rThomas
Simulate Thomas Process
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 toas.owin.
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
kappais afunction(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
muis afunction(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 tomu(x,y) * f(x,y)wherefis the Gaussian density centred at the parent point.
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.
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.
References
Waagepetersen, R. (2006) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Submitted for publication.
See Also
rpoispp,
rMatClust,
rGaussPoisson,
rNeymanScott,
thomas.estK,
kppm
Examples
#homogeneous
X <- rThomas(10, 0.2, 5)
#inhomogeneous
Z <- as.im(function(x,y){ 5 * exp(2 * x - 1) }, owin())
Y <- rThomas(10, 0.2, Z)