# rMaternII

0th

Percentile

##### Simulate Matern Model II

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

Keywords
spatial, datagen
##### 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.
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 latex{Mat'ern}{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 latex{Mat'ern}{Matern}'s Model II.

The difference between latex{Mat'ern}{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 (an object of class "ppp") if nsim=1, or a list of point patterns if nsim > 1.

rpoispp, rMatClust, rMaternI
X <- rMaternII(20, 0.05)
Y <- rMaternII(20, 0.05, stationary=FALSE)