Computes and plots the empirical distribution function (EDF) of the
point-to-point nearest neighbor distances for a spatial point pattern.
USAGE:
Ghat(object, dist.ghat=all.dists, plot.it=T)
REQUIRED ARGUMENTS:
object:
an object of class "spp" representing a spatial point pattern,
or a data frame or matrix with first two columns containing locations
of a point pattern.
OPTIONAL ARGUMENTS:
dist.ghat:
a numeric vector containing the distances for which Ghat will be computed.
Default is to compute Ghat at every neighbor distance.
See DETAILS for definition of Ghat.
plot.it:
logical flag: should the resulting EDF be plotted? Defaults to TRUE.
VALUE:
a matrix with two columns containing the neighbor distances and corresponding
values for the EDF.
SIDE EFFECTS:
if plot.it=TRUE, a plot of Ghat versus distance of will be produced.
DETAILS:
Ghat provides an estimate of G(y), the proportion of points in a spatial
point pattern within a distance y of their nearest neighbor.
For a completely spatially random process without edge effects the theoretical distribution of G(y) is:
G(y) = 1 - exp(-pi * intensity * y^2).
where the intensity is the number of points per unit area.
REFERENCES:
Diggle, Peter J. (1983).
Statistical Analysis of Spatial Point Patterns.
Academic Press, London.