rThomas {spatstat} | R Documentation |
Generate a random point pattern, a realisation of the Thomas cluster process.
rThomas(kappa, sigma, mu, win = owin(c(0,1),c(0,1)))
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 |
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.
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
.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
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 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)