# rMaternII

##### Simulate Matern Model II

Generate a random point pattern, a simulated realisation of the Mat'ern Model II inhibition process.

##### Usage

`rMaternII(kappa, r, win = owin(c(0,1),c(0,1)))`

##### 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`

.

##### Details

This algorithm generates a realisation of Mat'ern'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`

inside the window.
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 Mat'ern's Model II.

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

##### Value

- The simulated point pattern (an object of class
`"ppp"`

).

##### See Also

##### Examples

`pp <- rMaternII(20, 0.05)`

*Documentation reproduced from package spatstat, version 1.10-3, License: GPL version 2 or newer*