spatstat (version 1.16-1)

# rpoint: Generate N Random Points

## Description

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.

## Value

• The simulated point pattern (an object of class `"ppp"`).

## 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.
The algorithm for pixel images is more efficient than that for functions.

`ppp.object`, `owin.object`, `runifpoint`

## Examples

Run this code
``````# 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)``````

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