spatstat (version 1.23-1)

Lest: L-function

Description

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

Usage

Lest(...)

Arguments

...

Arguments passed to Kest to estimate the $K$-function.

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.

Details

This command computes an estimate of the $L$-function for a spatial point pattern. 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.

References

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

See Also

Kest, pcf

Examples

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