pcfcross: Multitype pair correlation function (cross-type)

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Multitype pair correlation function (cross-type)

Description

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

Usage

  pcfcross(X, i, j, ...) 

Arguments

X	The observed point pattern, from which an estimate of the cross-type pair correlation function g_{ij}(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).
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).
...	Arguments passed to pcfmulti to control the computation.

Details

The cross-type pair correlation function is a generalisation of the pair correlation function pcf to multitype point patterns.

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

p(r) = \lambda_i \lambda_j g_{i,j}(r) \,{\rm d}x \, {\rm d}y

where \lambda_i is the intensity of the points of type i. For a completely random Poisson marked point process, p(r) = \lambda_i \lambda_j so g_{i,j}(r) = 1. Indeed for any marked point pattern in which the points of type i are independent of the points of type j, the theoretical value of the cross-type pair correlation is g_{i,j}(r) = 1.

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

g_{i,j}(r) = \frac{K_{i,j}^\prime(r)}{2\pi r}

where K_{i,j}^\prime is the derivative of the cross-type K function K_{i,j}(r). of the point process. See Kest for information about K(r).

The command pcfcross computes a kernel estimate of the cross-type pair correlation function between marks i and j.

The companion function pcfdot computes the corresponding analogue of Kdot.

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 g_{i,j} has been estimated
theo	the theoretical value g_{i,j}(r) = 1 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

and \rolf

See Also

Mark connection function markconnect.

Multitype pair correlation pcfdot, pcfmulti.

Pair correlation pcf,pcf.ppp.

Kcross

Examples

 p <- pcfcross(amacrine, "off", "on")
 p <- pcfcross(amacrine, "off", "on", stoyan=0.1)
 plot(p)

spatstat.explore documentation built on March 22, 2026, 5:06 p.m.