Simulate Inhomogeneous Poisson Cluster Process

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Description

Generate a random point pattern, a simulated realisation of the Inhomogeneous Poisson Cluster Process.

Usage

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rIPCP(x, lambda = NULL, type = 1, lmax = NULL, win = owin(c(0, 1), c(0, 1)), ...)

Arguments

x

an object of class 'ecespa.minconfit', resulting from the function ipc.estK.

lambda

Optional. Values of the estimated intensity function as a pixel image (object of class "im" of spatstat) giving the intensity values at all locations.

type

Type of 'prethining' employed in the simulation. See details.

lmax

Optional. Upper bound on the values of lambda.

win

Optional. Window of the simulated pattern.

...

Optional. Arguments passed to as.im.

Details

This function simulates the Inhomogeneous Poisson Cluster process from an object of class 'ecespa.minconfit', resulting from fitting an IPCP to some 'original' point pattern using the function ipc.estK. Following the approach of Waagepetersen (2007), the simulation involves a first step in which an homogeneous aggregated pattern is simulated (from the fitted parameters of the 'ecespa.minconfit' object, using function rThomas of spatstat) and a second one in which the homogeneous pattern is thinned with a spatially varying thinning probability f (s) proportional to the spatially varying intensity, i.e. f (s) = lambda(s) / max[lambda(s)]. To obtain a 'final' density similar to that of the original point pattern, a "prethinning" must be performed. There are two alternatives. If the argument 'type' is set equal to '1', the expected number of points per cluster (mu parameter of rThomas is thinned as mu <- mu.0 / mean[f(s)], where mu.0 is the mean number of points per cluster of the original pattern. This alternative produces point patterns most similar to the 'original'. If the argument 'type' is set equal to '2', the fitted intensity of the Poisson process of cluster centres (kappa parameter of rThomas, i.e. the intensity of 'parent' points) is thinned as kappa <- kappa / mean[f(s)]. This alternative produces patterns more uniform than the 'original' and it is provided only for experimental purposes.

Value

A point pattern, with the format of the ppp objects of spatstat.

Author(s)

Marcelino de la Cruz Rot marcelino.delacruz@upm.es

References

Waagepetersen, R. 2007. An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63:252-258.

See Also

sim.poissonc to simulate homogeneous PCP; rNeymanScott and rThomas in spatstat are the basis of this function

Examples

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  ## Not run: 
  
    data(gypsophylous)
  
    plot(gypsophylous) 
    
    ## It 'seems' that the pattern is clustered, so 
    ## fit a Poisson Cluster Process. The limits of integration 
    ## rmin and rmax are setup to 0 and 60, respectively.
    
   cosa.pc2 <- ipc.estK(gypsophylous, r = seq(0, 60, by=0.2))

   ## Create one instance of the fitted PCP:

   pointp <- rIPCP( cosa.pc2)
   
   plot(pointp)
   
   
   
    #####################
    ## Inhomogeneous example

    data(urkiola)

    # get univariate pp
    I.ppp <- split.ppp(urkiola)$birch

    plot(I.ppp)

    #estimate inhomogeneous intensity function
    I.lam <- predict (ppm(I.ppp, ~polynom(x,y,2)), type="trend", ngrid=200)

    # It seems that there is short scale clustering; lets fit an IPCP: 

    I.ki <- ipc.estK(mippp=I.ppp, lambda=I.lam, correction="trans")

    ## Create one instance of the fitted PCP:

    pointpi <- rIPCP( I.ki)
   
    plot(pointpi)
 
## End(Not run)