Multitype L-function (cross-type)
Calculates an estimate of the cross-type L-function for a multitype point pattern.
Lcross(X, i, j, ..., from, to, correction)
X |
The observed point pattern, from which an estimate of the cross-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 |
The type (mark value)
of the points in |
j |
The type (mark value)
of the points in |
correction,... |
Arguments passed to |
from,to |
An alternative way to specify |
The cross-type L-function is a transformation of the cross-type K-function,
Lij(r) = sqrt(Kij(r)/pi)
where Kij(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
Lij(r) = r.
The square root also has the effect of stabilising
the variance of the estimator, so that Lij is more appropriate
for use in simulation envelopes and hypothesis tests.
Essentially a data frame containing columns
r |
the vector of values of the argument r at which the function Lij has been estimated |
theo |
the theoretical value Lij(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 Lij obtained by the edge corrections
named.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
data(amacrine) L <- Lcross(amacrine, "off", "on") plot(L)
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