# 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(), expand=TRUE, nsim=1, drop=TRUE)`

##### 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. - 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
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.
}
`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.

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.

*Statistical Inference and Simulation for Spatial Point Processes.*
Chapman and Hall/CRC.
}
[object Object],[object Object]
`rmh`

,
`DiggleGatesStibbard`

.

`rStrauss`

,
`rHardcore`

,
`rStraussHard`

,
`rDiggleGratton`

,
`rPenttinen`

.

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