Umbral nature of the Poisson random variables
Probability
2007-05-23 v1 Combinatorics
Abstract
Extending the rigorous presentation of the classical umbral calculus given by Rota and Taylor in 1994, the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new short proof of the Lagrange inversion formula is given.
Keywords
Cite
@article{arxiv.math/0412054,
title = {Umbral nature of the Poisson random variables},
author = {E. Di Nardo and D. Senato},
journal= {arXiv preprint arXiv:math/0412054},
year = {2007}
}
Comments
23 pages