CHARACTERIZATION OF MARKOV-BERNOULLI GEOMETRIC DISTRIBUTION RELATED TO RANDOM SUMS

The Markov-Bernoulli geometric distribution is obtained when a generalization, as a Markov process, of the independent Bernoulli sequence of random variables is introduced by considering the success probability changes with respect to the Markov chain. The resulting model is called the Markov- Bernoulli model and it has a wide variety of application fields. In this study, some characterizations are given concerning the Markov-Bernoulli geometric distribution as the distribution of the summation index of independent randomly truncated non-negative integer valued random variables. The achieved results generalize the corresponding characterizations concerning the usual geometric distribution.