Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials-Reference-Cited by-同舟云学术

Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials

Published:2023-02-15 Issue:2 Volume:12 Page:206
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Caratelli Diego¹²^ORCID,Sabbadini Ruben³,Ricci Paolo Emilio⁴^ORCID

Affiliation:

1. The Antenna Company, High Tech Campus 41, 5656 AE Eindhoven, The Netherlands

2. Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

3. Liceo Scientifico Statale Farnesina, Via dei Giuochi Istmici, 64, 00135 Roma, Italy

4. Department of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

Abstract

Bell’s polynomials are used in many different fields of mathematics, ranging from number theory to operator theory. This paper shows a relevant application in probability theory aimed at computing the moments of generalized Gaussian distributions. To this end, a table containing the first values of the complete Bell’s polynomials is provided. Furthermore, a dedicated code for approximating the moments of the general distributions in terms of complete Bell’s polynomials is detailed. Several test cases concerning different nested functions are discussed.

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/2/206/pdf

Reference16 articles.

1. Exponential polynomials;Bell;Ann. Math.,1934

2. Riordan, J. (1958). An Introduction to Combinatorial Analysis, John Wiley & Sons.

3. Faà di Bruno, F. (1876). Théorie des Formes Binaires, Brero.

4. Comtet, L. (1974). Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer.

5. Invariants orthogonaux pour certaines classes d’operateurs;Robert;Annales Mathém. Pures Appl.,1973