论文标题
检查溢出分布
An examination of the spillage distribution
论文作者
论文摘要
我们检查了一个离散概率分布的家族，该家族描述了扩展的bins模型中的“溢出数”。溢出数的定义是占用垃圾箱的球数减去占用垃圾箱的总数。这种概率分布可以被描述为第二种中央stirl数字的第二类非中心stirl数字的扩展的规范版本。另外，它可以从扩展的bins模型以自然的方式得出。我们得出了该分布的生成函数和分布的重要时刻。我们还得出了一种用于分布质量值的递归计算算法。最后，我们检查了溢出分布的渐近行为以及对分布的近似的性能。
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.
