> Matthew... what do you think of the union of intervals as an alternative
to the usual ranges in integrate/Integral?
Seems like a decent plan. I haven't been actively working on stats in a
while so I don't have strong opinions here.
On Thu, Mar 26, 2015 at 6:50 PM, Aaron Meurer <asmeu...@gmail.com> wrote:
> I think integrating over sets is a useful thing to allow, but we
> definitely need to be more careful about symbolic intervals. And given
> that, it probably means that sympy.stats should just do normal
> integrals, since it can make assumptions about symbolic intervals that
> won't be present when passed to Integral.
>
> Aaron Meruer
>
> On Thu, Mar 26, 2015 at 6:54 PM, Francesco Bonazzi
> <franz.bona...@gmail.com> wrote:
> > Matthew... what do you think of the union of intervals as an alternative
> to
> > the usual ranges in integrate/Integral?
> >
> > I suppose that you wrote the code outputting that integral, which
> currently
> > does not work, and I want to make it work.
> >
> > I am undecided on whether to edit sympy.stats in order to give Integral(
> ...
> > , (x, -oo, -1)) + Integral( ... , (x, 1, oo)) instead of Integral( ... ,
> (x,
> > Union(Interval(-oo, -1), Interval(1, oo)))).
> >
> > On the other hand, this alternative notation may be useful.
> Unfortunately it
> > would require some algorithmic changes and I am a bit wary about a
> > substantial edit of the integration algorithm.
> >
> > On Thursday, March 26, 2015 at 9:12:37 PM UTC+1, Matthew wrote:
> >>
> >> You don't need to square the random variable to compute the result. You
> >> just need to integrate the pdf over x < -1 and x > 1
> >>
> >> On Thu, Mar 26, 2015 at 5:42 AM, Francesco Bonazzi <franz....@gmail.com
> >
> >> wrote:
> >>>
> >>>
> >>> Well, I was a bit surprised too, but the stats module apparently does
> so,
> >>> as shown in this example:
> >>>
> >>> In [1]: from sympy.stats import *
> >>>
> >>> In [2]: var('sigma', positive=True)
> >>> Out[2]: σ
> >>>
> >>> In [3]: N = Normal('X', mu, sigma)
> >>>
> >>> In [6]: P(N**2>1, evaluate=False)
> >>> Out[6]:
> >>> (-∞, -1) ∪ (1, ∞)
> >>> ⌠
> >>> ⎮ 2
> >>> ⎮ -(z - μ)
> >>> ⎮ ──────────
> >>> ⎮ 2
> >>> ⎮ ___ 2⋅σ
> >>> ⎮ ╲╱ 2 ⋅ℯ
> >>> ⎮ ───────────────── dz
> >>> ⎮ ___
> >>> ⎮ 2⋅╲╱ π ⋅σ
> >>> ⌡
> >>>
> >>>
> >>> In [7]: srepr(P(N**2>1, evaluate=False))
> >>> Out[7]: "Integral(Mul(Rational(1, 2), Pow(Integer(2), Rational(1, 2)),
> >>> Pow(pi, Rational(-1, 2)), Pow(Symbol('sigma'), Integer(-1)),
> >>> exp(Mul(Integer(-1), Rational(1, 2), Pow(Symbol('sigma'), Integer(-2)),
> >>> Pow(Add(Dummy('z'), Mul(Integer(-1), Symbol('mu'))), Integer(2))))),
> >>> Tuple(Dummy('z'), Union(Interval(-oo, Integer(-1), S.true, S.true),
> >>> Interval(Integer(1), oo, S.true, S.true))))"
> >>>
> >>>
> >>> Apart the fact that such an integral looks wrong to me, i.e. there is
> no
> >>> account for the random variable being squared (or am I missing
> something?),
> >>> it looks like SymPy is OK with intervals, but not with unions of
> intervals:
> >>>
> >>>
> >>>
> https://github.com/sympy/sympy/blob/9242d31f6d31a1d9c3464264a5a6e61eab8acfb8/sympy/concrete/expr_with_limits.py#L37
> >>>
> >>> That's the point where an Interval gets parsed by the integration
> >>> algorithm.
> >>>
> >>> I think it's an easy fix to add the processing for unions of intervals.
> >>>
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