On 17/09/2014 3:46 PM, Giovanni Petris wrote:
Hi Duncan,

You are right. The idea of the derivation consists in 'throwing' k placeholders 
("*" in the example below) in the list of the individuals of the population. 
For example, if the population is letters[1:6], and the sample size is 4, the following 
code generates uniformly a 'sample'.

> n <- 6; k <- 4
> set.seed(2)
> xxx <- rep("*", n + k)
> ind <- sort(sample(2 : (n+k), k))
> xxx[setdiff(1 : (n+k), ind)] <- letters[seq.int(n)]
> noquote(xxx)
  [1] a b * c d * * e f *

This represents the sample (b, d, d, f). I am still missing the "all" I need to 
do that you mention, that is how I can transform the vector xxx into something more 
readily usable, like c(b, d, d, f), or even a summary of counts. I guess I am looking for 
a bit of R trickery here...

I think this works, but you'd better check!

Sample the placeholders:

ind <- sort( sample(n + k -1, n-1) )  # I don't think sort() is necessary...

Add placeholders at the start and end:

ind <- c(0, ind, n+k)

Take the diffs, and subtract one:

diff(ind) - 1

I think this gives the counts you want.

Duncan Murdoch

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