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 $K$ is more appropriate for use in simulation envelopes and hypothesis tests.
See Kest
for the list of arguments.
Value
- An object of class
"fv"
, seefv.object
, which can be plotted directly usingplot.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 $\hat L(r)$ 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
data(cells)
L <- Lest(cells)
plot(L, main="L function for cells")