R: K Function or Pair Correlation Function of Gibbs Point...

Kmodel.ppm {spatstat.core} | R Documentation

## 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 class 'ppm'
    Kmodel(model, ...)

       ## S3 method for class '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.

### 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.

### Value

A `function` in the R language, which takes one argument `r`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Gopalan Nair.

### 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)

[Package spatstat.core version 1.65-5 Index]