# rpoint

From spatstat v1.19-2
by Adrian Baddeley

##### Generate N Random Points

Generate a random point pattern containing $n$ independent, identically distributed random points with any specified distribution.

##### Usage

`rpoint(n, f, fmax=NULL, win=unit.square(), ..., giveup=1000, verbose=FALSE)`

##### Arguments

- n
- Number of points to generate.
- f
- The probability density of the points,
possibly un-normalised.
Either a constant,
a function
`f(x,y,...)`

, or a pixel image object. - fmax
- An upper bound on the values of
`f`

. If missing, this number will be estimated. - win
- Window in which to simulate the pattern.
Ignored if
`f`

is a pixel image. - ...
- Arguments passed to the function
`f`

. - giveup
- Number of attempts in the rejection method after which the algorithm should stop trying to generate new points.
- verbose
- Flag indicating whether to report details of performance of the simulation algorithm.

##### Details

This function generates `n`

independent, identically distributed
random points with common probability density proportional to
`f`

.

The argument `f`

may be
[object Object],[object Object],[object Object]
The algorithm is as follows:

- If
`f`

is a constant, we invoke`runifpoint`

. - If
`f`

is a function, then we use the rejection method. Proposal points are generated from the uniform distribution. A proposal point$(x,y)$is accepted with probability`f(x,y,...)/fmax`

and otherwise rejected. The algorithm continues until`n`

points have been accepted. It gives up after`giveup * n`

proposals if there are still fewer than`n`

points. - If
`f`

is a pixel image, then a random sequence of pixels is selected (using`sample`

) with probabilities proportional to the pixel values of`f`

. Then for each pixel in the sequence we generate a uniformly distributed random point in that pixel.

##### Value

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

).

##### See Also

##### Examples

```
# 100 uniform random points in the unit square
X <- rpoint(100)
# 100 random points with probability density proportional to x^2 + y^2
X <- rpoint(100, function(x,y) { x^2 + y^2}, 1)
# `fmax' may be omitted
X <- rpoint(100, function(x,y) { x^2 + y^2})
# irregular window
data(letterR)
X <- rpoint(100, function(x,y) { x^2 + y^2}, win=letterR)
# make a pixel image
Z <- setcov(letterR)
# 100 points with density proportional to pixel values
X <- rpoint(100, Z)
```

*Documentation reproduced from package spatstat, version 1.19-2, License: GPL (>= 2)*

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