R: Calculate simulation envelope for a Poisson Cluster Process
Kenv.pcp
R Documentation
Calculate simulation envelope for a Poisson Cluster Process
Description
This function computes the envelope of Khat from simulations of a Poisson Cluster Process for a given polygon
Usage
Kenv.pcp(rho, m, s2, region.poly, larger.region=NULL, nsim, r, vectorise.loop=TRUE)
Arguments
rho
intensity of the parent process
m
average number of offsprings per parent
s2
variance of location of offsprings relative to their parent
region.poly
a polygon defining the region in which the process is to be generated
larger.region
a rectangle containing the region of interest given in the form (xl,xu,yl,yu), defaults to sbox() around region.poly
nsim
number of simulations required
r
vector of distances at which the K function has to be estimated
vectorise.loop
if TRUE, use new vectorised code, if FALSE, use loop as before
Value
ave
mean of simulations
upper
upper bound of envelope
lower
lower bound of envelope
Author(s)
Giovanni Petris <GPetris@uark.edu>, Roger.Bivand@nhh.no
References
Diggle, P. J. (1983) Statistical analysis of spatial point
patterns, London: Academic Press, pp. 55-57 and 78-81; Bailey, T. C. and
Gatrell, A. C. (1995) Interactive spatial data analysis, Harlow:
Longman, pp. 106-109.
See Also
pcp, pcp.sim, khat
Examples
data(cardiff)
polymap(cardiff$poly)
pointmap(as.points(cardiff), add=TRUE)
title("Locations of homes of 168 juvenile offenders")
pcp.fit <- pcp(as.points(cardiff), cardiff$poly, h0=30, n.int=30)
pcp.fit
m <- npts(as.points(cardiff))/(areapl(cardiff$poly)*pcp.fit$par[2])
r <- seq(2,30,by=2)
K.env <- Kenv.pcp(pcp.fit$par[2], m, pcp.fit$par[1], cardiff$poly,
nsim=20, r=r)
L.env <- lapply(K.env, FUN=function(x) sqrt(x/pi)-r)
limits <- range(unlist(L.env))
plot(r, sqrt(khat(as.points(cardiff),cardiff$poly,r)/pi)-r, ylim=limits,
main="L function with simulation envelopes and average", type="l",
xlab="distance", ylab="")
lines(r, L.env$lower, lty=5)
lines(r, L.env$upper, lty=5)
lines(r, L.env$ave, lty=6)
abline(h=0)