spatstat (version 1.17-0)

rMaternII: Simulate Matern Model II

Description

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

Usage

rMaternII(kappa, r, win = owin(c(0,1),c(0,1)))

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.

Value

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

Details

This algorithm generates a realisation of Mat'ern'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 inside the window. 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 Mat'ern's Model II.

The difference between Mat'ern'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

pp <- rMaternII(20, 0.05)