DOI: 10.5176/2251-3388_2.1.32
Authors: Mahid M. Mangontarum and Roberto B. Corcino
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.
Keywords: Stirling numbers of the second kind, Unified Stirling numbers, nth moment, Factorial moment
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