The Generalized Factorial Moments in Terms of a Poisson Random Variable

Abstract

Let X be a random variable having a Poisson distribution
and mean . Using the unified generalizations of Stirling
numbers, a pair of generalizations for the nth factorial moment
E[(X)n] of X is defined. Through this, some generalizations for
the nth moment E[Xn] of X are established in terms of other
generalizations of the Stirling numbers of the second kind. Also,
relationships between these new generalized moments and some
well-known identities are mentioned.