rMaternI: Simulate Matern Model I

Description

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

Usage

rMaternI(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.

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.

Value

A point pattern (an object of class "ppp") if nsim=1, or a list of point patterns if nsim > 1.

Details

This algorithm generates one or more realisations of latex{Mat'ern}{Matern}'s Model I 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.

A proposal point is then deleted if it lies within r units' distance of another proposal point. Otherwise it is retained. The retained points constitute latex{Mat'ern}{Matern}'s Model I.

Examples

Run this code

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