Re: infinite moments

From: Ian Jermyn (Ian.Jermyn_at_sophia.inria.fr)
Date: 07/21/04 

Date: Wed, 21 Jul 2004 17:38:31 +0200

I don't think anyone is in any doubt that it can have pragmatic
applications. I do not believe there is a well-defined question, but
whatever it is, it is not that.

Ian. 

-- 
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Ian Jermyn
INRIA (Ariana)
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"Richard Ulrich" <Rich.Ulrich@comcast.net> a écrit dans le message de
news:3c1tf09juviahnlbmpt0shtngnlr61qd9i@4ax.com...
> On Wed, 21 Jul 2004 10:19:36 +0200, "Ian Jermyn"
> <Ian.Jermyn@sophia.inria.fr> wrote:
>
> > Did I say 'finite quantities' implied 'finite mean'? One can always
> > construct infinities by using bad co-ordinates, as you do in the example
of
> > the angle and its tangent. If one uses bad co-ordinates, one has to be
> > careful how they are interpreted. In any case, co-ordinates have no
physical
> > significance in themselves. How will you measure this infinite quantity?
> >
> > In addition to the above, there is the objection that you raise
yourself,
> > that the system you describe does not exist. In a real physical system
there
> > will be all sorts of other factors, including, in some limit, quantum
> > mechanics, that will prevent your analysis from being correct.
>
> Is the question is whether the Cauchy distribution, with undefined
> mean and infinite variance, has pragmatic applications?
>
> Funny you should mention quantum mechanics.
>
> I quote myself, quoting in a post in 2000:
>  - From Philip Bevington's book "Data Reduction...",
> (page 49, 1969 edition) concerning the Lorentzian
> (Cauchy) distribution, "which occurs quite often
> in nuclear physics data reduction."
>
>     "It is an appropriate distribution for describing data
> corresponding to resonance behavior, such as the
> variation with energy of the cross section of a nuclear
> reaction or the variation with velocity of absorption
> of radiation in the Mossbauer effect."
>
>
>
> -- 
> Rich Ulrich, wpilib@pitt.edu
> http://www.pitt.edu/~wpilib/index.html

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