Re: generalized mean and moments

whatafish_at_hotmail.com
Date: 12/11/04 

Date: 11 Dec 2004 14:01:19 -0800

Or do you
> want to express <x^2> not only in terms of <x> but also in terms of
<x^3>,
> <x^4>, ...?

Yes, that's what I'm asking. How would I express a generalized mean
<x^a>^(1/a) in terms of a series: f(a) = f_1(a) <x> + f_2(a) <x^2> +
... Or as a series of orthogonal moments. What I would like to do is to
approximate the generalized mean formula using a few simple moments
(the distribution functions that I'm working with are simple enough,
have only one peak, and have moments of finite value).

Note that for a=2, the generalized mean has the form <x^2>^(1/2), and
not simply as <x^2>.

If anyone knows any good reference about this question, I would
appreciate it if you could post it. I've been searching lately but
haven't found a useful one.

Thanks,

David

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