spatstat.core (version 2.1-2)

rMaternII: 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.

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.

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.

See Also

rpoispp, rMatClust, rMaternI

Examples

# NOT RUN {
 X <- rMaternII(20, 0.05)
 Y <- rMaternII(20, 0.05, stationary=FALSE)
# }