obtained by the delta method from the variance approximations described in `Kest`.

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## References

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

`Kest`, `pcf`

## Examples

 ```1 2 3``` ``` data(cells) L <- Lest(cells) plot(L, main="L function for cells") ```

### Example output

```Loading required package: nlme