matclust.estpcf(X, startpar=c(kappa=1,scale=1), lambda=NULL,
q = 1/4, p = 2, rmin = NULL, rmax = NULL, ...,
pcfargs=list())
optim
to control the optimisation algorithm. See Details.pcf.ppp
to control the smoothing in the estimation of the
pair correlation function. The argument X
can be either
[object Object],[object Object]
The algorithm fits the Matern Cluster point process to X
,
by finding the parameters of the Matern Cluster model
which give the closest match between the
theoretical pair correlation function of the Matern Cluster process
and the observed pair correlation function.
For a more detailed explanation of the Method of Minimum Contrast,
see mincontrast
.
The Matern Cluster point process is described in scale
. The named vector of stating values can use
either R
or scale
as the name of the second component,
but the latter is recommended for consistency with other cluster models.
The theoretical pair correlation function of the Matern Cluster process is
$$g(r) = 1 + \frac 1 {4\pi R \kappa r} h(\frac{r}{2R})$$
where the radius R is the parameter scale
and
$$h(z) = \frac {16} \pi [ z \mbox{arccos}(z) - z^2 \sqrt{1 - z^2} ]$$
for $z <= 1$,="" and="" $h(z)="0$" for="" $z=""> 1$.
The theoretical intensity
of the Matern Cluster process
is $\lambda = \kappa \mu$.=>
In this algorithm, the Method of Minimum Contrast is first used to find optimal values of the parameters $\kappa$ and $R$. Then the remaining parameter $\mu$ is inferred from the estimated intensity $\lambda$.
If the argument lambda
is provided, then this is used
as the value of $\lambda$. Otherwise, if X
is a
point pattern, then $\lambda$
will be estimated from X
.
If X
is a summary statistic and lambda
is missing,
then the intensity $\lambda$ cannot be estimated, and
the parameter $\mu$ will be returned as NA
.
The remaining arguments rmin,rmax,q,p
control the
method of minimum contrast; see mincontrast
.
The Matern Cluster process can be simulated, using
rMatClust
.
Homogeneous or inhomogeneous Matern Cluster models can also be
fitted using the function kppm
.
The optimisation algorithm can be controlled through the
additional arguments "..."
which are passed to the
optimisation function optim
. For example,
to constrain the parameter values to a certain range,
use the argument method="L-BFGS-B"
to select an optimisation
algorithm that respects box constraints, and use the arguments
lower
and upper
to specify (vectors of) minimum and
maximum values for each parameter.
}
"minconfit"
. There are methods for printing
and plotting this object. It contains the following main components:
"fv"
)
containing the observed values of the summary statistic
(observed
) and the theoretical values of the summary
statistic computed from the fitted model parameters.
}
Waagepetersen, R. (2007)
An estimating function approach to inference for
inhomogeneous Neyman-Scott processes.
Biometrics 63, 252--258.
}
[object Object]
kppm
,
matclust.estK
,
thomas.estpcf
,
thomas.estK
,
lgcp.estK
,
mincontrast
,
pcf
,
rMatClust
to simulate the fitted model.