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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
<divergent.tseries@gmail.com> 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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