[R] Efficient sampling from a discrete distribution in R

[Prof Brian Ripley]

On Mon, 3 Sep 2007, Issac Trotts wrote:

> Hello r-help,
>
> As far as I've seen, there is no function in R dedicated to sampling
> from a discrete distribution with a specified mass function.  The
> standard library doesn't come with anything called rdiscrete or rpmf,
> and I can't find any such thing on the cheat sheet or in the
> Probability Distributions chapter of _An Introduction to R_.  Googling
> also didn't bring back anything.  So, here's my first attempt at a
> solution.  I'm hoping someone here knows of a more efficient way.

It's called sample().

There are much more efficient algorithms than the one you used, and 
sample() sometimes uses one of them (Walker's alias method): see any good 
book on simulation (including my 'Stochastic Simulation, 1987).

> # Sample from a discrete distribution with given probability mass function
> rdiscrete = function(size, pmf) {
>  stopifnot(length(pmf) > 1)
>  cmf = cumsum(pmf)
>  icmf = function(p) {
>    min(which(p < cmf))
>  }
>  ps = runif(size)
>  sapply(ps, icmf)
> }
>
> test.rdiscrete = function(N = 10000) {
>  err.tol = 6.0 / sqrt(N)
>  xs = rdiscrete(N, c(0.5, 0.5))
>  err = abs(sum(xs == 1) / N - 0.5)
>  stopifnot(err < err.tol)
>  list(e = err, xs = xs)
> }
>
> Thanks,
> Issac
>
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-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
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