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

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.

Keywords

• moments of a continuous distribution
• Bell’s polynomials
• generalized Gaussian distributions