A concentrated Cauchy distribution with finite moments

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The Cauchy distribution with a,b real, b>0, has no moments (expected value, variance, etc.), because the defining integrals diverge. An obvious way to "concentrate" the Cauchy distribution, in order to get finite moments, is by truncation, restricting it to a finite domain. An alternative, suggested by an elementary problem in mechanics, is the distribution with a,b as above and a third parameter g≥0. It has the Cauchy distribution C(a,b) as the special case with g=0, and for any g>0, C{black-letter}g(a,b) has finite moments of all orders, while keeping the useful "fat tails" property of C{black-letter}(a,b).

Original languageEnglish (US)
Pages (from-to)147-153
Number of pages7
JournalAnnals of Operations Research
Issue number1
StatePublished - Sep 2013

All Science Journal Classification (ASJC) codes

  • Decision Sciences(all)
  • Management Science and Operations Research


  • Cauchy distribution
  • Lorentz distribution
  • Moments


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