The Cauchy distribution has no moments (expected value, variance, etc.), because the defining integrals diverge. A way to “concentrate” the Cauchy distribution, in order to get finite moments, is suggested by an elementary problem in mechanics, giving the Cauchy distribution as a special case. The concentrated distribution has finite moments of all orders, while keeping the useful “fat tails” property of the Cauchy distribution.
Citation
Anals of Oper. Res. (to appear)