spatstat (version 1.39-0)

rMaternII: Simulate Matern Model II

Description

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

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).

Value

• The simulated point pattern (an object of class "ppp").

Details

This algorithm generates a realisation 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.

See Also

rpoispp, rMatClust, rMaternI

Examples

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