rCauchy
Simulate Neyman-Scott Point Process with Cauchy cluster kernel
Generate a random point pattern, a simulated realisation of the Neyman-Scott process with Cauchy cluster kernel.
Usage
rCauchy(kappa, scale, mu, win = owin(), thresh = 0.001,
nsim=1, drop=TRUE,
saveLambda=FALSE, expand = NULL, ...)
Arguments
- kappa
- Intensity of the Poisson process of cluster centres. A single positive number, a function, or a pixel image.
- scale
- 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
"owin"
or something acceptable toas.owin
. - thresh
- Threshold relative to the cluster kernel value at the origin (parent
location) determining when the cluster kernel will be treated as
zero for simulation purposes. Will be overridden by argument
expand
if that is given. - nsim
- Number of simulated realisations to be generated.
- drop
- Logical. If
nsim=1
anddrop=TRUE
(the default), the result will be a point pattern, rather than a list containing a point pattern. - saveLambda
- Logical. If
TRUE
then the random intensity corresponding to the simulated parent points will also be calculated and saved, and returns as an attribute of the point pattern. - expand
- Numeric. Size of window expansion for generation of parent
points. By default determined by calling
clusterradius
with the numeric threshold value given inthresh
. - ...
- Passed to
clusterfield
to control the image resolution whensaveLambda=TRUE
and toclusterradius
whenexpand
is
Details
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,
maximum composite likelihood or Palm likelihood using
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 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. - The offspring points can be inhomogeneous. If the
argument
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).
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
.
Value
- A point pattern (an object of class
"ppp"
) ifnsim=1
, or a list of point patterns ifnsim > 1
.Additionally, some intermediate results of the simulation are returned as attributes of this point pattern (see
rNeymanScott
). Furthermore, the simulated intensity function is returned as an attribute"Lambda"
, ifsaveLambda=TRUE
.
References
Ghorbani, M. (2013) Cauchy cluster process. Metrika 76, 697-706.
Jalilian, A., Guan, Y. and Waagepetersen, R. (2013) Decomposition of variance for spatial Cox processes. Scandinavian Journal of Statistics 40, 119-137.
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.
See Also
rpoispp
,
rMatClust
,
rThomas
,
rVarGamma
,
rNeymanScott
,
rGaussPoisson
,
kppm
,
clusterfit
.
Examples
# 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)