Some results associated with the longest run statistic in a sequence of Markov dependent trials

Abstract: We express the longest run statistic as the maximum of a sequence whose members are subject to a Markov chain condition. Via this setup some results for the exact expression and bounds for the distribution of the longest run in a sequence of Markov dependent trials are presented. Extension of the results to the second order Markov dependent trials are also provided. [Copyright &y& Elsevier]