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February 13th, 2014, 10:37 AM   #1
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Ref: Proof of non-central moments of the normal distribution

Hi, I am currently reading through an article where they using the noncentral moments for the normal distribution (and actually also the chi-squared distribution), but what i need to know is how these non-central moments has been determined. I have tried googling the answer without luck. In most places, i.e wikipedia they just state the moments - so i have the answer. But what i am looking for is a proof of how to archieve the answer.

Can anybody help me with an reference? Preferable online, but a book would also suffice.

----

So for clarification, if
when i want to determine what

In particular I'm interested in the 4. moment., so a proof only for the absolute moments would be fine - if it makes a difference.
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February 13th, 2014, 01:39 PM   #2
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Re: Ref: Proof of non-central moments of the normal distribu

(Answered in another forum). y = x - ? gives the non-central moment as a finite linear combination of central moments.
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February 17th, 2014, 05:30 AM   #3
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Re: Ref: Proof of non-central moments of the normal distribu

Thanks man, I also found another solution. I solved it with taylorexpansion of e^tx like this:



And using that on the normal distribution i first calculated the integral



And then it is possible to differentiate n times (to find the n'th moment) and evaluate at t=0, which yields that

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