# rDGS

##### Perfect Simulation of the Diggle-Gates-Stibbard Process

Generate a random pattern of points, a simulated realisation of the Diggle-Gates-Stibbard process, using a perfect simulation algorithm.

##### Usage

`rDGS(beta, rho, W = owin())`

##### Arguments

- beta
- intensity parameter (a positive number).
- rho
- interaction range (a non-negative number).
- W
- window (object of class
`"owin"`

) in which to generate the random pattern. Currently this must be a rectangular window.

##### Details

This function generates a realisation of the
Diggle-Gates-Stibbard point process in the window `W`

using a

Diggle, Gates and Stibbard (1987) proposed a pairwise interaction point process in which each pair of points separated by a distance $d$ contributes a factor $e(d)$ to the probability density, where $$e(d) = \sin^2\left(\frac{\pi d}{2\rho}\right)$$ for $d < \rho$, and $e(d)$ is equal to 1 for $d \ge \rho$.

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.

##### Value

- A point pattern (object of class
`"ppp"`

).

##### References

Berthelsen, K.K. and Moller, J. (2002)
A primer on perfect simulation for spatial point processes.
*Bulletin of the Brazilian Mathematical Society* 33, 351-367.

Berthelsen, K.K. and Moller, J. (2003)
Likelihood and non-parametric Bayesian MCMC inference
for spatial point processes based on perfect simulation and
path sampling.
*Scandinavian Journal of Statistics* 30, 549-564.

Diggle, P.J., Gates, D.J., and Stibbard, A. (1987)
A nonparametric estimator for pairwise-interaction point processes.
Biometrika **74**, 763 -- 770.
*Scandinavian Journal of Statistics* **21**, 359--373.

Moller, J. and Waagepetersen, R. (2003).
*Statistical Inference and Simulation for Spatial Point Processes.*
Chapman and Hall/CRC.

##### See Also

`rmh`

,
`DiggleGatesStibbard`

,
`rStrauss`

,
`rHardcore`

,
`rDiggleGratton`

.

##### Examples

`X <- rDGS(50, 0.05)`

*Documentation reproduced from package spatstat, version 1.29-0, License: GPL (>= 2)*