Generate a sequence of random numbers that sum up to 1?

[Alex Martelli]

fumanchu <fumanchu at amor.org> wrote:

> I'm surprised noone has pursued a course of subtraction rather than
> division. Say you want 10 numbers:
> 
> >>> s = 1.0
> >>> n = []
> >>> for x in xrange(9):
> ...   value = random.random() * s
> ...   n.append(value)
> ...   s -= value
> ...
> >>> n.append(s)
> >>> n
> [0.7279111122901516, 0.082128708606867745, 0.0080516733577621798,
> 0.12122060245902817, 0.0034460458833209676, 0.0021046234724371184,
> 0.054109424914363845, 0.00035750970249204185, 0.00051175075536832372,
> 0.00015854855820800087]
> >>> sum(n)
> 1.0
> 
> 
> Either:
>  1) Just because they're *ordered* doesn't mean they're not *random*,
> or
>  2) You all now know why I'm not a mathematician. ;)
> 
> It seems to me that the only constraint on the randomness of my results
> is the OP's constraint: that they sum to 1. I'd be fascinated to learn
> if and why that wouldn't work.

n[0] is uniformly distributed between 0 and 1; n[1] is not -- not sure
how to characterize its distribution, but it's vastly skewed to favor
smaller values -- and further n[x] values for x>1 are progressively more
and more skewed similarly.

Such total disuniformity, where the very distribution of each value is
skewed by the preceding one, may still be "random" for some sufficiently
vague meaning of "random", but my intuition suggests it's unlikely to
prove satisfactory for the OP's purposes.


Alex