spatstat (version 1.16-1)

# rThomas: Simulate Thomas Process

## Description

Generate a random point pattern, a realisation of the Thomas cluster process.

## Usage

`rThomas(kappa, sigma, mu, win = owin(c(0,1),c(0,1)))`

## Arguments

kappa
Intensity of the Poisson process of cluster centres. A single positive number.
sigma
Standard deviation of displacement of a point from its cluster centre.
mu
Expected number of points per cluster.
win
Window in which to simulate the pattern. An object of class `"owin"` or something acceptable to `as.owin`.

## 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 `rNeymanScott`.

## Details

This algorithm generates a realisation of the Thomas process, a special case of the Neyman-Scott process. The algorithm generates a uniform Poisson point process of ``parent'' points with intensity `kappa`. Then each parent point is replaced by a random cluster of points, the number of points per cluster being Poisson (`mu`) distributed, and their positions being isotropic Gaussian displacements from the cluster parent location.

This classical model can be fitted to data by the method of minimum contrast, using `thomas.estK` or `kppm`. The algorithm can also generate spatially inhomogeneous versions of the Thomas process:

• The parent points can be spatially inhomogeneous. If the argument`kappa`is a`function(x,y)`or a pixel image (object of class`"im"`), then it is taken as specifying the intensity function of an inhomogeneous Poisson process that generates the parent points.
• The offspring points can be inhomogeneous. If the argument`mu`is a`function(x,y)`or a pixel image (object of class`"im"`), then it is interpreted as the reference density for offspring points, in the sense of Waagepetersen (2006). For a given parent point, the offspring constitute a Poisson process with intensity function equal to`mu(x,y) * f(x,y)`where`f`is the Gaussian density centred at the parent point.
When the parents are homogeneous (`kappa` is a single number) and the offspring are inhomogeneous (`mu` is a function or pixel image), the model can be fitted to data using `kppm`, or using `thomas.estK` applied to the inhomogeneous \$K\$ function.

## References

Waagepetersen, R. (2006) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Submitted for publication.

`rpoispp`, `rMatClust`, `rGaussPoisson`, `rNeymanScott`, `thomas.estK`, `kppm`
``````#homogeneous