Yes, the summation module could certainly use more work. I think that this
has been on the GSoC project list for a while.
Fortunately this work can happen separately from work in stats. There is a
pretty clear separation between the two modules.
On Thu, Jan 16, 2014 at 2:13 PM, F. B. <franz.bona...@gmail.com> wrote:
> On Wed, Jan 15, 2014 at 1:17 PM, Matthew Rocklin <mroc...@gmail.com>wrote:
>
>> Discrete is the newest and least mature and could presumably use work.
>>
>
> I tried to define a binomial distribution manually and do some
> calculations using summation:
>
> In [1]: n, k = var('n k', positive=True, integer=True)
>
> In [2]: p = var('p', positive=True)
>
> In [3]: binomial_dist = binomial(n, k)*p**k*(1-p)**(n-k)
>
> In [6]: summation(binomial_dist, (k, 0, n)).simplify()
> ⎧ │ 1 │
> ⎪ 1 for p⋅│─────│ ≤ 1
> ⎪ │p - 1│
> ⎪
> ⎪ n
> ⎪ ____
> ⎪ ╲
> ⎨ ╲ k -k n ⎛n⎞
> ⎪ ╲ p ⋅(-p + 1) ⋅(-p + 1) ⋅⎜ ⎟
> ⎪ ╱ ⎝k⎠ otherwise
> ⎪ ╱
> ⎪ ╱
> ⎪ ‾‾‾‾
> ⎪k = 0
> ⎩
>
>
> This is technically correct, but is practically useless as a result.
>
> Even worse with a slight modification:
>
> >>> summation(binomial_dist*k, (k, 0, n))
> TypeError: unsupported operand type(s) for *: 'NoneType' and 'Add'
>
> I think that the summation module needs some further work.
>
>
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