溢出分布的检查

摘要：

我们研究一个家庭的离散概率分布，描述了“溢出数”的扩展球在箱子模型。溢出数被定义为占据其仓的球的数量减去占据仓的总数。这个概率分布可以被表征为第二类非中心Stirling数根据第二类中心Stirling数展开的赋范形式。或者，它可以从扩展的球箱模型中以自然的方式导出。我们推导出该分布的生成函数和分布的重要时刻。我们还推导出一个算法递归计算的质量值的分布。最后，我们研究的溢出分布和性能的近似分布的渐近行为。

英文摘要：

We examine a family of discrete probability distributions that describes the "spillage number" in the extended balls-in-bins model. The spillage number is defined as the number of balls that occupy their bins minus the total number of occupied bins. This probability distribution can be characterised as a normed version of the expansion of the noncentral Stirling numbers of the second kind in terms of the central Stirling numbers of the second kind. Alternatively it can be derived in a natural way from the extended balls-in-bins model. We derive the generating functions for this distribution and important moments of the distribution. We also derive an algorithm for recursive computation of the mass values for the distribution. Finally, we examine the asymptotic behaviour of the spillage distribution and the performance of an approximation to the distribution.

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