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Citation - WoS: 5
Citation - Scopus: 6
On the Mean and Extreme Distances Between Failures in Markovian Binary Sequences
(Elsevier Science Bv, 2011) Eryilmaz, Serkan; Yalcin, Femin
This paper is concerned with the mean, minimum and maximum distances between two successive failures in a binary sequence consisting of Markov dependent elements. These random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes. Exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented. (C) 2011 Elsevier B.V. All rights reserved.
Citation - WoS: 13
Citation - Scopus: 12
q-geometric and q-binomial Distributions of Order k
(Elsevier Science Bv, 2014) Yalcin, Femin; Eryilmaz, Serkan
In this paper, we generalize geometric and binomial distributions of order k to q-geometric and q-binomial distributions of order k using Bernoulli trials with a geometrically varying success probability. In particular, we derive expressions for the probability mass functions of these distributions. For q = 1, these distributions reduce to geometric and binomial distributions of order k which have been extensively studied in the literature. (C) 2014 Elsevier B.V. All rights reserved.