On the computation of classical, boolean and free cumulants

Date
Authors
Di Nardo, E.
Oliva, I.
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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.
Comment: 14 pages. in press, Applied Mathematics and Computation
Keywords
Statistics - Computation, Mathematics - Combinatorics, Mathematics - Statistics Theory, 65C60, 05A40, 46L53
Citation
Collections