Generate a Poisson Cluster Process

The function generates a Poisson cluster process for a given polygon within a larger bounding region and given process parameters

pcp.sim(rho, m, s2, region.poly, larger.region=NULL, 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

vectorise.loop

if TRUE, use new vectorised code, if FALSE, use loop as before

Details

The function generates the parents in the larger bounding region, generates their children also in the larger bounding region, and then returns those inside the given polygon.

Value

A point object with the simulated pattern

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.

Author

Giovanni Petris <GPetris@uark.edu>, Roger.Bivand@nhh.no

See also

pcp, Kenv.pcp, 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
#> $par
#>         s2        rho 
#> 6.16109743 0.01136752 
#> 
#> $value
#> [1] 0.02734823
#> 
#> $counts
#> function gradient 
#>       77       NA 
#> 
#> $convergence
#> [1] 0
#> 
#> $message
#> NULL
#> 
m <- npts(as.points(cardiff))/(areapl(cardiff$poly)*pcp.fit$par[2])
sims <- pcp.sim(pcp.fit$par[2], m, pcp.fit$par[1], cardiff$poly)
pointmap(as.points(sims), add=TRUE, col="red")