Fhat(obj1, obj2, nx=sqrt(n), ny=sqrt(n), dist.fhat=all.dists, plot.it=T)
"spp"
representing a spatial point pattern, or a data frame
or matrix with first two columns containing locations of a point pattern.
"spp"
representing a spatial point pattern,
or a data frame or matrix with first two columns containing the origins
from which the distances to the points in
obj1
are to be computed.
See DETAILS for computation of
Fhat
.
obj2
is missing, a grid of size (
nx
by
ny
) is computed to be used as
set of origins.
Defaults to the square root of the total number of points in
obj1
.
Fhat
values are desired. See DETAILS. By default,
all distances between
obj1
and
obj2
will be used.
TRUE
.
Fhat
was computed.
The second column contains the corresponding
Fhat
values.
plot.it=TRUE
, a plot of
Fhat
versus distance is produced.
Fhat
provides an estimate of
F(y)
,
the proportion of points on a grid (
obj2
) within distance
y
of the nearest point in the original pattern (
obj1
).
For a completely spatially random process without edge effects, the theoretical
distribution of
F(y)
is:
F(y) = 1 - exp(-pi * intensity * y^2)
where the intensity is the number of points per unit area.
If
obj2
is not supplied, an origin grid with dimension (
nx
x
ny
) is
created on the same area as the original data. The distances between each
origin in
obj2
and its nearest neighbor in
obj1
are computed using
find.neighbor
.
Diggle, Peter J. (1983). Statistical Analysis of Spatial Point Patterns. Academic Press, London.
lans.fhat <- Fhat(lansing)