Distribution Theory of Runs: A Markov Chain Approach
本文提出一种基于有限马尔可夫链嵌入技术的统一方法，推导了伯努利试验中成功游程统计量的精确分布，适用于同分布和不同分布情形，并得到特定游程第m次出现等待时间的精确分布。
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.