Mathematica Integration help
- To: mathgroup at smc.vnet.net
- Subject: [mg86126] Mathematica Integration help
- From: Francogrex <franco at grex.org>
- Date: Sun, 2 Mar 2008 13:58:27 -0500 (EST)
Hi I'm new to Mathematica, I don't know if there are other help forums
beside this one. I need help estimating the integrated likelihood
function with mathematica 6.
My function is below(all equations below are in mathematica raw input
form, pls convert to standard form to see how they really look like):
Integrate[Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))*
Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}], \[Mu]]
The result that it's giving me is the following:
-(2^(-(1/2) - n/2)*
E^((n*(-\[Mu] + Subscript[x, i])^2)/(2*\[Sigma]^2))*
Pi^(1/2 - n/2)*\[Sigma]*
(Sqrt[\[Sigma]^2]/(E^((-\[Mu] +
Subscript[x, i])^2/(2*\[Sigma]^2))*\[Sigma]^2))^n*
Erf[(Sqrt[n]*(-\[Mu] + Subscript[x, i]))/(Sqrt[2]*\[Sigma])])/
Sqrt[n]
But I know from a publication I've read that the result doesn't
involve the Erf, but it's the following:
1/(E^(Sum[(Subscript[x, i] - OverBar[x])^2, {i, 1,
n}]/(2*\[Sigma]^2))*
(Sqrt[n]*(2*Pi*\[Sigma]^2)^((n - 1)/2)))
where: OverBar[x] = Sum[Subscript[x, i], {i, 1, n}]/n
Is there any way to get Mathematica to output that? Thanks