Distributions of runs and consecutive systems on directed trees

作     者：Aki, S 

作者机构：Osaka Univ Dept Math Sci Osaka 5608531 Japan 

出 版 物：《ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS》 (Annal. Inst. Stat. Math.)

年 卷 期：1999年第51卷第1期

页      面：1-15页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：probability generating function discrete distributions run directed tree graph reliability Markov tree lifetime consecutive system order statistics 

摘      要：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.