CHARACTERIZATION OF MARKOV-BERNOULLI GEOMETRIC DISTRIBUTION RELATED TO RANDOM SUMS

The Markov-Bernoulli geometric distribution is obta ined when a generalization, as a Markov process, of the independent Bernoulli sequence of random variab les is introduced by considering the success probability changes with respect to the Markov chai n. The resulting model is called the MarkovBernoulli model and it has a wide variety of applic ation fields. In this study, some characterizations are given concerning the Markov-Bernoulli geometric distribution as the distribution of the summation inde x of independent randomly truncated non-negative inte ger valued random variables. The achieved results generalize the corresponding characterizations conc erning the usual geometric distribution.