rNeymanScott {spatstat}R Documentation

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, or other data specifying the random cluster mechanism. See Details.

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.

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. These clusters are combined together to yield a single point pattern which is then returned as the result of rNeymanScott.

The argument rcluster specifies the cluster mechanism. It may be either:

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.

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.

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

References

Neyman, J. and Scott, E.L. (1958) A statistical approach to problems of cosmology. Journal of the Royal Statistical Society, Series B 20, 1–43.

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

See Also

rpoispp, rThomas, rGaussPoisson, rMatClust, rCauchy, rVarGamma

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))

[Package spatstat version 1.25-3 Index]