Status: Accepted
Owner: ----
CC: [email protected]
Labels: Type-Defect Priority-Medium Integration
New issue 3016 by [email protected]: Integrals involving symbolic Beta
distributions hang
http://code.google.com/p/sympy/issues/detail?id=3016
Some statistical integrals involving beta distributions fail. The integrals
hang. I've included the sympy.stats code as well as copy-paste-able
integral expressions and their expected results.
a, b, x = symbols('a b x', positive=True)
B = Beta(a,b, symbol=x)
E(B, evaluate=False)
Integral(x*x**(a - 1)*(-x + 1)**(b - 1)*gamma(a + b)/(gamma(a)*gamma(b)),
(x, 0, 1))
E(B)
Hangs
Should evaluate to
a / (a + b)
Similarly
Var(B) should equal (a*b) / ((a+b)**2 * (a+b+1))
Var(B, evaluate=False)
-Integral(x*x**(a - 1)*(-x + 1)**(b - 1)*gamma(a + b)/(gamma(a)*gamma(b)),
(x, 0, 1))**2 + Integral(x**2*x**(a - 1)*(-x + 1)**(b - 1)*gamma(a +
b)/(gamma(a)*gamma(b)), (x, 0, 1))
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