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 [G.-C. Rota, B.D. Taylor, The classical umbral calculus, SIAM J. Math. Anal. 25 (2) (1994) 694–711], 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.

On the computation of classical, boolean and free cumulants.

DI NARDO, Elvira;
2009-01-01

Abstract

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 [G.-C. Rota, B.D. Taylor, The classical umbral calculus, SIAM J. Math. Anal. 25 (2) (1994) 694–711], 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.
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/1616
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