Distribution Theory of Runs: A Markov Chain Approach
Distribution Theory of Runs: A Markov Chain Approach
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DOI：
10.1080/01621459.1994.10476841
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发表时间：
1994-09
影响因子：
3.7
通讯作者：
J. Fu;M. Koutras
中科院分区：
文献类型：
--
作者：
J. Fu;M. Koutras
伯努利试验成功次数的统计在许多统计领域都有应用。近世纪来，即使在最简单的独立同分布的伯努利试验中，许多运行统计量的确切分布仍然是未知的。与传统的组合方法不同，本文提出了一种基于有限马尔可夫链嵌入技术的游程分布理论的简单统一方法。我们的结果不仅包括相同的伯努利试验，而且还包括不相同的伯努利试验。作为一个副产品，我们的结果也产生了一个特定的运行的第m次出现的等待时间的确切分布。
Abstract The statistics of the number of success runs in a sequence of Bernoulli trials have been used in many statistical areas. For almost a century, even in the simplest case of independent and identically distributed Bernoulli trials, the exact distributions of many run statistics still remain unknown. Departing from the traditional combinatorial approach, in this article we present a simple unified approach for the distribution theory of runs based on a finite Markov chain imbedding technique. Our results cover not only the identical Bernoulli trials, but also the nonidentical Bernoulli trials. As a byproduct, our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run.