rMaternII: Simulate Matern Model II

In spatstat.random: Random Generation Functionality for the 'spatstat' Family

Simulate Matern Model II

Description

Generate a random point pattern, a simulated realisation of the \Matern Model II inhibition process.

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. Alternatively a higher-dimensional box of class "box3" or "boxx".
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 \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 \Matern's Model II.

The difference between \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 if nsim=1, or a list of point patterns if nsim > 1. Each point pattern is normally an object of class "ppp", but may be of class "pp3" or "ppx" depending on the window.

Author(s)

Ute Hahn, \spatstatAuthors.

See Also

rpoispp, rMatClust, rMaternI

Examples

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

spatstat.random documentation built on Sept. 30, 2024, 9:46 a.m.