论文标题
扩展占用问题中的三个分布
Three Distributions in the Extended Occupancy Problem
论文作者
论文摘要
经典和扩展的占用分布对于检查涉及球随机分配给垃圾箱的问题的占用垃圾箱的数量很有用。我们通过将其作为马尔可夫链并得出过渡概率矩阵的光谱分解来检查扩展的占用问题。我们查看问题引起的三个兴趣分布，所有分布都涉及第二类的非中性stirl数字。这些分布对二项式和负二项式分布进行了有用的概括。我们检查了这些分布如何相互关系，并得出了表征分布的递归特性和混合特性。
The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and deriving the spectral decomposition of the transition probability matrix. We look at three distributions of interest that arise from the problem, all involving the noncentral Stirling numbers of the second kind. These distributions give a useful generalisation to the binomial and negative-binomial distributions. We examine how these distributions relate to one another, and we derive recursive properties and mixture properties that characterise the distributions.
