Generates a random point pattern, a simulated realisation of the Baddeley-Silverman cell process model.
rcell(win=square(1), nx=NULL, ny=nx, …, dx=NULL, dy=dx, N=10, nsim=1, drop=TRUE)
Number of columns of cells in the window.
Number of rows of cells in the window.
Width of the cells. Incompatible with
Height of the cells.
Integer. Distributional parameter:
the maximum number of random points in each cell.
Number of simulated realisations to be generated.
drop=TRUE (the default), the
result will be a point pattern, rather than a list
containing a point pattern.
A point pattern (an object of class
nsim=1, or a list of point patterns if
nsim > 1.
This function generates a simulated realisation of the “cell process” (Baddeley and Silverman, 1984), a random point process with the same second-order properties as the uniform Poisson process. In particular, the \(K\) function of this process is identical to the \(K\) function of the uniform Poisson process (aka Complete Spatial Randomness). The same holds for the pair correlation function and all other second-order properties. The cell process is a counterexample to the claim that the \(K\) function completely characterises a point pattern.
A cell process is generated by dividing space into equal rectangular tiles. In each tile, a random number of random points is placed. By default, there are either \(0\), \(1\) or \(10\) points, with probabilities \(1/10\), \(8/9\) and \(1/90\) respectively. The points within a tile are independent and uniformly distributed in that tile, and the numbers of points in different tiles are independent random integers.
The tile width is determined
either by the number of columns
nx or by the
The tile height is determined
either by the number of rows
ny or by the
The cell process is then generated in these tiles.
The random numbers of points are generated by
Some of the resulting random points may lie outside the window
if they do, they are deleted.
The result is a point pattern inside the window
Baddeley, A.J. and Silverman, B.W. (1984) A cautionary example on the use of second-order methods for analyzing point patterns. Biometrics 40, 1089-1094.