Journal of Mathematics and Statistics

CHARACTERIZATION OF MARKOV-BERNOULLI GEOMETRIC DISTRIBUTION RELATED TO RANDOM SUMS

Mohamed Gharib, Mahmoud M. Ramadan and Khaled A.H. Al-Ajmi

DOI : 10.3844/jmssp.2014.186.191

Journal of Mathematics and Statistics

Volume 10, Issue 2

Pages 186-191

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 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.

Copyright

© 2014 Mohamed Gharib, Mahmoud M. Ramadan and Khaled A.H. Al-Ajmi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.