Envelope of K1hat-K2hat from random labelling of two point patterns

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Description

Compute envelope of K1hat-K2hat from random labelling of two point patterns

Usage

1
Kenv.label(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 labellings 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.

Details

The two point data sets are randomly labelled using rLabel, then Khat is called to estimate the K-function for each resulting set at the distances in s. The difference between these two estimates is then calculated. The maximum and minimum values of this difference at each distance,over the nlab labellings is returned.

Value

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

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: http://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.

See Also

rLabel,ikhat

Examples

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data(okwhite)
data(okblack)
okpoly <- list(x=c(okwhite$x, okblack$x), y=c(okwhite$y, okblack$y))
K1.hat <- khat(as.points(okwhite), bboxx(bbox(as.points(okpoly))), seq(5,80,5))
K2.hat <- khat(as.points(okblack), bboxx(bbox(as.points(okpoly))), seq(5,80,5))
K.diff <- K1.hat-K2.hat
plot(seq(5,80,5), K.diff, xlab="distance", ylab=expression(hat(K)[1]-hat(K)[2]), 
ylim=c(-11000,7000), type="l", main="Simulation envelopes, random labelling")
env.lab <- Kenv.label(as.points(okwhite), as.points(okblack), 
bboxx(bbox(as.points(okpoly))), nsim=29, s=seq(5,80,5))
lines(seq(5,80,5), env.lab$upper, lty=2)
lines(seq(5,80,5), env.lab$lower, lty=2)

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