rCauchy(kappa, scale, mu, win = owin(), thresh = 0.001, nsim=1, drop=TRUE, saveLambda=FALSE, expand = NULL, ..., poisthresh=1e-6, saveparents=TRUE)"owin"
or something acceptable to as.owin.
expand if that is given.
nsim=1 and drop=TRUE (the default), the
result will be a point pattern, rather than a list
containing a point pattern.
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.
clusterradius with the numeric threshold value given
in thresh.
clusterfield to control the image resolution
when saveLambda=TRUE and to clusterradius when
expand is missing or NULL.
"ppp") if nsim=1,
or a list of point patterns if nsim > 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", if
saveLambda=TRUE.
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:
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).
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.
If the pair correlation function of the model is very close
to that of a Poisson process, deviating by less than
poisthresh, then the model is approximately a Poisson process,
and will be simulated as a Poisson process with intensity
kappa * mu, using rpoispp.
This avoids computations that would otherwise require huge amounts
of memory.
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.
rpoispp,
rMatClust,
rThomas,
rVarGamma,
rNeymanScott,
rGaussPoisson,
kppm,
clusterfit.
# homogeneous
X <- rCauchy(30, 0.01, 5)
# inhomogeneous
ff <- function(x,y){ exp(2 - 3 * abs(x)) }
Z <- as.im(ff, W= owin())
Y <- rCauchy(50, 0.01, Z)
YY <- rCauchy(ff, 0.01, 5)
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