Characterizations of the Markov-Bernoulli geometric distribution

Characterization of Markov-Bernoulli Geometric Distribution Related to Random Sums

“…The resulting model is called the Markov-Bernoulli Model (MBM) or the Markov modulated Bernoulli process (Ozekici, 1997). Many researchers have been studied the MBM from the various aspects of probability, statistics and their applications, in particular the classical problems related to the usual Bernoulli model (Anis and Gharib, 1982;Gharib and Yehia, 1987;Inal, 1987;Yehia and Gharib, 1993;Ozekici, 1997;Ozekici and Soyer, 2003;Arvidsson and Francke, 2007;Omey et al, 2008;Maillart et al, 2008;Pacheco et al, 2009;Cekanavicius and Vellaisamy, 2010;Minkova and Omey, 2011). Further, due to the fact that the MBM operates in a random environment depicted by a Markov chain so that the probability of success at each trial depends on the state of the environment, this model represents an interesting application of stochastic processes and thus used by numerous authors in, stochastic modeling (Switzer, 1967;1969;Pedler, 1980;Satheesh et al, 2002;Özekici and Soyer, 2003;Xekalaki and Panaretos, 2004;Arvidsson and Francke, 2007;Nan et al, 2008;Pacheco et al, 2009;Doubleday and Esunge, 2011;Pires and Diniz, 2012).…”

“…Few authors have treated the characterization problem of the MBG distribution (Yehia and Gharib, 1993;Minkova and Omey, 2011).…”

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

“…It represents a generalization of the usual geometric distribution (ρ = 0). In the past works on the MBM some characterizations for the MBG distribution (1.2) are achieved (Minkova & Omey, 2011;Yehia & Gharib, 1993). The random sum of independent identically distributed (iid) nonnegative rv's; where the summation index is a geometric rv; is called a geometric compounding of the underlying rv's.…”