# rpoispp

##### Generate Poisson Point Pattern

Generate a random point pattern using the (homogeneous or inhomogeneous) Poisson process.

- Keywords
- spatial

##### Usage

`rpoispp(lambda, max, win, ...)`

##### Arguments

- 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.

##### Details

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
$p(x,y) = \lambda(x,y)/\mbox{max}$.

##### Value

- The simulated point pattern (an object of class
`"ppp"`

).

##### See Also

##### Examples

```
# 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)
```

*Documentation reproduced from package spatstat, version 1.2-1, License: GPL version 2 or newer*