# Kmodel.ppm

0th

Percentile

##### 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.

Keywords
models, spatial
##### 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 algorithm ppm.
...
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 function in the Rlanguage, which takes one argument r.

##### 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

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.

• Kmodel.ppm
• pcfmodel.ppm
##### Examples
fit <- ppm(swedishpines, ~1, Strauss(8))
p <- pcfmodel(fit)
K <- Kmodel(fit)
p(6)
K(8)
curve(K(x), from=0, to=15)
Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)

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