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

被引：0

作者：

Caratelli, Diego ^{[1
,2
]}

Sabbadini, Ruben ^{[3
]}

Ricci, Paolo Emilio ^{[4
]}

机构：

[1] Antenna Co, High Tech Campus 41, NL-5656 AE Eindhoven, Netherlands

[2] Eindhoven Univ Technol, Dept Elect Engn, POB 513, NL-5600 MB Eindhoven, Netherlands

[3] Liceo Sci Statale Farnesina, Via Giuochi Istm 64, I-00135 Rome, Italy

[4] Int Telemat Univ UniNettuno, Dept Math, Corso Vittorio Emanuele 2,39, I-00186 Rome, Italy

来源：

AXIOMS | 2023年 / 12卷 / 02期

关键词：

moments of a continuous distribution; Bell's polynomials; generalized Gaussian distributions;

D O I：

10.3390/axioms12020206

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：13

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