rNeymanScott: Simulate Neyman-Scott Process

Description

Generate a random point pattern using the Neyman-Scott cluster process.

Usage

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

Arguments

lambda

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 lambda when lambda is a function or pixel image.

Value

The simulated point pattern (an object of class "ppp").

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 lambda. Here lambda may be a single positive number, a function lambda(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.

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.

Examples

Run this code

nclust <-  function(x0, y0, radius, n) {
                           return(runifdisc(n, radius, x0, y0))
                         }
  X <- rNeymanScott(10, 0.2, nclust, radius=0.2, n=5)