Ldot

0th

Percentile

Multitype L-function (i-to-any)

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

Keywords
spatial, nonparametric
Usage
Ldot(X, i, ..., from)
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

The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).

Arguments passed to Kdot.

from

An alternative way to specify i.

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.

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}Li. obtained by the edge corrections named.

See Also

Kdot, Lcross, Lest

Aliases
  • Ldot
Examples
# NOT RUN {
 data(amacrine)
 L <- Ldot(amacrine, "off")
 plot(L)
# }
Documentation reproduced from package spatstat, version 1.59-0, License: GPL (>= 2)

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