vargamma.estK(X, startpar=c(kappa=1,eta=1), nu.ker = -1/4, lambda=NULL,
q = 1/4, p = 2, rmin = NULL, rmax = NULL, ...)-1/2.optim
to control the optimisation algorithm. See Details."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. The argument X can be either
[object Object],[object Object]
The algorithm fits the Neyman-Scott Cluster point process
with Variance Gamma kernel to X,
by finding the parameters of the model
which give the closest match between the
theoretical $K$ function of the model
and the observed $K$ function.
For a more detailed explanation of the Method of Minimum Contrast,
see mincontrast.
The Neyman-Scott cluster point process with Variance Gamma
kernel is described in Jalilian et al (2011).
It is a cluster process formed by taking a
pattern of parent points, generated according to a Poisson process
with intensity $\kappa$, and around each parent point,
generating a random number of offspring points, such that the
number of offspring of each parent is a Poisson random variable with mean
$\mu$, and the locations of the offspring points of one parent
have a common distribution described in Jalilian et al (2011).
If the argument lambda is provided, then this is used
as the value of the point process intensity $\lambda$.
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 corresponding model can be simulated using rVarGamma.
The parameter eta appearing in startpar is equivalent to the
scale parameter omega used in rVarGamma.
Homogeneous or inhomogeneous Neyman-Scott/VarGamma models can also be
fitted using the function kppm and the fitted models
can be simulated using simulate.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.
Waagepetersen, R. (2007) An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63, 252--258.
kppm,
vargamma.estpcf,
lgcp.estK,
thomas.estK,
cauchy.estK,
mincontrast,
Kest,
Kmodel. rVarGamma to simulate the model.
<testonly>u <- vargamma.estK(redwood, startpar=c(kappa=15, eta=0.075))</testonly>
if(interactive()) {
u <- vargamma.estK(redwood)
u
plot(u)
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