In this paper,we present a formula using Stirling numbers of the second kind to compute the m-th moment about the origin of the negative binomial distribution.By leveraging a recursive formula for these numbers,we derive a recursive expression for the moment.Additionally,we calculate explicit ex-pressions for the first six order moments and validate our findings by verifying the formula's accuracy using Maple software.
关键词
负二项分布/几何分布/原点矩/第二类Stirling数/广义二项式定理
Key words
negative binomial distribution/geometric distribution/moments about origin/Stirling number of the second kind/generalized binomial theorem
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