Kmodel.ppm: K Function or Pair Correlation Function of Gibbs Point Process model
Description
Returns the theoretical $K$ function or the pair correlation function
of a fitted Gibbs point process model.
Usage
"Kmodel"(model, ...)
"pcfmodel"(model, ...)
Arguments
model
A fitted Poisson or Gibbs point process model (object of
class "ppm") typically obtained from
the model-fitting algorithm ppm.
...
Ignored.
Value
A function in the R language,
which takes one argument r.
Details
This function computes an approximation to the $K$ function
or the pair correlation function of a Gibbs point process.
The functions Kmodel and pcfmodel are generic.
The functions documented here are the methods for the class
"ppm".
The approximation is only available for stationary
pairwise-interaction models.
It uses the second order Poisson-saddlepoint approximation
(Baddeley and Nair, 2012b) which is a combination of
the Poisson-Boltzmann-Emden and Percus-Yevick approximations.
The return value is a function in the R language,
which takes one argument r.
Evaluation of this function, on a numeric vector r,
yields values of the desired $K$ function or pair correlation
function at these distance values.
References
Baddeley, A. and Nair, G. (2012a)
Fast approximation of the intensity of Gibbs point processes.
Electronic Journal of Statistics6 1155--1169.
Baddeley, A. and Nair, G. (2012b)
Approximating the moments of a spatial point process.
Stat1, 1, 18--30.
doi: 10.1002/sta4.5
See Also
Kest or pcf
to estimate the $K$ function or pair correlation function
nonparametrically from data.