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Topic: Moments of non-standardized Student's t distribution
Replies: 1   Last Post: Mar 29, 2013 5:52 PM

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Ray Koopman

Posts: 3,383
Registered: 12/7/04
Re: Moments of non-standardized Student's t distribution
Posted: Mar 29, 2013 5:52 PM
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On Mar 29, 11:33 am, Paul <> wrote:
> I'm seeking a formula for the moments of the non-standardized Student's t distribution -- i.e., a variable mu + sigma * t, where t has a Student's t distribution.
> Any references most appreciated.
> Best wishes,
> Paul von Hippel

Use the binomial expansion, look up the moments of the standard t_n:

E[(m + s t)^r] = Sum{ r_Choose_k m^(r-k) s^k E[t^k],
k = 0, 2, ..., Min[r,n-1] },

where E[t^k] = n^(k/2) * 1*3*...*(k-1) / ((n-2)*(n-4)*...*(n-k)).

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