Envelope of K12hat from random toroidal shifts of two point patterns

Compute envelope of K12hat from random toroidal shifts of two point patterns.

Kenv.tor(pts1,pts2,poly,nsim,s,quiet=FALSE)

Arguments

pts1

First point data set.

pts2

Second point data set.

poly

Polygon containing the points.

nsim

Number of random toroidal shifts to do.

s

Vector of distances at which to calculate the envelope.

quiet

If FALSE, print a message after every simulation for progress monitoring. If true, print no messages.

Value

A list with two components, called $upper and $lower. Each component is a vector like s.

Details

The second point data set is randomly shifted using rtor.shift in the rectangle defined by poly. Then k12hat is called to compute K12hat for the two patterns. The upper and lower values of K12hat over the ntor toroidal shifts are returned.

See also

rtor.shift,k12hat

References

Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: https://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.

Examples

data(okwhite)
data(okblack)
okpoly <- list(x=c(okwhite$x, okblack$x), y=c(okwhite$y, okblack$y))
plot(seq(5,80,5), sqrt(k12hat(as.points(okwhite), as.points(okblack), 
bboxx(bbox(as.points(okpoly))), seq(5,80,5))/pi) - seq(5,80,5), xlab="distance", 
ylab=expression(hat(L)[12]), ylim=c(-35,35), type="l",
main="Simulation envelopes, random toroidal shifts")
env.ok <- Kenv.tor(as.points(okwhite), as.points(okblack), 
bboxx(bbox(as.points(okpoly))), nsim=29, s=seq(5,80,5))
#> Doing shift  1 / 29 
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#> Doing shift  29 / 29 
lines(seq(5,80,5), sqrt(env.ok$upper/pi)-seq(5,80,5), lty=2)
lines(seq(5,80,5), sqrt(env.ok$lower/pi)-seq(5,80,5), lty=2)