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A concentrated Cauchy distribution with finite moments

ADI BEN-ISRAEL(adi.benisrael***at***gmail.com)

Abstract: 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.

Keywords: Cauchy distribution, fat tails.

Category 1: Applications -- OR and Management Sciences

Citation: Anals of Oper. Res. (to appear)

Download: [PDF]

Entry Submitted: 09/23/2012
Entry Accepted: 09/24/2012
Entry Last Modified: 09/23/2012

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