rMatClust {spatstat} | R Documentation |
Generate a random point pattern, a simulated realisation of the Mat\'ern Cluster Process.
rMatClust(kappa, r, mu, win = owin(c(0,1),c(0,1)))
kappa |
Intensity of the Poisson process of cluster centres. A single positive number, a function, or a pixel image. |
r |
Radius parameter of the clusters. |
mu |
Mean number of points per cluster (a single positive number) or reference intensity for the cluster points (a function or a pixel image). |
win |
Window in which to simulate the pattern.
An object of class |
This algorithm generates a realisation of Mat\'ern's cluster process
inside the window 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
or kppm
.
The algorithm can also generate spatially inhomogeneous versions of the Mat\'ern cluster 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 the average value of
mu
inside the disc of radius r
centred on the parent
point, and zero intensity outside this disc.
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 matclust.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
Mat\'ern, B. (1960) Spatial Variation. Meddelanden fraan Statens Skogsforskningsinstitut, volume 59, number 5. Statens Skogsforskningsinstitut, Sweden.
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
,
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)