# Lcross

0th

Percentile

##### Multitype L-function (cross-type)

Calculates an estimate of the cross-type L-function for a multitype point pattern.

Keywords
spatial, nonparametric
##### Usage
Lcross(X, i, j, ..., from, to, correction)
##### Arguments
X

The observed point pattern, from which an estimate of the cross-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).

j

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

correction,…

Arguments passed to Kcross.

from,to

An alternative way to specify i and j respectively.

##### Details

The cross-type L-function is a transformation of the cross-type K-function, $$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$ where $$K_{ij}(r)$$ is the cross-type K-function from type i to type j. See Kcross for information about the cross-type K-function.

The command Lcross first calls Kcross to compute the estimate of the cross-type K-function, and then applies the square root transformation.

For a marked point pattern in which the points of type i are independent of the points of type j, the theoretical value of the L-function is $$L_{ij}(r) = r$$. The square root also has the effect of stabilising the variance of the estimator, so that $$L_{ij}$$ 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 $$L_{ij}$$ has been estimated

theo

the theoretical value $$L_{ij}(r) = r$$ 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_{ij}Lij obtained by the edge corrections named.

Kcross, Ldot, Lest

• Lcross
##### Examples
# NOT RUN {
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)
# }

Documentation reproduced from package spatstat, version 1.62-2, License: GPL (>= 2)

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