I ran across this density the other day. Has someone given this a name?

$f(x) = \log(1 + x^{-2}) / 2\pi$

The density is infinite at the origin and it also has fat tails. I saw it used as a prior distribution in a context where many observations were expected to either be small although large values were expected as well.

I ran across this density the other day. Has someone given this a name?

$f(x) = \log(1 + x^{-2}) / 2\pi$

The density is infinite at the origin and it also has fat tails. I saw it used as a prior distribution in a context where many observations were expected to be small, though large values were expected as well.