pcfdot {spatstat}R Documentation

Multitype pair correlation function (i-to-any)

Description

Calculates an estimate of the multitype pair correlation function (from points of type i to points of any type) for a multitype point pattern.

Usage

  pcfdot(X, i, ...)

Arguments

X

The observed point pattern, from which an estimate of the dot-type pair correlation function gdot[i](r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).

i

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

...

Arguments passed to pcf.ppp.

Details

This is a generalisation of the pair correlation function pcf to multitype point patterns.

For two locations x and y separated by a nonzero distance r, the probability p(r) of finding a point of type i at location x and a point of any type at location y is

p(r) = lambda[i] * lambda * gdot[i](r) dx dy

where lambda is the intensity of all points, and lambda[i] is the intensity of the points of type i. For a completely random Poisson marked point process, p(r) = lambda[i] * lambda so gdot[i](r) = 1.

For a stationary multitype point process, the type-i-to-any-type pair correlation function between marks i and j is formally defined as

g(r) = Kdot[i]'(r)/ ( 2 * pi * r)

where Kdot[i]'(r) is the derivative of the type-i-to-any-type K function Kdot[i](r). of the point process. See Kdot for information about Kdot[i](r).

The command pcfdot computes a kernel estimate of the multitype pair correlation function from points of type i to points of any type. It uses pcf.ppp to compute kernel estimates of the pair correlation functions for several unmarked point patterns, and uses the bilinear properties of second moments to obtain the multitype pair correlation.

See pcf.ppp for a list of arguments that control the kernel estimation.

The companion function pcfcross computes the corresponding analogue of Kcross.

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 gdot[i] has been estimated

theo

the theoretical value gdot[i](r) = r for independent marks.

together with columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function g[i,j] obtained by the edge corrections named.

Author(s)

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

See Also

Mark connection function markconnect.

Multitype pair correlation pcfcross.

Pair correlation pcf,pcf.ppp.

Kdot

Examples

 data(amacrine)
 p <- pcfdot(amacrine, "on")
 p <- pcfdot(amacrine, "on", stoyan=0.1)
 plot(p)

[Package spatstat version 1.25-3 Index]