On 17/09/2014 3:07 PM, Duncan Murdoch wrote:
On 17/09/2014 2:25 PM, Giovanni Petris wrote:
> Hello,
>
> I am trying to interface in my teaching some elementary probability with
Monte Carlo ideas. In sampling from a finite population, the number of distinct
samples of size 'k' from a population of size 'n' , when individuals are selected
with replacement and the selection order does not matter, is choose(n + k -1, k).
Does anyone have a suggestion about how to simulate (uniformly!) one of these
possible samples? In a Monte Carlo framework I would like to do it repeatedly, so
efficiency is of some relevance.
>
> Thank you in advance!
I forget the details of the derivation of that count, but the number
suggests it is found by selecting k things without replacement from
n+k-1. The sample() function in R can easily give you a sample of k
integers from 1:(n+k-1); "all" you need to do is map those numbers into
your original sample of k from n. For that you need to remember the
derivation of that formula!
The derivation is on this web page:
http://mathworld.wolfram.com/Multichoose.html .
Duncan Murdoch
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