2008/11/20 by Elvira Di Nardo, E. Di Nardo, Di Nardo, E. +3
Mathematics · #05A40 #46L53 #65C60 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Random Matrices and Applications #Statistics Theory (math.ST) #math.CO #math.ST #msc:05A40 #msc:46L53 #msc:65C60 #stat.CO #stat.TH
paper · pdf · doi:10.48550/arxiv.0811.3342
14 pages. in press, Applied Mathematics and Computation
arxiv created 2008/11/20 · openalex publication_date 2008/11/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.