Kmodel.ppm
K Function or Pair Correlation Function of Gibbs Point Process model
Returns the theoretical $K$ function or the pair correlation function of a fitted Gibbs point process model.
Usage
## S3 method for class 'ppm':
Kmodel(model, \dots) ## S3 method for class 'ppm':
pcfmodel(model, \dots)
Arguments
- model
- A fitted Poisson or Gibbs point process model (object of
class
"ppm") typically obtained from the model-fitting algorithmppm. - ...
- Ignored.
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 Rlanguage,
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.
Value
- A
functionin the Rlanguage, which takes one argumentr.
References
Baddeley, A. and Nair, G. (2012a) Fast approximation of the intensity of Gibbs point processes. Electronic Journal of Statistics 6 1155--1169. Baddeley, A. and Nair, G. (2012b) Approximating the moments of a spatial point process. Stat 1, 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.
ppm to fit Gibbs models.
Kmodel for the generic functions.
Kmodel.kppm for the method for cluster/Cox processes.
Examples
fit <- ppm(swedishpines, ~1, Strauss(8))
p <- pcfmodel(fit)
K <- Kmodel(fit)
p(6)
K(8)
curve(K(x), from=0, to=15)