论文标题
力矩生成Stirling数字和应用程序
Moment Generating Stirling Numbers and Applications
论文作者
论文摘要
在本文中，我们研究了某些组合数，即\ textit {moment生成stirling数字}。它们是HSU广泛的Stirling数字的特殊情况，并且满足了比一般情况下已知的更多属性和组合身份。随着应用，我们提供了相类型分布的力矩和中心矩，马尔可夫链中的复发时间，几何分布，负二项式分布以及一类概括了负二项式分布的分布。所有计算都可以以封闭形式执行而无需递归。我们还提出了与马尔可夫更新过程的关系。
In this paper, we investigate certain combinatorial numbers, the \textit{moment generating Stirling numbers}. They are a special case of Hsu's generalized Stirling numbers and satisfy many more properties and combinatorial identities than are known in the general case. As application, we provide the computation of the moments and central moments of the phase type distribution, the recurrence time in Markov chains, the geometric distribution, the negative binomial distribution and of a class of distributions generalizing the negative binomial distribution. All computations can be performed in closed form without recursion. We also present the relationship to the Markov renewal process.
