Re: alpha stable distribution
From: Herman Rubin (hrubin_at_odds.stat.purdue.edu)
Date: 07/29/04
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Date: 29 Jul 2004 13:23:03 -0500
In article <f2407f76.0407280244.3b59208a@posting.google.com>,
zlatko <zlatkopetrov@yahoo.com> wrote:
>Dear friends,
>this is my first post at this group and I am not statistician.
>I am trying to model the real data from the foliage clutter of
>groud radar as alpha stable distribution.
>Because the lack of books and serious papers maybe I have made some
>mistakes.
>The first step in my analysis is preliminary data analysis, aiming
>the answering of questions - if my distribution is heavy-tailed or no? and
>if the data is stable or no? The preliminary analysis includes
>the following steps:
I suggest you find out what a stable distribution is.
You have done some of this, but not enough.
Except for the normal (alpha = 2), an alpha-stable
distribution has only moments (in the general sense)
of order less than alpha, and alpha < 2. The tails
are very heavy. Using sample variances and higher
moments is not a good idea, as you have found.
How large is your sample? I can produce tests for
you, which are probably not in the literature. Fitting
stable distributions is not particularly easy; for
symmetric ones, it is easier, but not by the most
commonly used methods.
Do you have a competent theoretical statistician
available? I doubt that the books have anything
useful; I would have to make up procedures.
-- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
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