spatstat (version 1.23-1)

Ldot: Multitype L-function (i-to-any)

Description

Calculates an estimate of the multitype L-function (from type i to any type) for a multitype point pattern.

Usage

Ldot(X, i, ...)

Arguments

X

The observed point pattern, from which an estimate of the dot-type $L$ function $L_{ij}(r)$ will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.

i

Number or character string identifying the type (mark value) of the points in X from which distances are measured.

...

Arguments passed to Kdot.

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 $L_{i\bullet}$ has been estimated
• theo
  the theoretical value $L_{i\bullet}(r) = r$ 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 $L_{i\bullet}$ obtained by the edge corrections named.

Details

This command computes $$L_{i\bullet}(r) = \sqrt{\frac{K_{i\bullet}(r)}{\pi}}$$ where $K_{i\bullet}(r)$ is the multitype $K$-function from points of type i to points of any type. See Kdot for information about $K_{i\bullet}(r)$.

The command Ldot first calls Kdot to compute the estimate of the i-to-any $K$-function, and then applies the square root transformation.

For a marked Poisson point process, the theoretical value of the L-function is $L_{i\bullet}(r) = r$. The square root also has the effect of stabilising the variance of the estimator, so that $L_{i\bullet}$ is more appropriate for use in simulation envelopes and hypothesis tests.

See Also

Kdot, Lcross, Lest

Examples

data(amacrine)
 L <- Ldot(amacrine, "off")
 plot(L)