Re: Recovering a probability distribution from its moments

From: Karl (breitu_at_arcor.de)
Date: 09/25/04 

Date: Sat, 25 Sep 2004 05:40:34 +0200

Hi,
what you are looking for, is called "Edgeworth expansion". You will find
something for example in "The advanced theory of statistics" by
"Kendall/Stuart", Vol. I. There are different approaches how to expand.

The bad news. Usually it doesn't work, see the example in the reference.
You will get negative probabilities or densities. In reliability every
5-10 years somebody comes up with this expansion as solution for almost
all problems and then it is forgotten again, because it doesn't work,

If you don't want the exact distribution, but some approximation, use
Pearson's system (see also in the ref.). This gives you, if the first
four moments are given, a distribution with these moments.
Ciao
Karl
>

Quantcast