Simulate Matern Model II
Generate a random point pattern, a simulated realisation of the Matern Model II inhibition process.
rMaternII(kappa, r, win = owin(c(0,1),c(0,1)), stationary=TRUE, ...,
nsim=1, drop=TRUE)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 |
stationary |
Logical. Whether to start with a stationary process of proposal points
( |
... |
Ignored. |
nsim |
Number of simulated realisations to be generated. |
drop |
Logical. If |
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.
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
, Ute Hahn, Rolf Turner r.turner@auckland.ac.nz
and Ege Rubak rubak@math.aau.dk
X <- rMaternII(20, 0.05) Y <- rMaternII(20, 0.05, stationary=FALSE)
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