On the computation of classical, boolean and free cumulants

Details On the computation of classical, boolean and free cumulants On the computation of classical, boolean and free cumulants

2008-11-20

arxiv.org/abs/0811.3342v1

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14 pages. in press, Applied Mathematics and Computation

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This 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.

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