A probabilistic interpretation of the Bell polynomials. Issue 4 (4th July 2022)

• Record Type: Journal Article
• Authors: Kataria, Kuldeep Kumar; Vellaisamy, Palaniappan; Kumar, Vijay
• Is Part Of: Stochastic analysis and applications. Volume 40:Issue 4(2022)
• Page Start: 610
• Page End: 622
• Publication Date: 2022-07-04
• Subjects: Bell polynomials -- Poisson distribution of order n -- probabilistic method -- recurrence relations -- Adomian polynomials; 60E05 -- 05A19; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2021.1942917
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this paper, we obtain a probabilistic relationship between the exponential Bell polynomials and the weighted sums of independent Poisson random variables. A recently established probabilistic connection between the Adomian polynomials and independent Poisson random variables can be derived from the obtained relationship. This result has importance because any known identity for the exponential Bell polynomials will generate a new identity for the Poisson random variables. We use the obtained relationship to derive several new identities for the joint distribution of weighted sums of independent Poisson random variables. Few examples are provided that substantiate the obtained identities.