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

M. Gharib, M. M. Ramadan, Kh. A. H. Al-Ajmi


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 non-negative 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.

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International Journal of Statistics and Probability   ISSN 1927-7032(Print)   ISSN 1927-7040(Online)

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