Envelope of Khat from simulations of complete spatial randomness

Compute envelope of Khat from simulations of complete spatial randomness.

Kenv.csr(nptg,poly,nsim,s,quiet=FALSE)

Arguments

nptg

Number of points to generate in each simulation.

poly

Polygon in which to generate the points.

nsim

Number of simulations 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. The two components contain the upper and lower bound of the Khat envelope.

See also

csr, khat

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(cardiff)
UL.khat <- Kenv.csr(length(cardiff$x), cardiff$poly, nsim=29, seq(2,30,2))
#> Doing simulation  1 
#> Doing simulation  2 
#> Doing simulation  3 
#> Doing simulation  4 
#> Doing simulation  5 
#> Doing simulation  6 
#> Doing simulation  7 
#> Doing simulation  8 
#> Doing simulation  9 
#> Doing simulation  10 
#> Doing simulation  11 
#> Doing simulation  12 
#> Doing simulation  13 
#> Doing simulation  14 
#> Doing simulation  15 
#> Doing simulation  16 
#> Doing simulation  17 
#> Doing simulation  18 
#> Doing simulation  19 
#> Doing simulation  20 
#> Doing simulation  21 
#> Doing simulation  22 
#> Doing simulation  23 
#> Doing simulation  24 
#> Doing simulation  25 
#> Doing simulation  26 
#> Doing simulation  27 
#> Doing simulation  28 
#> Doing simulation  29 
plot(seq(2,30,2), sqrt(khat(as.points(cardiff), cardiff$poly, 
seq(2,30,2))/pi)-seq(2,30,2), type="l", xlab="Splancs - polygon boundary", 
ylab="Estimated L", ylim=c(-1,1.5))
lines(seq(2,30,2), sqrt(UL.khat$upper/pi)-seq(2,30,2), lty=2)
lines(seq(2,30,2), sqrt(UL.khat$lower/pi)-seq(2,30,2), lty=2)