rMatClust(kappa, r, mu, win = owin(c(0,1),c(0,1)))"owin"
or something acceptable to as.owin."ppp"). Additionally, some intermediate results of the simulation are
returned as attributes of this point pattern.
See rNeymanScott.
win. In the simplest case, where kappa and mu
are single numbers, the algorithm
generates a uniform Poisson point process of kappa. Then each parent point is
replaced by a random cluster of mu)
distributed, and their
positions being placed and uniformly inside
a disc of radius r centred on the parent point.
The resulting point pattern
is a realisation of the classical
win.
This point process has intensity kappa * mu.
The algorithm can also generate spatially inhomogeneous versions of
the
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.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 (2007).
For a given parent point, the offspring constitute a Poisson process
with intensity function equal tomu/(pi * r^2)inside the disc of radiusrcentred on the parent
point, and zero intensity outside this disc.
Equivalently we first generate,
for each parent point, a Poisson ($M$) random number of
offspring (where$M$is the maximum value ofmu)
placed independently and uniformly in the disc of radiusrcentred on the parent location, and then randomly thin the
offspring points, with retention probabilitymu/M. Note that if kappa is a pixel image, its domain must be larger
than the window win. This is because an offspring point inside
win could have its parent point lying outside win.
In order to allow this, the simulation algorithm
first expands the original window win
by a distance r and generates the Poisson process of
parent points on this larger window. If kappa is a pixel image,
its domain must contain this larger window.
The intensity of the kappa * mu
if either kappa or mu is a single number. In the general
case the intensity is an integral involving kappa, mu
and r.
The kappa is a single number)
can be fitted to data using kppm or related functions.
Currently it is not possible to fit the
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.
rpoispp,
rThomas,
rGaussPoisson,
rNeymanScott,
matclust.estK,
matclust.estpcf,
kppm.# homogeneous
X <- rMatClust(10, 0.05, 4)
# inhomogeneous
Z <- as.im(function(x,y){ 4 * exp(2 * x - 1) }, owin())
Y <- rMatClust(10, 0.05, Z)Run the code above in your browser using DataLab