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

`Lest(X, ..., correction)`

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.

- 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()`

.- correction,...
Other arguments passed to

`Kest`

to control the estimation procedure.

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`

.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz

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.

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

`Kest`

,
`pcf`

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

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