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
kappa
is 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
mu
is 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)
wheref
is 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)