Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Richard Ulrich

Posts: 2,852
Registered: 12/13/04
Re: Analytic distribution with a mean but no defined variance
Posted: Dec 12, 2012 1:54 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.