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:

, .

EXAMPLES:

lans.ghat <- Ghat(lansing)