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

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...

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Bibliographic Details
Published in:Axioms 2023-02, Vol.12 (2), p.206
Main Authors: Caratelli, Diego, Sabbadini, Ruben, Ricci, Paolo Emilio
Format: Article
Language:English
Subjects:
Approximation
Bell’s polynomials
Gaussian processes
generalized Gaussian distributions
Mathematical analysis
Mathematical research
moments of a continuous distribution
Normal distribution
Number theory
Polynomials
Probability theory
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Summary: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.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12020206