The Generalized Factorial Moments in Terms of a Poisson Random Variable
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.