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#1




Shortcut kth central moment
I remember taking statistics course in college and my professor taught us shortcut on how to calculate kth central moments where k = 3,4,....n
Could anyone explain the shortcut to me? I really appreciate your time and help! Thanks! 
#3




Quote:
Common approach is to expand the term through algebra but the equation will get messy sometimes so I just want to find the alternative to save time. 
#4




The third central moment is the 3rd derivative of the natural log of the moment generating function at 0...
ie. the third central moment is The larger central moments aren't quite as easy. For instance the fourth central moment is or equivalently Is this what you were thinking of? There are nice shortcuts for certain distributions of course (like the normal). Could you have been remembering a shortcut that only works with certain distributions? Last edited by Z3ta; 09272016 at 08:51 PM.. 
#5




I just saw something in Mahler today (only for Poisson). The second central moment of a Compound Poisson Count and Gamma Severity distribution was E[N]*E[X^2] and the 3rd central moment was E[N]*E[X^3].
Last edited by Demo99; 10012016 at 02:47 PM.. Reason: correction 
#9




Formula based upon Poisson frequency. Does not hold in general.

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