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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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/2/206 |
| _version_ | 1797622383733899264 |
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| author | Diego Caratelli Ruben Sabbadini Paolo Emilio Ricci |
| author_facet | Diego Caratelli Ruben Sabbadini Paolo Emilio Ricci |
| author_sort | Diego Caratelli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T09:10:33Z |
| format | Article |
| id | doaj.art-ef0599cff62d447491e4d24b2f235fe9 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:10:33Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-ef0599cff62d447491e4d24b2f235fe92023-11-16T19:06:46ZengMDPI AGAxioms2075-16802023-02-0112220610.3390/axioms12020206Approximating the Moments of Generalized Gaussian Distributions via Bell’s PolynomialsDiego Caratelli0Ruben Sabbadini1Paolo Emilio Ricci2The Antenna Company, High Tech Campus 41, 5656 AE Eindhoven, The NetherlandsLiceo Scientifico Statale Farnesina, Via dei Giuochi Istmici, 64, 00135 Roma, ItalyDepartment of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, ItalyBell’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.https://www.mdpi.com/2075-1680/12/2/206moments of a continuous distributionBell’s polynomialsgeneralized Gaussian distributions |
| spellingShingle | Diego Caratelli Ruben Sabbadini Paolo Emilio Ricci Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials Axioms moments of a continuous distribution Bell’s polynomials generalized Gaussian distributions |
| title | Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials |
| title_full | Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials |
| title_fullStr | Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials |
| title_full_unstemmed | Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials |
| title_short | Approximating the Moments of Generalized Gaussian Distributions via Bell’s Polynomials |
| title_sort | approximating the moments of generalized gaussian distributions via bell s polynomials |
| topic | moments of a continuous distribution Bell’s polynomials generalized Gaussian distributions |
| url | https://www.mdpi.com/2075-1680/12/2/206 |
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