Combinatorial expressions of cumulants and moments
We recall here the definition of cumulant, and we present several of its properties. A classic discussion of cumulants is contained in the book by Shiryaev ; see also the papers by Rota and Shen , Speed  and Surgailis , as well as Pitman [119, pp. 20-23] and the references therein. From now on, we assume that every random variable is defined on a common suitable probability space (Ω, F,ℙ). The symbol E indicates the mathematical expectation associated with the probability measure ℙ.
KeywordsPoisson Distribution Poisson Random Variable Bell Polynomial Combinatorial Expression Bell Number
Unable to display preview. Download preview PDF.