`rStrauss(beta, gamma = 1, R = 0, W = owin())`

beta

intensity parameter (a positive number).

gamma

interaction parameter (a number between 0 and 1, inclusive).

R

interaction radius (a non-negative number).

W

window (object of class

`"owin"`

) in which to
generate the random pattern. Currently this must be a rectangular
window.- A point pattern (object of class
`"ppp"`

).

`W`

using a The Strauss process (Strauss, 1975; Kelly and Ripley, 1976)
is a model for spatial inhibition, ranging from
a strong `hard core' inhibition to a completely random pattern
according to the value of `gamma`

.

The Strauss process with interaction radius $R$ and parameters $\beta$ and $\gamma$ is the pairwise interaction point process with probability density $$f(x_1,\ldots,x_n) = \alpha \beta^{n(x)} \gamma^{s(x)}$$ where $x_1,\ldots,x_n$ represent the points of the pattern, $n(x)$ is the number of points in the pattern, $s(x)$ is the number of distinct unordered pairs of points that are closer than $R$ units apart, and $\alpha$ is the normalising constant. Intuitively, each point of the pattern contributes a factor $\beta$ to the probability density, and each pair of points closer than $r$ units apart contributes a factor $\gamma$ to the density.

The interaction parameter $\gamma$ must be less than or equal to $1$ in order that the process be well-defined (Kelly and Ripley, 1976). This model describes an ``ordered'' or ``inhibitive'' pattern. If $\gamma=1$ it reduces to a Poisson process (complete spatial randomness) with intensity $\beta$. If $\gamma=0$ it is called a ``hard core process'' with hard core radius $R/2$, since no pair of points is permitted to lie closer than $R$ units apart.

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

, whose output
is only approximately correct).

The implementation is currently **experimental**.
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.

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.

Kelly, F.P. and Ripley, B.D. (1976)
On Strauss's model for clustering.
*Biometrika* **63**, 357--360.

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

Strauss, D.J. (1975)
A model for clustering.
*Biometrika* **63**, 467--475.

`rmh`

```
X <- rStrauss(0.05,0.2,1.5,square(141.4))
Z <- rStrauss(100,0.7,0.05)
```

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