An application of the method of finite Markov chain imbedding to runs tests

Abstract The method of finite Markov chain imbedding developed by Fu and Koutras (1994) has become a popular and useful tool for studying runs and patterns-related problems. In this article, their approach is used as an alternative for obtaining the exact conditional distribution of the success runs statistic given the number of successes in a sequence of n i.i.d. Bernoulli trials, which, in the past, was computed mainly from traditional combinatorics.