rMaternII

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Simulate Matern Model II

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

Keywords
spatial, datagen
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.