On Tue, 11 Dec 2012 16:46:49 -0800 (PST), Dave <email@example.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.