中文摘要：

转移概率流图方法是研究较为复杂的离散型随机过程整体特性的重要工具，特别是对获取某些重要随机变量的概率母函数和主要转移路径的转移概率函数更是一种有效的方法．本文运用转移概率流图方法讨论了帕斯卡分布，导出了两个组合数恒等式；对各种推广的帕斯卡分布的数学期望、方差和分布律等特性进行了研究，得到了系列结果．

英文摘要：

The method of transition probability flow graphs is an important tool for study- ing the overall characteristics of discrete stochastic processes. It is especially effective for obtaining the probability generating functions of random variables and the transition prob- ability functions of transition routes. In this paper, by applying transition probability flow graphs methods, we discuss the Pascal distribution, derive 2 combinatorial identities; study the means, variances and probability distributions of the I-type and II-type generalized Pascal distributions. And we obtain some new results in the research.