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February 13th, 2014, 11:37 AM  #1 
Newbie Joined: Feb 2014 Posts: 3 Thanks: 0  Ref: Proof of noncentral 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 chisquared distribution), but what i need to know is how these noncentral 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. 
February 13th, 2014, 02:39 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,628 Thanks: 622  Re: Ref: Proof of noncentral moments of the normal distribu
(Answered in another forum). y = x  ? gives the noncentral moment as a finite linear combination of central moments.

February 17th, 2014, 06:30 AM  #3 
Newbie Joined: Feb 2014 Posts: 3 Thanks: 0  Re: Ref: Proof of noncentral 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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