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ve {voronoi}

Voronoi intensity estimation
Package: 
voronoi
Version: 
1.1

Description

Obtain the Voronoi intensity estimate for a point pattern.

Usage

ve(x, rw=NULL, locations=NULL)

Arguments

x
An M-by-2 matrix or data frame representing a point pattern, a deldir object, or a ve object.
rw
An optional vector of length 4 describing the corners of the rectangular space of the data. The values should be in the order of (xmin, xmax, ymin, ymax). The default window is 20 percent larger than the range in each dimension -- 10 percent below and 10 percent above the minimum and maximum. This argument is only utilized when x is a matrix or data frame.
locations
A N-by-2 matrix of locations to identify the Voronoi estimate.

Details

The intensity estimate is the inverse-area of each Voronoi cell.

Values

The output object is of class "", which itself is a list with the following items:

p
A matrix of the points.
z
A vector of the Voronoi estimates at the points.
T
A deldir object for the points.
rw
The rectangular space used for the data in the order of (xmin, xmax, ymin, ymax).
est
A matrix with three columns, where the first two columns represent the argument locations and the third column is the Voronoi estimates at those locations.

References

C.D Barr and F.P Schoenberg. On the Voronoi Estimator for the Intensity of an Inhomogeneous Planar Poisson Process. Biometrika, 1:1-15, 2010.

See Also

centroidal, fd

Examples

#=====> Equivalent Constructions <=====#
x <- rnorm(50, 1)
y <- rnorm(50, 6, 3)
d <- deldir(x, y)
t1 <- ve(cbind(x,y))
t2 <- ve(d)
identical(t1,t2)
par(mfrow=c(1,2))
plot(t1)
plot(t2)
points(t2)
 
#=====> Four Simulated Patterns <=====#
par(mfrow=c(2,2))
 
x  <- rnorm(100)
y  <- rnorm(100)
d1 <- deldir(x,y)
t3 <- ve(d1)
temp <- summary(t3)
plot(temp)
 
p    <- pattern.sim(6.5, type='linear')
t4   <- ve(p, rw=c(0,1,0,1))
st4  <- summary(t4)
plot(st4)
 
p  <- pattern.sim(6.5, type='moon')
t5 <- ve(p, rw=c(0,1,0,1))
plot(t5)
points(t5, cex=0.2)
 
p   <- pattern.sim(6.5, type='ridge')
t6  <- ve(p, rw=c(0,1,0,1))
plot(t6)
points(t6, cex=0.2)

Author(s)

Christopher D. Barr, Travis A. Gerke, David M. Diez

Documentation reproduced from package voronoi, version 1.1. License: GPL-3