Kenv.pcp: Calculate simulation envelope for a Poisson Cluster Process

In splancs: Spatial and Space-Time Point Pattern Analysis

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 <[e-mail]>, [e-mail]

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)

splancs documentation built on May 29, 2024, 6:22 a.m.