# rPenttinen

##### Perfect Simulation of the Penttinen Process

Generate a random pattern of points, a simulated realisation of the Penttinen process, using a perfect simulation algorithm.

##### Usage

`rPenttinen(beta, gamma=1, R, W = owin(), expand=TRUE, nsim=1, drop=TRUE)`

##### Arguments

- beta
- intensity parameter (a positive number).
- gamma
- Interaction strength parameter (a number between 0 and 1).
- R
- disc radius (a non-negative number).
- W
- window (object of class
`"owin"`

) in which to generate the random pattern. - expand
- Logical. If
`FALSE`

, simulation is performed in the window`W`

, which must be rectangular. If`TRUE`

(the default), simulation is performed on a larger window, and the result is clipped to the original wind - nsim
- Number of simulated realisations to be generated.
- drop
- Logical. If
`nsim=1`

and`drop=TRUE`

(the default), the result will be a point pattern, rather than a list containing a point pattern.

##### Details

This function generates a realisation of the
Penttinen point process in the window `W`

using a

Penttinen (1984, Example 2.1, page 18), citing Cormack (1979), described the pairwise interaction point process with interaction factor $$h(d) = e^{\theta A(d)} = \gamma^{A(d)}$$ between each pair of points separated by a distance $d$. Here $A(d)$ is the area of intersection between two discs of radius $R$ separated by a distance $d$, normalised so that $A(0) = 1$.

The simulation algorithm used to generate the point pattern
is `rmh`

, whose output
is only approximately correct).

There is a tiny chance that the algorithm will
run out of space before it has terminated. If this occurs, an error
message will be generated.
}
`nsim = 1`

, a point pattern (object of class `"ppp"`

).
If `nsim > 1`

, a list of point patterns.*Bulletin of the Brazilian Mathematical Society* 33, 351-367.

Berthelsen, K.K. and *Scandinavian Journal of Statistics* 30, 549-564.

Cormack, R.M. (1979)
Spatial aspects of competition between individuals.
Pages 151--212 in *Spatial and Temporal Analysis in Ecology*,
eds. R.M. Cormack and J.K. Ord, International Co-operative
Publishing House, Fairland, MD, USA.

*Statistical Inference and Simulation for Spatial Point Processes.*
Chapman and Hall/CRC.

Penttinen, A. (1984)
*Modelling Interaction in Spatial Point Patterns:
Parameter Estimation by the Maximum Likelihood Method.*
**7**,
University of `rmh`

,
`Penttinen`

.

`rStrauss`

,
`rHardcore`

,
`rStraussHard`

,
`rDiggleGratton`

,
`rDGS`

.

*Documentation reproduced from package spatstat, version 1.44-0, License: GPL (>= 2)*