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")