rVarGamma(kappa, nu.ker, omega, mu, win = owin(),
eps = 0.001, nu.pcf=NULL)
"owin"
or something acceptable to as.owin
."ppp"
). Additionally, some intermediate results of the simulation are
returned as attributes of this point pattern.
See rNeymanScott
.
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 Variance Gamma kernel.
The shape of the kernel is determined by the dimensionless
index nu.ker
. This is the parameter
$\nu^\prime = \alpha/2-1$ appearing in
equation (12) on page 126 of Jalilian et al (2013).
Instead of specifying nu.ker
the user can specify
nu.pcf
which is the parameter $\nu=\alpha-1$
appearing in equation (13), page 127 of Jalilian et al (2013).
These are related by nu.pcf = 2 * nu.ker + 1
and nu.ker = (nu.pcf - 1)/2
.
Exactly one of nu.ker
or nu.pcf
must be specified.
The scale of the kernel is determined by the argument omega
,
which is the parameter
$\eta$ appearing in equations (12) and (13) of
Jalilian et al (2013).
It is expressed in units of length (the same as the unit of length for
the window win
).
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
. It can also be fitted by maximum composite
likelihood using kppm
.
The algorithm can also generate spatially inhomogeneous versions of
the cluster process:
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.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
, or using cauchy.estK
or cauchy.estpcf
applied to the inhomogeneous $K$ function.rpoispp
,
rNeymanScott
,
cauchy.estK
,
cauchy.estpcf
,
kppm
.# homogeneous
X <- rVarGamma(30, 2, 0.02, 5)
# inhomogeneous
Z <- as.im(function(x,y){ exp(2 - 3 * x) }, W= owin())
Y <- rVarGamma(30, 2, 0.02, Z)
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