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Topic: Analytic distribution with a mean but no defined variance
Replies: 4   Last Post: Dec 12, 2012 11:22 AM

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Richard Ulrich

Posts: 2,961
Registered: 12/13/04
Re: Analytic distribution with a mean but no defined variance
Posted: Dec 12, 2012 1:54 AM
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On Tue, 11 Dec 2012 16:46:49 -0800 (PST), Dave
<> wrote:

>I am looking for a known distribution with a defined mean, but no defined variance. In particular, I am interested in one whose pdf is analytically defined. I know distributions with a first central moment, but no second moment exist, but I am looking for an example.
>Any ideas?

The Cauchy has infinite (not defined) variance; and by the usual math
definition, it has no mean.

I think that you have to be peculiar about your definition of mean
in order to get a defined mean with infinite variance. I rather
like the "property" that the mean is the value that minimizes
the squared deviations ... and that implies, There is a variance.

I don't know how essential that property is.

Maybe someone will contribute who has deeper knowledge
than mine.

Rich Ulrich

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