EDF of Point-to-Point Nearest Neighbor Distances

DESCRIPTION:
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.

SEE ALSO:
Fhat , find.neighbor .

EXAMPLES:
lans.ghat <- Ghat(lansing)