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 "owin"
or something acceptable to as.owin .
|
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
.
The algorithm can also generate spatially inhomogeneous versions of the Mat'ern cluster process:
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.
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 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@maths.uwa.edu.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
.
# 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)