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 .
|
... |
Arguments passed to lambda if it is a function.
|
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) # How to tune the coefficient of x lamb <- function(x,y,a) { 100 * exp( - a * x)} pp <- rpoispp(lamb, 100, a=3)