<i>q</I>-geometric and <i>q</I>-binomial Distributions of Order <i>k</I>

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2014

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Elsevier Science Bv

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Industrial Engineering
(1998)
Industrial Engineering is a field of engineering that develops and applies methods and techniques to design, implement, develop and improve systems comprising of humans, materials, machines, energy and funding. Our department was founded in 1998, and since then, has graduated hundreds of individuals who may compete nationally and internationally into professional life. Accredited by MÜDEK in 2014, our student-centered education continues. In addition to acquiring the knowledge necessary for every Industrial engineer, our students are able to gain professional experience in their desired fields of expertise with a wide array of elective courses, such as E-commerce and ERP, Reliability, Tabulation, or Industrial Engineering Applications in the Energy Sector. With dissertation projects fictionalized on solving real problems at real companies, our students gain experience in the sector, and a wide network of contacts. Our education is supported with ERASMUS programs. With the scientific studies of our competent academic staff published in internationally-renowned magazines, our department ranks with the bests among other universities. IESC, one of the most active student networks at our university, continues to organize extensive, and productive events every year.

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Abstract

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.

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Yalcin, Femin/0000-0003-0602-9392; Eryilmaz, Serkan/0000-0002-2108-1781
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Yalcin, Femin ORCID logo
Eryilmaz, Serkan ORCID logo

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Distributions of order k, q-distributions, Runs

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Volume

271

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Start Page

31

End Page

38

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https://doi.org/10.1016/j.cam.2014.03.025
 https://hdl.handle.net/20.500.14411/181

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