| rpoispp {spatstat} | R Documentation |
Generate a random point pattern using the (homogeneous or inhomogeneous) Poisson process.
rpoispp(lambda, max, win)
lambda |
Intensity of the Poisson process.
Either a single positive number, or a function(x,y).
|
max |
An upper bound for the value of lambda(x,y),
if lambda is a function.
|
win |
Window in which to simulate the pattern.
An object of class "owin"
or something acceptable to as.owin.
|
If lambda is a single number,
then this algorithm generates a realisation
of the uniform Poisson process inside the window win with
intensity lambda (points per unit area).
If lambda is a function, then this algorithm generates a realisation
of the inhomogeneous Poisson process with intensity function
lambda(x,y) at spatial location (x,y).
The function lambda must work correctly with vectors x
and y.
The value max must be given and must be an upper bound on the
values of lambda(x,y) for all locations (x, y)
inside the window win.
To generate an inhomogeneous Poisson process
the algorithm uses ``rejection filtering'': it first generates a uniform
Poisson process of intensity max,
then thins it by randomly deleting or retaining each point independently,
with retention probability
p(x,y) = lambda(x,y)/max.
The simulated point pattern (an object of class "ppp").
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
# uniform Poisson process with intensity 100 in the unit square
pp <- rpoispp(100)
# uniform Poisson process with intensity 1 in a 10 x 10 square
pp <- rpoispp(1, win=owin(c(0,10),c(0,10)))
# plots should look similar !
# inhomogeneous Poisson process in unit square
# with intensity lambda(x,y) = 100 * exp(-3*x)
# Intensity is bounded by 100
pp <- rpoispp(function(x,y) {100 * exp(-3*x)}, 100)