# Lest

0th

Percentile

##### 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
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, $$L(r) = \sqrt{\frac{K(r)}{\pi}}$$ 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 $K$ 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

• rthe vector of values of the argument $r$ at which the function $L$ has been estimated
• theothe 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 $\hat L(r)$ 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.

Kest, pcf

• Lest
##### Examples
data(cells)
L <- Lest(cells)
plot(L, main="L function for cells")
Documentation reproduced from package spatstat, version 1.28-1, License: GPL (>= 2)

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