spatstat (version 1.64-1)

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

# S3 method for ppm
Kmodel(model, …)
   # S3 method for ppm
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 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

# NOT RUN {
  fit <- ppm(swedishpines, ~1, Strauss(8))
  p <- pcfmodel(fit)
  K <- Kmodel(fit)
  p(6)
  K(8)
  curve(K(x), from=0, to=15)
# }