Pair Correlation Function
Estimate the pair correlation function.
pcf(X, ...)
X |
Either the observed data point pattern, or an estimate of its K function, or an array of multitype K functions (see Details). |
... |
Other arguments passed to the appropriate method. |
The pair correlation function of a stationary point process is
g(r) = K'(r)/ ( 2 * pi * r)
where K'(r) is the derivative of K(r), the
reduced second moment function (aka “Ripley's K function”)
of the point process. See Kest for information
about K(r). For a stationary Poisson process, the
pair correlation function is identically equal to 1. Values
g(r) < 1 suggest inhibition between points;
values greater than 1 suggest clustering.
This routine computes an estimate of g(r) either directly from a point pattern, or indirectly from an estimate of K(r) or one of its variants.
This function is generic, with methods for
the classes "ppp", "fv" and "fasp".
If X is a point pattern (object of class "ppp")
then the pair correlation function is estimated using
a traditional kernel smoothing method (Stoyan and Stoyan, 1994).
See pcf.ppp for details.
If X is a function value array (object of class "fasp"),
then it is assumed to contain estimates of several K functions
(typically obtained from Kmulti or
alltypes). This routine computes
an estimate of g(r) for each cell in the array,
using smoothing splines to approximate the derivatives.
See pcf.fasp for details.
Either a function value table
(object of class "fv", see fv.object)
representing a pair correlation function,
or a function array (object of class "fasp",
see fasp.object)
representing an array of pair correlation functions.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk
Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
# ppp object X <- simdat p <- pcf(X) plot(p) # fv object K <- Kest(X) p2 <- pcf(K, spar=0.8, method="b") plot(p2) # multitype pattern; fasp object amaK <- alltypes(amacrine, "K") amap <- pcf(amaK, spar=1, method="b") plot(amap)
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