The Markov Binomial Distribution: an Explicit Solution by a Regenerative Approach

The coefficients of the Markov binomial distribution are solved in terms of the underlying state-contingent probabilities of the Markov chain. This will be useful for researchers concerned with the analysis of data generated by a discrete Markov chain. The paper exploits the regenerative nature of the problem and solves the difference equations known to define the distribution. The LLN, CLT and LIL are then available by standard methods. The LIL may be new, while the CLT coincides with existing work.