Distributions of Runs and Consecutive Systems on Directed Trees
Distributions of Runs and Consecutive Systems on Directed Trees
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有向树上游程和连续系统的分布
DOI：
10.1023/a:1003877016437
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发表时间：
1999
影响因子：
1
通讯作者：
S. Aki
中科院分区：
文献类型：
--
作者：
S. Aki
本文研究有向树上游程的精确分布。在假设以有向树的顶点为指标的随机变量集合具有有向马尔可夫分布的前提下，将游程的精确分布理论从基于随机序列扩展到基于有向树。求出了有向树上指定长度的成功游程数沿方向的分布。引入并研究了有向树上的连续k取n：F系统。通过假设元件的寿命是独立且同分布的，我们给出了连续系统寿命的精确分布。所得结果不仅具有理论意义，而且适合于计算。
In this paper we study exact distributions of runs on directed trees. On the assumption that the collection of random variables indexed by the vertices of a directed tree has a directed Markov distribution, the exact distribution theory of runs is extended from based on random sequences to based on directed trees. The distribution of the number of success runs of a specified length on a directed tree along the direction is derived. A consecutive-k-out-of-n:F system on a directed tree is introduced and investigated. By assuming that the lifetimes of the components are independent and identically distributed, we give the exact distribution of the lifetime of the consecutive system. The results are not only theoretical but also suitable for computation.