R: Calculate simulation envelope for a Poisson Cluster Process

Kenv.pcp {splancs} | 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)

[Package splancs version 2.01-40 Index]