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
. The process is constructed by first
generating a 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 in each
cluster being random with a Poisson (mu
) distribution,
and the points being placed independently and uniformly inside
a disc of radius r
centred on the parent point.In this implementation, parent points are not restricted to lie in the window; the parent process is effectively the uniform Poisson process on the infinite plane.
This classical model can be fitted to data by the method of minimum contrast,
using matclust.estK
.
The algorithm can also generate spatially inhomogeneous versions of
the Mat'ern cluster process:
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.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 to theaveragevalue ofmu
inside the disc of radiusr
centred on the parent
point, and zero intensity outside this disc.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 matclust.estK
applied to the inhomogeneous
$K$ function.Mat'ern, B. (1986) Spatial Variation. Lecture Notes in Statistics 36, Springer-Verlag, New York.
Waagepetersen, R. (2006) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Submitted for publication.
rpoispp
,
rThomas
,
rGaussPoisson
,
rNeymanScott
,
matclust.estK
.# 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 DataCamp Workspace