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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

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Dan Heyman

Posts: 167
Registered: 12/13/04
Re: Analytic distribution with a mean but no defined variance
Posted: Dec 12, 2012 10:03 AM
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On Tuesday, December 11, 2012 7:46:49 PM UTC-5, 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.
>
>
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> Any ideas?

Look up the Pareto distribution. It's analytic, and the shape parameter can be chosen to yield a finite mean and infinite variance.

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