# rMaternII

0th

Percentile

##### Simulate Matern Model II

Generate a random point pattern using the Mat'ern Model II inhibition process.

Keywords
spatial, datagen
##### 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").

rpoispp, rMatClust, rMaternI
pp <- rMaternII(20, 0.05)