# 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 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

##### 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)
```

*Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)*