rCauchy {spatstat} | R Documentation |
Generate a random point pattern, a simulated realisation of the Neyman-Scott process with Cauchy cluster kernel.
rCauchy(kappa, omega, mu, win = owin(), eps = 0.001)
kappa |
Intensity of the Poisson process of cluster centres. A single positive number, a function, or a pixel image. |
omega |
Scale parameter for cluster kernel. Determines the size of clusters. A positive number, in the same units as the spatial coordinates. |
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 |
eps |
Threshold below which the values of the cluster kernel will be treated as zero for simulation purposes. |
This algorithm generates a realisation of the Neyman-Scott process
with Cauchy cluster kernel, 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
according to a Cauchy kernel.
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 model can be fitted to data by the method of minimum contrast,
using cauchy.estK
, cauchy.estpcf
or kppm
.
The algorithm can also generate spatially inhomogeneous versions of the 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).
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 cauchy.estK
or cauchy.estpcf
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
.
Abdollah Jalilian and Rasmus Waagepetersen. Adapted for spatstat by Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/
Jalilian, A., Guan, Y. and Waagepetersen, R. (2011) Decomposition of variance for spatial Cox processes. Manuscript submitted for publication.
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252–258.
rpoispp
,
rNeymanScott
,
cauchy.estK
,
cauchy.estpcf
,
kppm
.
# homogeneous X <- rCauchy(30, 0.01, 5) # inhomogeneous Z <- as.im(function(x,y){ exp(2 - 3 * x) }, W= owin()) Y <- rCauchy(50, 0.01, Z)