rMaternII

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Simulate Matern Model II

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

Keywords
spatial, datagen
Usage
rMaternII(kappa, r, win = owin(c(0,1),c(0,1)), stationary=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).
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. 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 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

• rMaternII
Examples
X <- rMaternII(20, 0.05)
Y <- rMaternII(20, 0.05, stationary=FALSE)
Documentation reproduced from package spatstat, version 1.25-1, License: GPL (>= 2)

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