spatstat (version 1.16-2)

rNeymanScott: Simulate Neyman-Scott Process

Description

Generate a random point pattern, a realisation of the Neyman-Scott cluster process.

Usage

rNeymanScott(kappa, rmax, rcluster, win = owin(c(0,1),c(0,1)), ..., lmax=NULL)

Arguments

kappa

Intensity of the Poisson process of cluster centres. A single positive number, a function, or a pixel image.

rmax

Maximum radius of a random cluster.

rcluster

A function which generates random clusters.

win

Window in which to simulate the pattern. An object of class "owin" or something acceptable to as.owin.

...

Arguments passed to rcluster

lmax

Optional. Upper bound on the values of kappa when kappa is a function or pixel image.

Value

• The simulated point pattern (an object of class "ppp"). Additionally, some intermediate results of the simulation are returned as attributes of this point pattern: see Details.

Details

This algorithm generates a realisation of the general Neyman-Scott process, with the cluster mechanism given by the function rcluster. The clusters must have a finite maximum possible radius rmax.

First, the algorithm generates a Poisson point process of ``parent'' points with intensity kappa. Here kappa may be a single positive number, a function kappa(x, y), or a pixel image object of class "im" (see im.object). See rpoispp for details. Second, each parent point is replaced by a random cluster of points, created by calling the function rcluster. These clusters are combined together to yield a single point pattern which is then returned as the result of rNeymanScott.

The function rcluster should expect to be called as rcluster(xp[i],yp[i],...) for each parent point at a location (xp[i],yp[i]). The return value of rcluster should be a list with elements x,y which are vectors of equal length giving the absolute $x$ and y coordinates of the points in the cluster.

If the return value of rcluster is a point pattern (object of class "ppp") then it may have marks. The result of rNeymanScott will then be a marked point pattern.

If required, the intermediate stages of the simulation (the parents and the individual clusters) can also be extracted from the return value of rNeymanScott through the attributes "parents" and "parentid". The attribute "parents" is the point pattern of parent points. The attribute "parentid" is an integer vector specifying the parent for each of the points in the simulated pattern.

See Also

rpoispp, rThomas, rGaussPoisson, rMatClust

Examples

# each cluster consist of 10 points in a disc of radius 0.2
  nclust <- function(x0, y0, radius, n) {
              return(runifdisc(n, radius, centre=c(x0, y0)))
            }
  plot(rNeymanScott(10, 0.2, nclust, radius=0.2, n=5))

  # multitype Neyman-Scott process (each cluster is a multitype process)
  nclust2 <- function(x0, y0, radius, n, types=c("a", "b")) {
     X <- runifdisc(n, radius, centre=c(x0, y0))
     M <- sample(types, n, replace=TRUE)
     marks(X) <- M
     return(X)
  }
  plot(rNeymanScott(15,0.1,nclust2, radius=0.1, n=5))