Ldot {spatstat}R Documentation

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 Lij(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.

Details

This command computes

Li.(r) = sqrt(Ki.(r)/pi)

where Ki.(r) is the multitype K-function from points of type i to points of any type. See Kdot for information about Ki.(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 Li.(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that L_{i\bullet}{Li.} is more appropriate for use in simulation envelopes and hypothesis tests.

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 Li. has been estimated
theo the theoretical value Li.(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 Li. obtained by the edge corrections named.

Author(s)

Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

See Also

Kdot, Lcross, Lest

Examples

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

[Package spatstat version 1.14-0 Index]