Some New Characterizations of Markov-Bernoulli Geometric Distribution Related to Random Sums

Abstract

The Markov-Bernoulli geometric distribution is obtained when a generalization, as a Markov process, of the independent Bernoulli sequence of random variables, is introduced. In this paper, new characterizations of the Markov-Bernoulli geometric distribution, as the distribution of the summation index of randomly truncated nonnegative integer valued random variables, are given in terms of moment relations of the sum and summands. The achieved results generalize the corresponding characterizations concerning the usual geometric distribution.