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number generator

Hendrik van Rooyen mail at microcorp.co.za
Tue Mar 13 02:20:49 EDT 2007 
 "Nick Craig-Wood" <nick at craig-wood.com> wrote:

> Paul Rubin <http> wrote:
> >  The fencepost method still seems to be simplest:
> > 
> >      t = sorted(random.sample(xrange(1,50), 4))
> >      print [(j-i) for i,j in zip([0]+t, t+[50])]
> 
> Mmm, nice.
> 
> Here is another effort which is easier to reason about the
> distribution produced but not as efficient.
> 
> def real(N, M):
>     while 1:
>         t = [ random.random() for i in range(N) ]
>         factor = M / sum(t)
>         t = [ int(round(x * factor)) for x in t]
>         if sum(t) == M:
>             break
>         print "again"
>     assert len(t) == N
>     assert sum(t) == M
>     return t
> 
> It goes round the while loop on average 0.5 times.
> 
> If 0 isn't required then just test for it and go around the loop again
> if found.  That of course skews the distribution in difficult to
> calculate ways!
> 

I have been wondering about the following as this thread unrolled:

Is it possible to devise a test that can distinguish between sets
of:

- five random numbers that add to 50, and
- four random numbers and a fudge number that add to 50?

My stats are way too small and rusty to attempt to answer 
the question, but it seems intuitively a very difficult thing.

- Hendrik
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