Waiting time problems in a two-state Markov chain

被引：11
|
作者：
Han, Q [1 ]
Aki, S [1 ]
机构：
[1] Osaka Univ, Grad Sch Engn Sci, Dept Informat & Math Sci, Toyonaka, Osaka 5608531, Japan
来源：
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS | 2000年 / 52卷 / 04期
关键词：
waiting time problems; discrete distributions of order k; Markov chain; Markov chain imbedding method; probability generating function;
D O I：
10.1023/A:1017537629251
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Let F-0 be the event that l(0) 0-runs of length k(0) occur and F-1 be the event that l(1) 1-runs of length k(1) occur in a two-state Markov chain. In this paper using a combinatorial method and the Markov chain imbedding method, we obtained explicit formulas of the probability generating functions of the sooner and later waiting time between F-0 and F-1 by the non-overlapping, overlapping and "greater than or equal" enumeration scheme. These formulas are convenient for evaluating the distributions of the sooner and later waiting time problems.
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页码：778 / 789
页数：12
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