First, thanks for posting the question on stack overflow, I think that we
should use that more. Unfortunately, few of us (maybe only Aaron?)
actually checks SO, again, I think that we should use it more.
Sympy.stats is producing an integral that looks like the following:
In [1]: from sympy.stats import *
In [2]: a, b, c, d, = symbols('a b c d', real=True, positive=True)
In [3]: G1 = GammaInverse("G1", a, b)
In [4]: G2 = GammaInverse("G2", c, d)
In [5]: G3 = S(7)/10*G1 + S(3)/10*G2
In [7]: density(G3, evaluate=False)(x)
Out[7]:
∞
⌠
⎮ ∞
⎮ ⌠
⎮ ⎮ -b
⎮ ⎮ ───
⎮ -d ⎮ -a - 1 a G₁ ⎛7⋅G₁ 3⋅G₂ ⎞
⎮ ─── ⎮ G₁ ⋅b ⋅ℯ ⋅DiracDelta⎜──── + ──── - x⎟
⎮ -c - 1 c G₂ ⎮ ⎝ 10 10 ⎠
⎮ G₂ ⋅d ⋅ℯ ⋅⎮ ──────────────────────────────────────────── d(G₁)
⎮ ⎮ Γ(a)
⎮ ⌡
⎮ 0
⎮ ─────────────────────────────────────────────────────────────────────
d(G₂)
⎮ Γ(c)
⌡
0
So one could reduce your question into a question like, "does anyone have
any thoughts on how SymPy could solve this integral?"
On Tue, Apr 1, 2014 at 6:26 AM, John Griffiths
<[email protected]>wrote:
>
>
> Does anyone have any thoughts on how to solve this problem:
>
> When I try to take a weighted mixture of inverse gamma distributions
> using sympy.stats I get the following error
>
> %matplotlib inlinefrom matplotlib import pyplot as pltfrom sympy.stats import
> GammaInverse, densityimport numpy as np
>
> f1 = 0.7; f2 = 1-f1
> G1 = GammaInverse("G1", 5, 120/(5.5*2.5E-7))
> G2 = GammaInverse("G2", 4, 120/(5.5*1.5E-7))
> G3 = f1*G1 + f2*G2
> D1 = density(G1);
> D2 = density(G2);
> D3 = density(G3);
> v1 = [D1(i).evalf() for i in u]
> v2 = [D2(i).evalf() for i in u]
> v3 = [D3(i).evalf() for i in u]
>
> ...which errors at D3 = density(G3). The error includes
>
> PolynomialDivisionFailed: couldn't reduce degree in a polynomial
> division algorithm when dividing [231761.370742578/(0.0011381138741823*G2**2 -
> 0.007587425827882*G2*_z + 0.0126457097131367*_z**2), 0.0]
> by [263.770831541635/263.770831541635, 0.0].
> This can happen when it's not possible to detect zero in the coefficient
> domain. The domain of computation is RR(G2,_t0,_z). Zero detection is
> guaranteed in this
> coefficient domain. This may indicate a bug in SymPy or the domain is user
> definedand doesn't implement zero detection properly.
>
> (also get this when I take mixture of inverse Gamma with Normal and
> Uniform distributions)
>
> Should this be possible?
>
>
> Cheers.
>
>
>
> (p.s. apologies for redundancy with recent SO post)
>
>
>
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