On the computation of classical, boolean and free cumulants

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dc.creatorDi Nardo, E.
dc.creatorOliva, I.
dc.date2008-11-20
dc.date.accessioned2026-07-07T10:19:46Z
dc.date.available2026-07-07T10:19:46Z
dc.descriptionThis paper introduces a simple and computationally efficient algorithm for conversion formulae between moments and cumulants. The algorithm provides just one formula for classical, boolean and free cumulants. This is realized by using a suitable polynomial representation of Abel polynomials. The algorithm relies on the classical umbral calculus, a symbolic language introduced by Rota and Taylor in 1994, that is particularly suited to be implemented by using software for symbolic computations. Here we give a MAPLE procedure. Comparisons with existing procedures, especially for conversions between moments and free cumulants, as well as examples of applications to some well-known distributions (classical and free) end the paper.
dc.description14 pages. in press, Applied Mathematics and Computation
dc.identifierhttps://arxiv.org/abs/0811.3342
dc.identifierhttp://arxiv.org/abs/0811.3342
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174630
dc.subjectComputation
dc.subjectCombinatorics
dc.subjectStatistics Theory
dc.subject65C60, 05A40, 46L53
dc.titleOn the computation of classical, boolean and free cumulants
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