# rMaternII

##### Simulate Matern Model II

Generate a random point pattern, a simulated realisation of the Matern Model II inhibition process.

##### Usage

```
rMaternII(kappa, r, win = owin(c(0,1),c(0,1)), stationary=TRUE, ...,
nsim=1, drop=TRUE)
```

##### Arguments

- kappa
Intensity of the Poisson process of proposal points. A single positive number.

- r
Inhibition distance.

- win
Window in which to simulate the pattern. An object of class

`"owin"`

or something acceptable to`as.owin`

. Alternatively a higher-dimensional box of class`"box3"`

or`"boxx"`

.- stationary
Logical. Whether to start with a stationary process of proposal points (

`stationary=TRUE`

) or to generate the proposal points only inside the window (`stationary=FALSE`

).- …
Ignored.

- 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 algorithm generates one or more realisations
of Matern's Model II
inhibition process inside the window `win`

.

The process is constructed by first
generating a uniform Poisson point process of ``proposal'' points
with intensity `kappa`

. If `stationary = TRUE`

(the
default), the proposal points are generated in a window larger than
`win`

that effectively means the proposals are stationary.
If `stationary=FALSE`

then the proposal points are
only generated inside the window `win`

.

Then each proposal point is marked by an ``arrival time'', a number uniformly distributed in \([0,1]\) independently of other variables.

A proposal point is deleted if it lies within `r`

units' distance
of another proposal point *that has an earlier arrival time*.
Otherwise it is retained.
The retained points constitute Matern's Model II.

The difference between Matern's Model I and II is the italicised statement above. Model II has a higher intensity for the same parameter values.

##### Value

A point pattern
if `nsim=1`

, or a list of point patterns if `nsim > 1`

.
Each point pattern is normally an object of class `"ppp"`

,
but may be of class `"pp3"`

or `"ppx"`

depending on the window.

##### See Also

##### Examples

```
# NOT RUN {
X <- rMaternII(20, 0.05)
Y <- rMaternII(20, 0.05, stationary=FALSE)
# }
```

*Documentation reproduced from package spatstat, version 1.56-1, License: GPL (>= 2)*